{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T21:51:28Z","timestamp":1775512288500,"version":"3.50.1"},"reference-count":60,"publisher":"Frontiers Media SA","license":[{"start":{"date-parts":[[2023,8,31]],"date-time":"2023-08-31T00:00:00Z","timestamp":1693440000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["frontiersin.org"],"crossmark-restriction":true},"short-container-title":["Front. Comput. Neurosci."],"abstract":"<jats:p>Simplicial complexes are mathematical constructions that describe higher-order interactions within the interconnecting elements of a network. Such higher-order interactions become increasingly significant in neuronal networks since biological backgrounds and previous outcomes back them. In light of this, the current research explores a higher-order network of the memristive Rulkov model. To that end, the master stability functions are used to evaluate the synchronization of a network with pure pairwise hybrid (electrical and chemical) synapses alongside a network with two-node electrical and multi-node chemical connections. The findings provide good insight into the impact of incorporating higher-order interaction in a network. Compared to two-node chemical synapses, higher-order interactions adjust the synchronization patterns to lower multi-node chemical coupling parameter values. Furthermore, the effect of altering higher-order coupling parameter value on the dynamics of neurons in the synchronization state is researched. It is also shown how increasing network size can enhance synchronization by lowering the value of coupling parameters whereby synchronization occurs. Except for complete synchronization, cluster synchronization is detected for higher electrical coupling strength values wherein the neurons are out of the completed synchronization state.<\/jats:p>","DOI":"10.3389\/fncom.2023.1248976","type":"journal-article","created":{"date-parts":[[2023,8,31]],"date-time":"2023-08-31T12:44:55Z","timestamp":1693485895000},"update-policy":"https:\/\/doi.org\/10.3389\/crossmark-policy","source":"Crossref","is-referenced-by-count":50,"title":["Synchronization in simplicial complexes of memristive Rulkov neurons"],"prefix":"10.3389","volume":"17","author":[{"given":"Mahtab","family":"Mehrabbeik","sequence":"first","affiliation":[]},{"given":"Sajad","family":"Jafari","sequence":"additional","affiliation":[]},{"given":"Matja\u017e","family":"Perc","sequence":"additional","affiliation":[]}],"member":"1965","published-online":{"date-parts":[[2023,8,31]]},"reference":[{"key":"B1","doi-asserted-by":"publisher","first-page":"333","DOI":"10.1016\/0375-9601(90)90136-C","article-title":"Chaotic neural networks","volume":"144","author":"Aihara","year":"1990","journal-title":"Phys. Lett. A"},{"key":"B2","doi-asserted-by":"publisher","first-page":"586","DOI":"10.1038\/s41562-020-01024-1","article-title":"Evolutionary dynamics of higher-order interactions in social networks","volume":"5","author":"Alvarez-Rodriguez","year":"2021","journal-title":"Nat. Hum. Behav"},{"key":"B3","doi-asserted-by":"publisher","first-page":"033125","DOI":"10.1063\/5.0074641","article-title":"Intralayer and interlayer synchronization in multiplex network with higher-order interactions","volume":"32","author":"Anwar","year":"2022","journal-title":"Chaos"},{"key":"B4","doi-asserted-by":"publisher","first-page":"3872573","DOI":"10.1155\/2018\/3872573","article-title":"Three-dimensional memristive Hindmarsh-Rose neuron model with hidden coexisting asymmetric behaviors","volume":"2018","author":"Bao","year":"2018","journal-title":"Complexity"},{"key":"B5","doi-asserted-by":"publisher","first-page":"2281","DOI":"10.1007\/s11431-021-1845-x","article-title":"Discrete memristive neuron model and its interspike interval-encoded application in image encryption","volume":"64","author":"Bao","year":"2021","journal-title":"Sci. China