{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,24]],"date-time":"2026-05-24T19:03:32Z","timestamp":1779649412498,"version":"3.53.1"},"reference-count":98,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T00:00:00Z","timestamp":1777420800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T00:00:00Z","timestamp":1777420800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"name":"Science and Engineering Research Board, IN","award":["CRG\/2023\/000583"],"award-info":[{"award-number":["CRG\/2023\/000583"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J. Math. Biol."],"published-print":{"date-parts":[[2026,5]]},"DOI":"10.1007\/s00285-026-02399-x","type":"journal-article","created":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T09:08:39Z","timestamp":1777453719000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Unravelling the spatiotemporal dynamics of amyloid-$$\\beta $$\u2013induced astrocyte\u2013neuron network model in Alzheimer\u2019s disease"],"prefix":"10.1007","volume":"92","author":[{"ORCID":"https:\/\/orcid.org\/0009-0000-4867-386X","authenticated-orcid":false,"given":"Debasish","family":"Pradhan","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1210-7804","authenticated-orcid":false,"given":"Ranjit Kumar","family":"Upadhyay","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,4,29]]},"reference":[{"issue":"12","key":"2399_CR1","doi-asserted-by":"publisher","first-page":"5088","DOI":"10.1523\/JNEUROSCI.23-12-05088.2003","volume":"23","author":"AY Abramov","year":"2003","unstructured":"Abramov AY, Canevari L, Duchen MR (2003) Changes in intracellular calcium and glutathione in astrocytes as the primary mechanism of amyloid neurotoxicity. J Neurosci 23(12):5088\u20135095","journal-title":"J Neurosci"},{"issue":"12","key":"2399_CR2","doi-asserted-by":"publisher","first-page":"746","DOI":"10.1038\/s41583-019-0223-4","volume":"20","author":"AR Adamantidis","year":"2019","unstructured":"Adamantidis AR, Herrera CG, Gent TC (2019) Oscillating circuitries in the sleeping brain. Nat Rev Neurosci 20(12):746\u2013762","journal-title":"Nat Rev Neurosci"},{"key":"2399_CR3","doi-asserted-by":"publisher","first-page":"413","DOI":"10.1007\/s10867-009-9166-8","volume":"35","author":"P Allegrini","year":"2009","unstructured":"Allegrini P, Fronzoni L, Pirino D (2009) The influence of the astrocyte field on neuronal dynamics and synchronization. J Biol Phys 35:413\u2013423","journal-title":"J Biol Phys"},{"key":"2399_CR4","doi-asserted-by":"publisher","first-page":"157","DOI":"10.1016\/j.neunet.2013.03.018","volume":"44","author":"M Amiri","year":"2013","unstructured":"Amiri M, Montaseri G, Bahrami F (2013) A phase plane analysis of neuron-astrocyte interactions. Neural Netw 44:157\u2013165","journal-title":"Neural Netw"},{"key":"2399_CR5","doi-asserted-by":"publisher","first-page":"489","DOI":"10.1007\/s10827-012-0432-6","volume":"34","author":"M Amiri","year":"2013","unstructured":"Amiri M, Hosseinmardi N, Bahrami F, Janahmadi M (2013) Astrocyte-neuron interaction as a mechanism responsible for generation of neural synchrony: a study based on modeling and experiments. J Comput Neurosci 34:489\u2013504","journal-title":"J Comput Neurosci"},{"issue":"5","key":"2399_CR6","doi-asserted-by":"publisher","first-page":"208","DOI":"10.1016\/S0166-2236(98)01349-6","volume":"22","author":"A Araque","year":"1999","unstructured":"Araque A, Parpura V, Sanzgiri RP, Haydon PG (1999) Tripartite synapses: glia, the unacknowledged partner. Trends Neurosci 22(5):208\u2013215","journal-title":"Trends Neurosci"},{"issue":"4","key":"2399_CR7","doi-asserted-by":"publisher","first-page":"1727","DOI":"10.1016\/S0006-3495(93)81191-3","volume":"65","author":"A Atri","year":"1993","unstructured":"Atri A, Amundson J, Clapham D, Sneyd J (1993) A single-pool model for intracellular calcium oscillations and waves in the xenopus laevis oocyte. Biophys J 65(4):1727\u20131739","journal-title":"Biophys J"},{"key":"2399_CR8","doi-asserted-by":"publisher","DOI":"10.1016\/j.ceca.2021.102359","volume":"94","author":"AV Berezhnov","year":"2021","unstructured":"Berezhnov AV, Fedotova EI, Sergeev AI, Teplov IY, Abramov AY (2021) Dopamine controls neuronal spontaneous calcium oscillations via astrocytic signal. Cell Calcium 94:102359","journal-title":"Cell Calcium"},{"issue":"4","key":"2399_CR9","doi-asserted-by":"publisher","first-page":"1261","DOI":"10.1152\/physrev.00006.2016","volume":"96","author":"MJ Berridge","year":"2016","unstructured":"Berridge MJ (2016) The inositol trisphosphate\/calcium signaling pathway in health and disease. Physiol Rev 96(4):1261\u20131296","journal-title":"Physiol Rev"},{"issue":"6","key":"2399_CR10","doi-asserted-by":"publisher","first-page":"2418","DOI":"10.1137\/23M1557842","volume":"83","author":"PR Borole","year":"2023","unstructured":"Borole PR, Rosado JM, Neal M, Queisser G (2023) Neuronal