Technol. Sci"},{"key":"B6","doi-asserted-by":"publisher","first-page":"1079","DOI":"10.1007\/s11571-022-09871-6","article-title":"Three-dimensional memristive Morris-Lecar model with magnetic induction effects and its FPGA implementation","volume":"17","author":"Bao","year":"2022","journal-title":"Cogn. Neurodyn"},{"key":"B7","doi-asserted-by":"publisher","first-page":"1093","DOI":"10.1038\/s41567-021-01371-4","article-title":"The physics of higher-order interactions in complex systems","volume":"17","author":"Battiston","year":"2021","journal-title":"Nat. Phys"},{"key":"B8","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.physrep.2020.05.004","article-title":"Networks beyond pairwise interactions: structure and dynamics","volume":"874","author":"Battiston","year":"2020","journal-title":"Phys. Rep"},{"key":"B9","doi-asserted-by":"publisher","first-page":"686","DOI":"10.1137\/21M1414024","article-title":"What are higher-order networks?","volume":"65","author":"Bick","year":"2023","journal-title":"SIAM Rev"},{"key":"B10","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.physrep.2023.04.002","article-title":"The structure and dynamics of networks with higher order interactions","volume":"1018","author":"Boccaletti","year":"2023","journal-title":"Phys. Rep"},{"key":"B11","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/S0370-1573(02)00137-0","article-title":"The synchronization of chaotic systems","volume":"366","author":"Boccaletti","year":"2002","journal-title":"Phys. Rep"},{"key":"B12","doi-asserted-by":"publisher","first-page":"175","DOI":"10.1016\/j.physrep.2005.10.009","article-title":"Complex networks: structure and dynamics","volume":"424","author":"Boccaletti","year":"2006","journal-title":"Phys. Rep"},{"key":"B13","doi-asserted-by":"publisher","first-page":"744","DOI":"10.3390\/e22070744","article-title":"Evolution of cooperation in the presence of higher-order interactions: from networks to hypergraphs","volume":"22","author":"Burgio","year":"2020","journal-title":"Entropy"},{"key":"B14","doi-asserted-by":"publisher","first-page":"035006","DOI":"10.1088\/2632-072X\/aba8e1","article-title":"Dynamical systems on hypergraphs","volume":"1","author":"Carletti","year":"2020","journal-title":"J. Phys"},{"key":"B15","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1016\/0010-0277(89)90006-1","article-title":"Neuronal models of cognitive functions","volume":"33","author":"Changeux","year":"1989","journal-title":"Cognition"},{"key":"B16","doi-asserted-by":"publisher","first-page":"1035","DOI":"10.1007\/s11431-019-1458-5","article-title":"Bifurcation analyses and hardware experiments for bursting dynamics in non-autonomous memristive FitzHugh-Nagumo circuit","volume":"63","author":"Chen","year":"2020","journal-title":"Sci. China Technol. Sci"},{"key":"B17","doi-asserted-by":"publisher","first-page":"461","DOI":"10.1016\/0960-0779(93)E0056-H","article-title":"Generic excitable dynamics on a two-dimensional map","volume":"5","author":"Chialvo","year":"1995","journal-title":"Chaos Solitons Fractals"},{"key":"B18","doi-asserted-by":"publisher","first-page":"5721","DOI":"10.1038\/s41598-023-32686-2","article-title":"A multiresolution framework for the analysis of community structure in international trade networks","volume":"13","author":"Cho","year":"2023","journal-title":"Sci. Rep"},{"key":"B19","doi-asserted-by":"publisher","first-page":"112899","DOI":"10.1016\/j.chaos.2022.112899","article-title":"Memristor synapse-coupled piecewise-linear simplified Hopfield neural network: dynamics analysis and circuit implementation","volume":"166","author":"Ding","year":"2023","journal-title":"Chaos Solitons Fractals"},{"key":"B20","doi-asserted-by":"publisher","first-page":"154454","DOI":"10.1016\/j.aeue.2022.154454","article-title":"Firing patterns