resilience and calcium signaling pathways in the context of synapse loss and calcium leaks: A computational modeling study and implications for alzheimer\u2019s disease. SIAM J Appl Math 83(6):2418\u20132442","journal-title":"SIAM J Appl Math"},{"key":"2399_CR11","doi-asserted-by":"publisher","first-page":"1125","DOI":"10.3389\/fnins.2019.01125","volume":"13","author":"Y Buskila","year":"2019","unstructured":"Buskila Y, Bellot-Saez A, Morley JW (2019) Generating brain waves, the power of astrocytes. Front Neurosci 13:1125","journal-title":"Front Neurosci"},{"issue":"2198","key":"2399_CR12","doi-asserted-by":"publisher","first-page":"20200267","DOI":"10.1098\/rsta.2020.0267","volume":"379","author":"A Calim","year":"2021","unstructured":"Calim A, Longtin A, Uzuntarla M (2021) Vibrational resonance in a neuron-astrocyte coupled model. Phil Trans R Soc A 379(2198):20200267","journal-title":"Phil Trans R Soc A"},{"issue":"5","key":"2399_CR13","doi-asserted-by":"publisher","first-page":"459","DOI":"10.1007\/s00422-017-0740-z","volume":"111","author":"SC Chan","year":"2017","unstructured":"Chan SC, Mok SY, Ng DWK, Goh SY (2017) The role of neuron-glia interactions in the emergence of ultra-slow oscillations. Biol Cybern 111(5):459\u2013472","journal-title":"Biol Cybern"},{"issue":"6","key":"2399_CR14","doi-asserted-by":"publisher","first-page":"983","DOI":"10.1016\/0896-6273(91)90238-U","volume":"6","author":"AC Charles","year":"1991","unstructured":"Charles AC, Merrill JE, Dirksen ER, Sandersont MJ (1991) Intercellular signaling in glial cells: calcium waves and oscillations in response to mechanical stimulation and glutamate. Neuron 6(6):983\u2013992","journal-title":"Neuron"},{"issue":"1","key":"2399_CR15","doi-asserted-by":"publisher","DOI":"10.1063\/5.0186814","volume":"14","author":"Y Chen","year":"2024","unstructured":"Chen Y, Ji Q (2024) Dynamics of coupled nonlinear neuronal-astrocyte model. AIP Adv 14(1):015066","journal-title":"AIP Adv"},{"issue":"1","key":"2399_CR16","doi-asserted-by":"publisher","first-page":"AN20090035","DOI":"10.1042\/AN20090035","volume":"2","author":"SK Chow","year":"2009","unstructured":"Chow SK, Yu D, MacDonald CL, Buibas M, Silva GA (2009) Amyloid $$\\beta $$-peptide directly induces spontaneous calcium transients, delayed intercellular calcium waves and gliosis in rat cortical astrocytes. ASN Neuro 2(1):AN20090035","journal-title":"ASN Neuro"},{"issue":"6292","key":"2399_CR17","doi-asserted-by":"publisher","first-page":"1464","DOI":"10.1126\/science.aaf0941","volume":"352","author":"AO Constantinescu","year":"2016","unstructured":"Constantinescu AO, O\u2019Reilly JX, Behrens TEJ (2016) Organizing conceptual knowledge in humans with a gridlike code. Science 352(6292):1464\u20131468","journal-title":"Science"},{"issue":"3","key":"2399_CR18","doi-asserted-by":"publisher","first-page":"429","DOI":"10.1016\/0896-6273(92)90271-E","volume":"8","author":"JW Dani","year":"1992","unstructured":"Dani JW, Chernjavsky A, Smith SJ (1992) Neuronal activity triggers calcium waves in hippocampal astrocyte networks. Neuron 8(3):429\u2013440","journal-title":"Neuron"},{"issue":"2","key":"2399_CR19","doi-asserted-by":"publisher","first-page":"403","DOI":"10.1523\/JNEUROSCI.5106-11.2012","volume":"32","author":"NJ Davis","year":"2012","unstructured":"Davis NJ, Tomlinson SP, Morgan HM (2012) The role of beta-frequency neural oscillations in motor control. J Neurosci 32(2):403\u2013404","journal-title":"J Neurosci"},{"issue":"20","key":"2399_CR20","doi-asserted-by":"publisher","first-page":"9895","DOI":"10.1073\/pnas.89.20.9895","volume":"89","author":"GW De Young","year":"1992","unstructured":"De Young GW, Keizer J (1992) A single-pool inositol 1, 4, 5-trisphosphate-receptor-based model for agonist-stimulated oscillations in ca2+ concentration. Proc Natl Acad Sci 89(20):9895\u20139899","journal-title":"Proc Natl Acad Sci"},{"issue":"9","key":"2399_CR21","doi-asserted-by":"publisher","first-page":"3824","DOI":"10.1523\/JNEUROSCI.4367-12.2013","volume":"33","author":"A Demuro","year":"2013","unstructured":"Demuro A, Parker I (2013) Cytotoxicity of intracellular a$$\\beta $$42 amyloid oligomers involves ca2+ release from the endoplasmic reticulum by stimulated production of inositol trisphosphate. J Neurosci 33(9):3824\u20133833","journal-title":"J Neurosci"},{"issue":"17","key":"2399_CR22","doi-asserted-by":"publisher","first-page":"12463","DOI":"10.1074\/jbc.R109.080895","volume":"285","author":"A Demuro","year":"2010","unstructured":"Demuro A, Parker I, Stutzmann GE (2010) Calcium signaling and amyloid toxicity in alzheimer disease. J Biol Chem 285(17):12463\u201312468","journal-title":"J Biol Chem"},{"issue":"3","key":"2399_CR23","doi-asserted-by":"publisher","first-page":"404","DOI":"10.3390\/biom16030404","volume":"16","author":"A Di Spiezio","year":"2026","unstructured":"Di Spiezio A, Zonta M (2026) Astrocyte ca2+ dysregulation in alzheimer\u2019s disease mouse models: Revisiting the dogma of hyperactivity. Biomolecules 16(3):404","journal-title":"Biomolecules"},{"issue":"1\u20133","key":"2399_CR24","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1159\/000102186","volume":"44","author":"DM Dooley","year":"1981","unstructured":"Dooley DM, Nisonson I (1981) Treatment of patients with degenerative diseases of the central nervous system by electrical stimulation of the spinal cord. Stereotact Funct Neurosurg 44(1\u20133):71\u201376","journal-title":"Stereotact Funct Neurosurg"},{"issue":"4","key":"2399_CR25","doi-asserted-by":"publisher","first-page":"311","DOI":"10.1016\/0143-4160(93)90052-8","volume":"14","author":"G Dupont","year":"1993","unstructured":"Dupont G, Goldbeter A (1993) One-pool model for ca2+ oscillations involving ca2+ and inositol 1, 4, 5-trisphosphate as co-agonists for ca2+ release. Cell Calcium 14(4):311\u2013322","journal-title":"Cell Calcium"},{"key":"2399_CR26","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2023.114223","volume":"177","author":"E Erkan","year":"2023","unstructured":"Erkan E (2023) Signal encoding performance of astrocyte-dressed morris lecar neurons. Chaos Solitons & Fractals 177:114223","journal-title":"Chaos Solitons & Fractals"},{"issue":"6","key":"2399_CR27","doi-asserted-by":"publisher","first-page":"445","DOI":"10.1016\/S0006-3495(61)86902-6","volume":"1","author":"R FitzHugh","year":"1961","unstructured":"FitzHugh R (1961) Impulses and physiological states in theoretical models of nerve membrane. Biophys J 1(6):445\u2013466","journal-title":"Biophys J"},{"issue":"8","key":"2399_CR28","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pcbi.1000909","volume":"6","author":"M Goldberg","year":"2010","unstructured":"Goldberg M, De Pitt\u00e0 M, Volman V, Berry H, Ben-Jacob E (2010) Nonlinear gap junctions enable long-distance propagation of pulsating calcium waves in astrocyte networks. PLoS Comput Biol 6(8):e1000909","journal-title":"PLoS Comput Biol"},{"issue":"8","key":"2399_CR29","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.90.088302","volume":"90","author":"Y Gong","year":"2003","unstructured":"Gong Y, Christini DJ (2003) Antispiral waves in reaction-diffusion systems. Phys Rev Lett 90(8):088302","journal-title":"Phys Rev Lett"},{"issue":"26","key":"2399_CR30","doi-asserted-by":"publisher","first-page":"15130","DOI":"10.1073\/pnas.93.26.15130","volume":"93","author":"TA Good","year":"1996","unstructured":"Good TA, Murphy RM (1996) Effect of $$\\beta $$-amyloid block of the fast-inactivating k+ channel on intracellular ca2+ and excitability in a modeled neuron. Proc Natl Acad Sci 93(26):15130\u201315135","journal-title":"Proc Natl Acad Sci"},{"issue":"13","key":"2399_CR31","doi-asserted-by":"publisher","first-page":"4637","DOI":"10.1073\/pnas.0308627101","volume":"101","author":"MD Greicius","year":"2004","unstructured":"Greicius MD, Srivastava G, Reiss AL, Menon V (2004) Default-mode network activity distinguishes alzheimer\u2019s disease from healthy aging: evidence from functional mri. Proc Natl Acad Sci 101(13):4637\u20134642","journal-title":"Proc Natl Acad Sci"},{"issue":"7052","key":"2399_CR32","doi-asserted-by":"publisher","first-page":"801","DOI":"10.1038\/nature03721","volume":"436","author":"T Hafting","year":"2005","unstructured":"Hafting T, Fyhn M, Molden S, Moser MB, Moser EI (2005) Microstructure of a spatial map in the entorhinal cortex. Nature 436(7052):801\u2013806","journal-title":"Nature"},{"issue":"4","key":"2399_CR33","doi-asserted-by":"publisher","first-page":"762","DOI":"10.1137\/0142054","volume":"42","author":"PS Hagan","year":"1982","unstructured":"Hagan PS (1982) Spiral waves in reaction-diffusion equations. SIAM J Appl Math 42(4):762\u2013786","journal-title":"SIAM J Appl Math"},{"issue":"2","key":"2399_CR34","doi-asserted-by":"publisher","first-page":"1045","DOI":"10.1152\/jn.1998.79.2.1045","volume":"79","author":"ME Harris-White","year":"1998","unstructured":"Harris-White ME, Zanotti SA, Frautschy SA, Charles AC (1998) Spiral intercellular calcium waves in hippocampal slice cultures. J Neurophysiol 79(2):1045\u20131052","journal-title":"J Neurophysiol"},{"issue":"5","key":"2399_CR35","doi-asserted-by":"publisher","first-page":"639","DOI":"10.1007\/s00332-011-9096-z","volume":"21","author":"E Harvey","year":"2011","unstructured":"Harvey E, Kirk V, Wechselberger M, Sneyd J (2011) Multiple timescales, mixed mode oscillations and canards in models of intracellular calcium dynamics. J Nonlinear Sci 21(5):639\u2013683","journal-title":"J Nonlinear Sci"},{"key":"2399_CR36","doi-asserted-by":"crossref","unstructured":"Hatton GI, Parpura V (2004) Glial $$\\iff $$ Neuronal Signaling, vol\u00a01. Springer Science & Business Media","DOI":"10.1007\/978-1-4020-7937-5"},{"issue":"3","key":"2399_CR37","doi-asserted-by":"publisher","first-page":"173","DOI":"10.1385\/NMM:3:3:173","volume":"3","author":"NJ Haughey","year":"2003","unstructured":"Haughey NJ, Mattson MP (2003) Alzheimer\u2019s amyloid $$\\beta $$-peptide enhances atp\/gap junction-mediated calcium-wave propagation in astrocytes. NeuroMol Med 3(3):173\u2013180","journal-title":"NeuroMol Med"},{"issue":"6","key":"2399_CR38","doi-asserted-by":"publisher","first-page":"1751","DOI":"10.1093\/brain\/awz116","volume":"142","author":"D Howett","year":"2019","unstructured":"Howett D, Castegnaro A, Krzywicka K, Hagman J, Marchment D, Henson R, Rio M, King JA, Burgess N, Chan D (2019) Differentiation of mild cognitive impairment using an entorhinal cortex-based test of virtual reality navigation. Brain 142(6):1751\u20131766","journal-title":"Brain"},{"issue":"44","key":"2399_CR39","doi-asserted-by":"publisher","first-page":"9897","DOI":"10.1523\/JNEUROSCI.2705-04.2004","volume":"24","author":"X Huang","year":"2004","unstructured":"Huang X, Troy WC, Yang Q, Ma H, Laing CR, Schiff SJ, Wu JY (2004) Spiral waves in disinhibited mammalian neocortex. J Neurosci 24(44):9897\u20139902","journal-title":"J Neurosci"},{"issue":"5","key":"2399_CR40","doi-asserted-by":"publisher","first-page":"978","DOI":"10.1016\/j.neuron.2010.11.007","volume":"68","author":"X Huang","year":"2010","unstructured":"Huang X, Weifeng X, Liang J, Takagaki K, Gao X, Jian-young W (2010) Spiral wave dynamics in neocortex. Neuron 68(5):978\u2013990","journal-title":"Neuron"},{"issue":"4","key":"2399_CR41","doi-asserted-by":"publisher","first-page":"834","DOI":"10.1063\/1.166370","volume":"8","author":"M Ipsen","year":"1998","unstructured":"Ipsen M, Hynne F, Sorensen PG (1998) Systematic derivation of amplitude equations and normal forms for dynamical systems. Chaos Interdiscip J Nonlinear Sci 8(4):834\u2013852","journal-title":"Chaos Interdiscip J Nonlinear Sci"},{"issue":"2","key":"2399_CR42","doi-asserted-by":"publisher","first-page":"315","DOI":"10.1137\/S0036144500382064","volume":"43","author":"EM Izhikevich","year":"2001","unstructured":"Izhikevich EM (2001) Synchronization of elliptic bursters. SIAM Rev 43(2):315\u2013344","journal-title":"SIAM Rev"},{"issue":"1\u20132","key":"2399_CR43","doi-asserted-by":"publisher","first-page":"85","DOI":"10.1016\/S0006-8993(96)01189-4","volume":"746","author":"TO Jalonen","year":"1997","unstructured":"Jalonen TO, Charniga CJ, Wielt DB (1997) $$\\beta $$-amyloid peptide-induced morphological changes coincide with increased k+ and cl- channel activity in rat cortical astrocytes. Brain Res 746(1\u20132):85\u201397","journal-title":"Brain Res"},{"issue":"8","key":"2399_CR44","doi-asserted-by":"publisher","first-page":"7713","DOI":"10.1007\/s11071-022-08202-y","volume":"111","author":"Q Ji","year":"2023","unstructured":"Ji Q, Qie X, Ye M (2023) Dynamical analysis of astrocyte-induced neuronal hyper-excitation. Nonlinear Dyn 111(8):7713\u20137728","journal-title":"Nonlinear Dyn"},{"issue":"2","key":"2399_CR45","doi-asserted-by":"publisher","first-page":"1098","DOI":"10.1152\/jn.1998.79.2.1098","volume":"79","author":"P Jung","year":"1998","unstructured":"Jung P, Cornell-Bell A, Madden KS, Moss F (1998) Noise-induced spiral waves in astrocyte syncytia show evidence of self-organized criticality. J Neurophysiol 79(2):1098\u20131101","journal-title":"J Neurophysiol"},{"issue":"8","key":"2399_CR46","doi-asserted-by":"publisher","first-page":"945","DOI":"10.1091\/mbc.6.8.945","volume":"6","author":"J Keizer","year":"1995","unstructured":"Keizer J, Li Y-X, Stojilkovi\u0107 S, Rinzel J (1995) Insp3-induced ca2+ excitability of the endoplasmic reticulum. Mol Biol Cell 6(8):945\u2013951","journal-title":"Mol Biol Cell"},{"issue":"12","key":"2399_CR47","doi-asserted-by":"publisher","first-page":"744","DOI":"10.1038\/s41583-022-00642-0","volume":"23","author":"M Khona","year":"2022","unstructured":"Khona M, Fiete IR (2022) Attractor and integrator networks in the brain. Nat Rev Neurosci 23(12):744\u2013766","journal-title":"Nat Rev Neurosci"},{"issue":"5999","key":"2399_CR48","doi-asserted-by":"publisher","first-page":"1616","DOI":"10.1126\/science.1179047","volume":"329","author":"S Kondo","year":"2010","unstructured":"Kondo S, Miura T (2010) Reaction-diffusion model as a framework for understanding biological pattern formation. Science 329(5999):1616\u20131620","journal-title":"Science"},{"issue":"5918","key":"2399_CR49","doi-asserted-by":"publisher","first-page":"1211","DOI":"10.1126\/science.1169096","volume":"323","author":"KV Kuchibhotla","year":"2009","unstructured":"Kuchibhotla KV, Lattarulo CR, Hyman BT, Bacskai BJ (2009) Synchronous hyperactivity and intercellular calcium waves in astrocytes in alzheimer mice. Science 323(5918):1211\u20131215","journal-title":"Science"},{"issue":"8","key":"2399_CR50","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0202503","volume":"13","author":"J