and synchronization of morris-lecar neuron model with memristive autapse","volume":"158","author":"Fan","year":"2023","journal-title":"Int. J. Electron. Commun"},{"key":"B21","doi-asserted-by":"publisher","first-page":"4131","DOI":"10.1140\/epjs\/s11734-022-00720-5","article-title":"Synchronization and chimera in a multiplex network of Hindmarsh-Rose neuron map with flux-controlled memristor","volume":"231","author":"Fan","year":"2022","journal-title":"Eur. Phys. J. Spec. Top"},{"key":"B22","doi-asserted-by":"publisher","first-page":"120","DOI":"10.1016\/j.physa.2014.02.030","article-title":"International transmission of shocks and fragility of a bank network","volume":"403","author":"Feng","year":"2014","journal-title":"Phys. A"},{"key":"B23","doi-asserted-by":"publisher","first-page":"445","DOI":"10.1016\/S0006-3495(61)86902-6","article-title":"Impulses and physiological states in theoretical models of nerve membrane","volume":"1","author":"FitzHugh","year":"1961","journal-title":"Biophys. J"},{"key":"B24","doi-asserted-by":"publisher","first-page":"263","DOI":"10.1038\/s42005-022-01040-9","article-title":"Synchronization induced by directed higher-order interactions","volume":"5","author":"Gallo","year":"2022","journal-title":"Commun. Phys"},{"key":"B25","doi-asserted-by":"publisher","first-page":"1255","DOI":"10.1038\/s41467-021-21486-9","article-title":"Stability of synchronization in simplicial complexes","volume":"12","author":"Gambuzza","year":"2021","journal-title":"Nat. Commun"},{"key":"B26","doi-asserted-by":"publisher","first-page":"120","DOI":"10.1038\/s42005-021-00605-4","article-title":"Higher-order simplicial synchronization of coupled topological signals","volume":"4","author":"Ghorbanchian","year":"2021","journal-title":"Commun. Phys"},{"key":"B27","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.physrep.2021.10.006","article-title":"The synchronized dynamics of time-varying networks","volume":"949","author":"Ghosh","year":"2022","journal-title":"Phys. Rep"},{"key":"B28","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1098\/rspb.1984.0024","article-title":"A model of neuronal bursting using three coupled first order differential equations","volume":"221","author":"Hindmarsh","year":"1984","journal-title":"Proc. R. Soc. B: Biol. Sci"},{"key":"B29","doi-asserted-by":"publisher","first-page":"500","DOI":"10.1113\/jphysiol.1952.sp004764","article-title":"A quantitative description of membrane current and its application to conduction and excitation in nerve","volume":"117","author":"Hodgkin","year":"1952","journal-title":"J. Physiol"},{"key":"B30","doi-asserted-by":"publisher","first-page":"1721","DOI":"10.1007\/s11071-019-05100-8","article-title":"Dynamic property analysis and circuit implementation of simplified memristive Hodgkin-Huxley neuron model","volume":"97","author":"Hu","year":"2019","journal-title":"Nonlin. Dyn"},{"key":"B31","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.physrep.2010.12.003","article-title":"Map-based models in neuronal dynamics","volume":"501","author":"Ibarz","year":"2011","journal-title":"Phys. Rep"},{"key":"B32","doi-asserted-by":"publisher","first-page":"012013","DOI":"10.1088\/1742-6596\/197\/1\/012013","article-title":"On the presence of high-order interactions among somatosensory neurons and their effect on information transmission","volume":"197","author":"Ince","year":"2009","journal-title":"J. Phys. Conf. Ser"},{"key":"B33","doi-asserted-by":"publisher","first-page":"3847","DOI":"10.1142\/S0218127404011739","article-title":"Classification of bursting mappings","volume":"14","author":"Izhikevich","year":"2004","journal-title":"Int. J. Bifurcat. Chaos"},{"key":"B34","doi-asserted-by":"publisher","first-page":"493","DOI":"10.1016\/j.physa.2005.06.059","article-title":"Network marketing on a small-world