Latulippe","year":"2018","unstructured":"Latulippe J, Lotito D, Murby D (2018) A mathematical model for the effects of amyloid beta on intracellular calcium. PLoS ONE 13(8):e0202503","journal-title":"PLoS ONE"},{"issue":"4","key":"2399_CR51","doi-asserted-by":"publisher","first-page":"553","DOI":"10.1016\/j.jtbi.2007.12.011","volume":"251","author":"M Lavrentovich","year":"2008","unstructured":"Lavrentovich M, Hemkin S (2008) A mathematical model of spontaneous calcium (ii) oscillations in astrocytes. J Theor Biol 251(4):553\u2013560","journal-title":"J Theor Biol"},{"issue":"1","key":"2399_CR52","doi-asserted-by":"publisher","first-page":"49","DOI":"10.3233\/JAD-130740","volume":"38","author":"L Lee","year":"2013","unstructured":"Lee L, Kosuri P, Arancio O (2013) Picomolar amyloid-$$\\beta $$ peptides enhance spontaneous astrocyte calcium transients. J Alzheimers Dis 38(1):49\u201362","journal-title":"J Alzheimers Dis"},{"issue":"6","key":"2399_CR53","doi-asserted-by":"publisher","first-page":"E1279","DOI":"10.1073\/pnas.1714409115","volume":"115","author":"C Lerdkrai","year":"2018","unstructured":"Lerdkrai C, Asavapanumas N, Brawek B, Kovalchuk Y, Mojtahedi N, del Moral MO, Garaschuk O (2018) Intracellular ca2+ stores control in vivo neuronal hyperactivity in a mouse model of alzheimer\u2019s disease. Proc Natl Acad Sci 115(6):E1279\u2013E1288","journal-title":"Proc Natl Acad Sci"},{"issue":"4","key":"2399_CR54","doi-asserted-by":"publisher","first-page":"461","DOI":"10.1006\/jtbi.1994.1041","volume":"166","author":"Y-X Li","year":"1994","unstructured":"Li Y-X, Rinzel J (1994) Equations for insp3 receptor-mediated [ca2+] i oscillations derived from a detailed kinetic model: a hodgkin-huxley like formalism. J Theor Biol 166(4):461\u2013473","journal-title":"J Theor Biol"},{"key":"2399_CR55","doi-asserted-by":"publisher","first-page":"1003","DOI":"10.1007\/s11431-016-9056-2","volume":"60","author":"JJ Li","year":"2017","unstructured":"Li JJ, Xie Y, YuGuo Yu, MengMeng D, Wang R, Ying W (2017) A neglected gabaergic astrocyte: calcium dynamics and involvement in seizure activity. SCIENCE CHINA Technol Sci 60:1003\u20131010","journal-title":"SCIENCE CHINA Technol Sci"},{"key":"2399_CR56","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1007\/112_2014_19","volume":"167","author":"D Lim","year":"2014","unstructured":"Lim D, Ronco V, Grolla AA, Verkhratsky A, Genazzani AA (2014) Glial calcium signalling in alzheimer\u2019s disease. Rev Physiol Biochem Pharmacol 167:45\u201365","journal-title":"Rev Physiol Biochem Pharmacol"},{"key":"2399_CR57","doi-asserted-by":"publisher","DOI":"10.3389\/fphys.2021.767892","volume":"12","author":"L Liu","year":"2021","unstructured":"Liu L, Gao H, Zaikin A, Chen S (2021) Unraveling a$$\\beta $$-mediated multi-pathway calcium dynamics in astrocytes: implications for alzheimer\u2019s disease treatment from simulations. Front Physiol 12:767892","journal-title":"Front Physiol"},{"issue":"12","key":"2399_CR58","doi-asserted-by":"publisher","first-page":"2644","DOI":"10.1093\/cercor\/bhab371","volume":"32","author":"C Liu","year":"2022","unstructured":"Liu C, Han T, Zhexue X, Liu J, Zhang M, Jialin D, Zhou Q, Duan Y, Li Y, Wang J et al (2022) Modulating gamma oscillations promotes brain connectivity to improve cognitive impairment. Cereb Cortex 32(12):2644\u20132656","journal-title":"Cereb Cortex"},{"key":"2399_CR59","doi-asserted-by":"publisher","first-page":"1569","DOI":"10.1007\/s11071-017-3565-3","volume":"89","author":"J Ma","year":"2017","unstructured":"Ma J, Tang J (2017) A review for dynamics in neuron and neuronal network. Nonlinear Dyn 89:1569\u20131578","journal-title":"Nonlinear Dyn"},{"issue":"2","key":"2399_CR60","doi-asserted-by":"publisher","first-page":"375","DOI":"10.1007\/s12021-023-09622-w","volume":"21","author":"T Manninen","year":"2023","unstructured":"Manninen T, A\u0107imovi\u0107 J, Linne M-L (2023) Analysis of network models with neuron-astrocyte interactions. Neuroinformatics 21(2):375\u2013406","journal-title":"Neuroinformatics"},{"issue":"2","key":"2399_CR61","doi-asserted-by":"publisher","first-page":"320","DOI":"10.1002\/hipo.20901","volume":"22","author":"H Mhatre","year":"2012","unstructured":"Mhatre H, Gorchetchnikov A, Grossberg S (2012) Grid cell hexagonal patterns formed by fast self-organized learning within entorhinal cortex. Hippocampus 22(2):320\u2013334","journal-title":"Hippocampus"},{"key":"2399_CR62","doi-asserted-by":"publisher","first-page":"93","DOI":"10.3389\/fncom.2012.00093","volume":"6","author":"R Min","year":"2012","unstructured":"Min R, Santello M, Nevian T (2012) The computational power of astrocyte mediated synaptic plasticity. Front Comput Neurosci 6:93","journal-title":"Front Comput Neurosci"},{"issue":"4","key":"2399_CR63","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.99.042307","volume":"99","author":"A