network","volume":"360","author":"Kim","year":"2006","journal-title":"Phys. A"},{"key":"B35","doi-asserted-by":"publisher","first-page":"112861","DOI":"10.1016\/j.chaos.2022.112861","article-title":"Synchronization transitions in a discrete memristor-coupled bi-neuron model","volume":"165","author":"Li","year":"2022","journal-title":"Chaos Solitons Fractals"},{"key":"B36","doi-asserted-by":"publisher","first-page":"1726","DOI":"10.1109\/TII.2021.3086819","article-title":"Memristive Rulkov neuron model with magnetic induction effects","volume":"18","author":"Li","year":"2021","journal-title":"IEEE Trans. Ind. Inf"},{"key":"B37","doi-asserted-by":"publisher","first-page":"3397","DOI":"10.1109\/TCSI.2021.3081150","article-title":"Neural bursting and synchronization emulated by neural networks and circuits","volume":"68","author":"Lin","year":"2021","journal-title":"IEEE Trans. Circuits Syst. I Regul. Pap"},{"key":"B38","doi-asserted-by":"publisher","first-page":"3472","DOI":"10.1109\/TCSII.2020.3000492","article-title":"A multi-stable memristor and its application in a neural network","volume":"67","author":"Lin","year":"2020","journal-title":"IEEE Trans. Circuits Syst. II Express Briefs"},{"key":"B39","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1038\/s42005-022-00858-7","article-title":"Higher-order motif analysis in hypergraphs","volume":"5","author":"Lotito","year":"2022","journal-title":"Commun. Phys"},{"key":"B40","doi-asserted-by":"publisher","first-page":"033410","DOI":"10.1103\/PhysRevResearch.2.033410","article-title":"Multiorder Laplacian for synchronization in higher-order networks","volume":"2","author":"Lucas","year":"2020","journal-title":"Phys. Rev. Res"},{"key":"B41","doi-asserted-by":"publisher","first-page":"1569","DOI":"10.1007\/s11071-017-3565-3","article-title":"A review for dynamics in neuron and neuronal network","volume":"89","author":"Ma","year":"2017","journal-title":"Nonlinear Dyn"},{"key":"B42","doi-asserted-by":"publisher","first-page":"100","DOI":"10.1016\/j.plrev.2018.09.003","article-title":"Chimera states in neuronal networks: a review","volume":"28","author":"Majhi","year":"2019","journal-title":"Phys. Life Rev"},{"key":"B43","doi-asserted-by":"publisher","first-page":"20220043","DOI":"10.1098\/rsif.2022.0043","article-title":"Dynamics on higher-order networks: a review","volume":"19","author":"Majhi","year":"2022","journal-title":"J. R. Soc. Interface"},{"key":"B44","doi-asserted-by":"publisher","first-page":"2811","DOI":"10.3390\/math11132811","article-title":"The impact of higher-order interactions on the synchronization of Hindmarsh-Rose neuron maps under different coupling functions","volume":"11","author":"Mehrabbeik","year":"2023","journal-title":"Mathematics"},{"key":"B45","doi-asserted-by":"publisher","first-page":"123133","DOI":"10.1063\/5.0117473","article-title":"Synchronization of a higher-order network of Rulkov maps","volume":"32","author":"Mirzaei","year":"2022","journal-title":"Chaos"},{"key":"B46","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1016\/S0006-3495(81)84782-0","article-title":"Voltage oscillations in the barnacle giant muscle fiber","volume":"35","author":"Morris","year":"1981","journal-title":"Biophys. J"},{"key":"B47","doi-asserted-by":"publisher","first-page":"013125","DOI":"10.1063\/5.0079834","article-title":"Synchronization in Hindmarsh-Rose neurons subject to higher-order interactions","volume":"32","author":"Parastesh","year":"2022","journal-title":"Chaos"},{"key":"B48","doi-asserted-by":"publisher","first-page":"2109","DOI":"10.1103\/PhysRevLett.80.2109","article-title":"Master stability functions for synchronized coupled systems","volume":"80","author":"Pecora","year":"1998","journal-title":"Phys. Rev. Lett"},{"key":"B49","doi-asserted-by":"publisher","first-page":"041922","DOI":"10.1103\/PhysRevE.65.041922","article-title":"Modeling