Mondal","year":"2019","unstructured":"Mondal A, Sharma SK, Upadhyay RK, Aziz-Alaoui MA, Kundu P, Hens C (2019) Diffusion dynamics of a conductance-based neuronal population. Phys Rev E 99(4):042307","journal-title":"Phys Rev E"},{"issue":"10","key":"2399_CR64","doi-asserted-by":"publisher","DOI":"10.1063\/5.0055389","volume":"31","author":"A Mondal","year":"2021","unstructured":"Mondal A, Mondal A, Sharma SK, Upadhyay RK, Antonopoulos CG (2021) Spatiotemporal characteristics in systems of diffusively coupled excitable slow-fast fitzhugh-rinzel dynamical neurons. Chaos Interdiscip J Nonlinear Sci 31(10):103122","journal-title":"Chaos Interdiscip J Nonlinear Sci"},{"issue":"3","key":"2399_CR65","doi-asserted-by":"publisher","first-page":"164","DOI":"10.1038\/nphys1609","volume":"6","author":"AE Motter","year":"2010","unstructured":"Motter AE (2010) Spontaneous synchrony breaking. Nat Phys 6(3):164\u2013165","journal-title":"Nat Phys"},{"issue":"26","key":"2399_CR66","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.91.268101","volume":"91","author":"S Nadkarni","year":"2003","unstructured":"Nadkarni S, Jung P (2003) Spontaneous oscillations of dressed neurons: a new mechanism for epilepsy? Phys Rev Lett 91(26):268101","journal-title":"Phys Rev Lett"},{"issue":"1","key":"2399_CR67","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1088\/1478-3967\/1\/1\/004","volume":"1","author":"S Nadkarni","year":"2004","unstructured":"Nadkarni S, Jung P (2004) Dressed neurons: modeling neural-glial interactions. Phys Biol 1(1):35","journal-title":"Phys Biol"},{"issue":"15","key":"2399_CR68","doi-asserted-by":"publisher","first-page":"7887","DOI":"10.3390\/ijms22157887","volume":"22","author":"C Nanclares","year":"2021","unstructured":"Nanclares C, Baraibar AM, Araque A, Kofuji P (2021) Dysregulation of astrocyte-neuronal communication in alzheimer\u2019s disease. Int J Mol Sci 22(15):7887","journal-title":"Int J Mol Sci"},{"issue":"38","key":"2399_CR69","doi-asserted-by":"publisher","first-page":"14733","DOI":"10.1021\/jp049213r","volume":"108","author":"EM Nicola","year":"2004","unstructured":"Nicola EM, Brusch L, B\u00e4r M (2004) Antispiral waves as sources in oscillatory reaction- diffusion media. J Phys Chem B 108(38):14733\u201314740","journal-title":"J Phys Chem B"},{"key":"2399_CR70","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2023.113222","volume":"169","author":"Z Ouyang","year":"2023","unstructured":"Ouyang Z, Yangyang Yu, Liu Z, Feng PH (2023) Transition of spatiotemporal patterns in neuron-astrocyte networks. Chaos Solitons & Fractals 169:113222","journal-title":"Chaos Solitons & Fractals"},{"issue":"5","key":"2399_CR71","doi-asserted-by":"publisher","DOI":"10.1063\/5.0093234","volume":"32","author":"T Palabas","year":"2022","unstructured":"Palabas T, Longtin A, Ghosh D, Uzuntarla M (2022) Controlling the spontaneous firing behavior of a neuron with astrocyte. Chaos Interdiscip J Nonlinear Sci 32(5):051101","journal-title":"Chaos Interdiscip J Nonlinear Sci"},{"issue":"1","key":"2399_CR72","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1186\/s12974-020-01774-9","volume":"17","author":"J Pan","year":"2020","unstructured":"Pan J, Ma N, Bo Yu, Zhang W, Wan J (2020) Transcriptomic profiling of microglia and astrocytes throughout aging. J Neuroinflammation 17(1):97","journal-title":"J Neuroinflammation"},{"issue":"18","key":"2399_CR73","doi-asserted-by":"publisher","first-page":"3897","DOI":"10.1097\/00001756-200112210-00008","volume":"12","author":"HR Parri","year":"2001","unstructured":"Parri HR, Crunelli V (2001) Pacemaker calcium oscillations in thalamic astrocytes in situ. NeuroReport 12(18):3897\u20133900","journal-title":"NeuroReport"},{"issue":"9","key":"2399_CR74","doi-asserted-by":"publisher","first-page":"2192","DOI":"10.1523\/JNEUROSCI.3965-04.2005","volume":"25","author":"G Perea","year":"2005","unstructured":"Perea G, Araque A (2005) Properties of synaptically evoked astrocyte calcium signal reveal synaptic information processing by astrocytes. J Neurosci 25(9):2192\u20132203","journal-title":"J Neurosci"},{"key":"2399_CR75","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2025.126861","volume":"276","author":"D Pradhan","year":"2025","unstructured":"Pradhan D, Upadhyay RK (2025) Deciphering the calcium dynamics of a fractional order alzheimer\u2019s disease model in astrocytes and their networks. Expert Syst Appl 276:126861","journal-title":"Expert Syst Appl"},{"issue":"3","key":"2399_CR76","doi-asserted-by":"publisher","first-page":"540","DOI":"10.3390\/cells10030540","volume":"10","author":"P Preman","year":"2021","unstructured":"Preman P, Alfonso-Triguero M, Alberdi E, Verkhratsky A, Arranz AM (2021) Astrocytes in alzheimer\u2019s disease: pathological significance and molecular pathways. Cells 10(3):540","journal-title":"Cells"},{"issue":"2","key":"2399_CR77","first-page":"428","volume":"10","author":"A