of spiking-bursting neural behavior using two-dimensional map","volume":"65","author":"Rulkov","year":"2002","journal-title":"Phys. Rev. E"},{"key":"B50","doi-asserted-by":"publisher","first-page":"105175","DOI":"10.1016\/j.cnsns.2020.105175","article-title":"Time delayed chemical synapses and synchronization in multilayer neuronal networks with ephaptic inter-layer coupling","volume":"84","author":"Shafiei","year":"2020","journal-title":"Commun. Nonlinear Sci. Numer. Simul"},{"key":"B51","doi-asserted-by":"publisher","first-page":"3854","DOI":"10.1038\/s41467-020-17540-7","article-title":"Synchronization of complex human networks","volume":"11","author":"Shahal","year":"2020","journal-title":"Nat. Commun"},{"key":"B52","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1109\/MNET.2004.1316761","article-title":"Time synchronization in sensor networks: a survey","volume":"18","author":"Sivrikaya","year":"2004","journal-title":"IEEE Netw"},{"key":"B53","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1038\/s42005-020-00485-0","article-title":"Higher order interactions in complex networks of phase oscillators promote abrupt synchronization switching","volume":"3","author":"Skardal","year":"2020","journal-title":"Commun. Phys"},{"key":"B54","doi-asserted-by":"publisher","first-page":"043193","DOI":"10.1103\/PhysRevResearch.3.043193","article-title":"Higher-order interactions can better optimize network synchronization","volume":"3","author":"Skardal","year":"2021","journal-title":"Phys. Rev. Res"},{"key":"B55","doi-asserted-by":"publisher","first-page":"056114","DOI":"10.1103\/PhysRevE.76.056114","article-title":"Network synchronization of groups","volume":"76","author":"Sorrentino","year":"2007","journal-title":"Phys. Rev. E"},{"key":"B56","doi-asserted-by":"publisher","first-page":"545","DOI":"10.3390\/electronics12030545","article-title":"Dynamical analysis and synchronization of a new memristive Chialvo neuron model","volume":"12","author":"Vivekanandhan","year":"2023","journal-title":"Electronics"},{"key":"B57","volume-title":"Theory and Computation of Tensors: Multi-Dimensional Arrays","author":"Wei","year":"2016"},{"key":"B58","doi-asserted-by":"publisher","first-page":"755","DOI":"10.1007\/s11571-022-09866-3","article-title":"Extreme multistability and phase synchronization in a heterogeneous bi-neuron Rulkov network with memristive electromagnetic induction","volume":"17","author":"Xu","year":"2023","journal-title":"Cogn. Neurodyn"},{"key":"B59","doi-asserted-by":"publisher","first-page":"62","DOI":"10.3389\/fncom.2020.00062","article-title":"Optimal self-induced stochastic resonance in multiplex neural networks: Electrical vs. chemical synapses","volume":"14","author":"Yamakou","year":"2020","journal-title":"Front. Comput. Neurosci"},{"key":"B60","doi-asserted-by":"publisher","first-page":"109558","DOI":"10.1016\/j.chaos.2019.109558","article-title":"One dimensional map-based neuron model: a phase space interpretation","volume":"132","author":"Zandi-Mehran","year":"2020","journal-title":"Chaos Solitons Fractals"}],"container-title":["Frontiers in Computational Neuroscience"],"original-title":[],"link":[{"URL":"https:\/\/www.frontiersin.org\/articles\/10.3389\/fncom.2023.1248976\/full","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,31]],"date-time":"2023-08-31T12:44:58Z","timestamp":1693485898000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.frontiersin.org\/articles\/10.3389\/fncom.2023.1248976\/full"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,8,31]]},"references-count":60,"alternative-id":["10.3389\/fncom.2023.1248976"],"URL":"https:\/\/doi.org\/10.3389\/fncom.2023.1248976","relation":{},"ISSN":["1662-5188"],"issn-type":[{"value":"1662-5188","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,8,31]]},"article-number":"1248976"}}