Rabinovitch","year":"2017","unstructured":"Rabinovitch A, Biton Y, Friedmabn M, Aviram I, Braunstein D (2017) A simple simulation model for spiral induced epilepsy. Brain Stimul Basic Transl Clin Res Neuromodulation 10(2):428","journal-title":"Brain Stimul Basic Transl Clin Res Neuromodulation"},{"issue":"5","key":"2399_CR78","doi-asserted-by":"publisher","first-page":"739","DOI":"10.1016\/j.neuron.2010.04.029","volume":"66","author":"M Renner","year":"2010","unstructured":"Renner M, Lacor PN, Velasco PT, Xu J, Contractor A, Klein WL, Triller A (2010) Deleterious effects of amyloid $$\\beta $$ oligomers acting as an extracellular scaffold for mglur5. Neuron 66(5):739\u2013754","journal-title":"Neuron"},{"issue":"4","key":"2399_CR79","doi-asserted-by":"publisher","first-page":"1797","DOI":"10.1152\/jn.1998.79.4.1797","volume":"79","author":"ET Rolls","year":"1998","unstructured":"Rolls ET, Treves A, Robertson RG, Georges-Fran\u00e7ois P, Panzeri S (1998) Information about spatial view in an ensemble of primate hippocampal cells. J Neurophysiol 79(4):1797\u20131813","journal-title":"J Neurophysiol"},{"issue":"1","key":"2399_CR80","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1159\/000369101","volume":"24","author":"S Sadigh-Eteghad","year":"2015","unstructured":"Sadigh-Eteghad S, Sabermarouf B, Majdi A, Talebi M, Farhoudi M, Mahmoudi J (2015) Amyloid-beta: a crucial factor in alzheimer\u2019s disease. Med Princ Pract 24(1):1\u201310","journal-title":"Med Princ Pract"},{"issue":"2","key":"2399_CR81","doi-asserted-by":"publisher","first-page":"154","DOI":"10.1038\/s41593-018-0325-8","volume":"22","author":"M Santello","year":"2019","unstructured":"Santello M, Toni N, Volterra A (2019) Astrocyte function from information processing to cognition and cognitive impairment. Nat Neurosci 22(2):154\u2013166","journal-title":"Nat Neurosci"},{"issue":"7","key":"2399_CR82","doi-asserted-by":"publisher","first-page":"677","DOI":"10.1111\/j.1528-1157.1998.tb01151.x","volume":"39","author":"SC Schachter","year":"1998","unstructured":"Schachter SC, Saper CB (1998) Vagus nerve stimulation. Epilepsia 39(7):677\u2013686","journal-title":"Epilepsia"},{"issue":"12","key":"2399_CR83","doi-asserted-by":"publisher","first-page":"2384","DOI":"10.1038\/s41593-024-01791-4","volume":"27","author":"A Serrano-Pozo","year":"2024","unstructured":"Serrano-Pozo A, Li H, Li Z, Mu\u00f1oz-Castro C, Jaisa-Aad M, Healey MA, Welikovitch LA, Jayakumar R, Bryant AG, Noori A et al (2024) Astrocyte transcriptomic changes along the spatiotemporal progression of alzheimer\u2019s disease. Nat Neurosci 27(12):2384\u20132400","journal-title":"Nat Neurosci"},{"issue":"19","key":"2399_CR84","doi-asserted-by":"publisher","first-page":"5180","DOI":"10.1523\/JNEUROSCI.0739-06.2006","volume":"26","author":"GE Stutzmann","year":"2006","unstructured":"Stutzmann GE, Smith I, Caccamo A, Oddo S, LaFerla FM, Parker I (2006) Enhanced ryanodine receptor recruitment contributes to ca2+ disruptions in young, adult, and aged alzheimer\u2019s disease mice. J Neurosci 26(19):5180\u20135189","journal-title":"J Neurosci"},{"issue":"1","key":"2399_CR85","doi-asserted-by":"publisher","first-page":"40","DOI":"10.1196\/annals.1379.004","volume":"1097","author":"T Takano","year":"2007","unstructured":"Takano T, Han X, Deane R, Zlokovic B, Nedergaard M (2007) Two-photon imaging of astrocytic ca2+ signaling and the microvasculature in experimental mice models of alzheimer\u2019s disease. Ann N Y Acad Sci 1097(1):40\u201350","journal-title":"Ann N Y Acad Sci"},{"issue":"7","key":"2399_CR86","doi-asserted-by":"publisher","first-page":"2963","DOI":"10.1523\/JNEUROSCI.22-07-02963.2002","volume":"22","author":"D Terman","year":"2002","unstructured":"Terman D, Rubin JE, Yew AC, Wilson CJ (2002) Activity patterns in a model for the subthalamopallidal network of the basal ganglia. J Neurosci 22(7):2963\u20132976","journal-title":"J Neurosci"},{"issue":"11","key":"2399_CR87","doi-asserted-by":"publisher","first-page":"4657","DOI":"10.1523\/JNEUROSCI.4509-14.2015","volume":"35","author":"RG Townsend","year":"2015","unstructured":"Townsend RG, Solomon SS, Chen SC, Pietersen ANJ, Martin PR, Solomon SG, Gong P (2015) Emergence of complex wave patterns in primate cerebral cortex. J Neurosci 35(11):4657\u20134662","journal-title":"J Neurosci"},{"key":"2399_CR88","doi-asserted-by":"publisher","first-page":"154","DOI":"10.1016\/j.apm.2024.01.013","volume":"128","author":"RK Upadhyay","year":"2024","unstructured":"Upadhyay RK, Pradhan D, Sharma SK, Mondal A (2024) Emergence of spiral and antispiral patterns and its cgle analysis in leech-heart interneuron model with electromagnetic induction. Appl Math Model 128:154\u2013167","journal-title":"Appl Math Model"},{"key":"2399_CR89","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2024.108396","volume":"140","author":"RK Upadhyay","year":"2025","unstructured":"Upadhyay RK, Pradhan D, Parshad RD, Roy P (2025) Existence of global attractor in reaction-diffusion model of obesity-induced alzheimer\u2019s disease and its control strategies. Commun Nonlinear Sci Numer Simul 140:108396","journal-title":"Commun Nonlinear Sci Numer Simul"},{"key":"2399_CR90","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejphar.2020.173554","volume":"887","author":"M Vaz","year":"2020","unstructured":"Vaz M, Silvestre S (2020) Alzheimer\u2019s disease: recent treatment strategies. Eur J Pharmacol 887:173554","journal-title":"Eur J Pharmacol"},{"issue":"1","key":"2399_CR91","doi-asserted-by":"publisher","first-page":"138","DOI":"10.1006\/jmaa.2000.7220","volume":"254","author":"L Wang","year":"2001","unstructured":"Wang L, Li MY (2001) Diffusion-driven instability in reaction-diffusion systems. J Math Anal Appl 254(1):138\u2013153","journal-title":"J Math Anal Appl"},{"key":"2399_CR92","doi-asserted-by":"publisher","first-page":"76","DOI":"10.3389\/fnagi.2017.00076","volume":"9","author":"HT Whittaker","year":"2017","unstructured":"Whittaker HT, Warren JD (2017) A neurochemical basis for phenotypic differentiation in alzheimer\u2019s disease? turing\u2019s morphogens revisited. Front Aging Neurosci 9:76","journal-title":"Front Aging Neurosci"},{"key":"2399_CR93","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2022.112969","volume":"166","author":"F Xiao","year":"2023","unstructured":"Xiao F, Ziying F, Jia Y, Yang L (2023) Resonance effects in neuronal-astrocyte model with ion channel blockage. Chaos Solitons & Fractals 166:112969","journal-title":"Chaos Solitons & Fractals"},{"issue":"1","key":"2399_CR94","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0055403","volume":"8","author":"W Xinyi","year":"2013","unstructured":"Xinyi W, Ma J (2013) The formation mechanism of defects, spiral wave in the network of neurons. PLoS ONE 8(1):e55403","journal-title":"PLoS ONE"},{"issue":"7","key":"2399_CR95","doi-asserted-by":"publisher","first-page":"1196","DOI":"10.1038\/s41562-023-01626-5","volume":"7","author":"X Yiben","year":"2023","unstructured":"Yiben X, Long X, Feng J, Gong P (2023) Interacting spiral wave patterns underlie complex brain dynamics and are related to cognitive processing. Nat Hum Behav 7(7):1196\u20131215","journal-title":"Nat Hum Behav"},{"issue":"1","key":"2399_CR96","doi-asserted-by":"publisher","first-page":"886","DOI":"10.1038\/s41467-022-28551-x","volume":"13","author":"J Ying","year":"2022","unstructured":"Ying J, Keinath AT, Lavoie R, Vigneault E, El Mestikawy S, Brandon MP (2022) Disruption of the grid cell network in a mouse model of early alzheimer\u2019s disease. Nat Commun 13(1):886","journal-title":"Nat Commun"},{"issue":"12","key":"2399_CR97","doi-asserted-by":"publisher","first-page":"2425","DOI":"10.1016\/j.cub.2023.04.065","volume":"33","author":"J Ying","year":"2023","unstructured":"Ying J, Reboreda A, Yoshida M, Brandon MP (2023) Grid cell disruption in a mouse model of early alzheimer\u2019s disease reflects reduced integration of self-motion cues. Curr Biol 33(12):2425\u20132437","journal-title":"Curr Biol"},{"key":"2399_CR98","doi-asserted-by":"publisher","DOI":"10.1016\/j.nonrwa.2023.103909","volume":"73","author":"Y You","year":"2023","unstructured":"You Y (2023) Exponential synchronization of memristive hindmarsh-rose neural networks. Nonlinear Anal Real World Appl 73:103909","journal-title":"Nonlinear Anal Real World Appl"}],"container-title":["Journal of Mathematical Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00285-026-02399-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00285-026-02399-x","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00285-026-02399-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,24]],"date-time":"2026-05-24T19:01:47Z","timestamp":1779649307000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00285-026-02399-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,4,29]]},"references-count":98,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2026,5]]}},"alternative-id":["2399"],"URL":"https:\/\/doi.org\/10.1007\/s00285-026-02399-x","relation":{},"ISSN":["0303-6812","1432-1416"],"issn-type":[{"value":"0303-6812","type":"print"},{"value":"1432-1416","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,4,29]]},"assertion":[{"value":"23 July 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"31 March 2026","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 April 2026","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 April 2026","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflicts of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflicts of Interest"}},{"value":"AI-based tools were employed solely to enhance clarity, grammar, and presentation.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethics"}}],"article-number":"81"}}