{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,21]],"date-time":"2026-10-21T17:11:23Z","timestamp":1792602683829,"version":"4.5.0"},"reference-count":61,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2024,9,1]],"date-time":"2024-09-01T00:00:00Z","timestamp":1725148800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,9,1]],"date-time":"2024-09-01T00:00:00Z","timestamp":1725148800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Acta Biotheor"],"published-print":{"date-parts":[[2024,9]]},"DOI":"10.1007\/s10441-024-09485-x","type":"journal-article","created":{"date-parts":[[2024,9,2]],"date-time":"2024-09-02T20:21:23Z","timestamp":1725308483000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Improved Mathematical Models of Parkinson's Disease with Hopf Bifurcation and Huntington's Disease with Chaos"],"prefix":"10.1007","volume":"72","author":[{"ORCID":"https:\/\/orcid.org\/0009-0007-2887-5756","authenticated-orcid":false,"given":"M. A.","family":"Elfouly","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2024,9,2]]},"reference":[{"key":"9485_CR1","doi-asserted-by":"publisher","DOI":"10.1007\/s12648-021-02263-2","author":"HN Agiza","year":"2022","unstructured":"Agiza HN, Sohaly MA, Elfouly MA (2022) Small two-delay differential equations for Parkinson\u2019s disease models using Taylor series transform. Indian J Phys. https:\/\/doi.org\/10.1007\/s12648-021-02263-2","journal-title":"Indian J Phys"},{"issue":"10","key":"9485_CR2","doi-asserted-by":"publisher","first-page":"366","DOI":"10.1016\/0166-2236(89)90074-X","volume":"12","author":"RL Albin","year":"1989","unstructured":"Albin RL, Young AB, Penney JB (1989) The functional anatomy of basal ganglia disorders. Trends Neurosci 12(10):366\u2013375. https:\/\/doi.org\/10.1016\/0166-2236(89)90074-X","journal-title":"Trends Neurosci"},{"issue":"3\u20135","key":"9485_CR3","doi-asserted-by":"publisher","first-page":"248","DOI":"10.1159\/000104368","volume":"22","author":"G Austin","year":"1962","unstructured":"Austin G, Tsai C (1962) A physiological basis and development of a model for parkinsonian tremor. Stereotact Funct Neurosurg 22(3\u20135):248\u2013258. https:\/\/doi.org\/10.1159\/000104368","journal-title":"Stereotact Funct Neurosurg"},{"issue":"2","key":"9485_CR4","doi-asserted-by":"publisher","first-page":"197","DOI":"10.1016\/s0197-4580(02)00065-9","volume":"24","author":"H Braak","year":"2003","unstructured":"Braak H, Del Tredici K, R\u00fcb U, de Vos RAI, Jansen Steur ENH, Braak E (2003) Staging of brain pathology related to sporadic Parkinson\u2019s disease. Neurobiol Aging 24(2):197\u2013211. https:\/\/doi.org\/10.1016\/s0197-4580(02)00065-9","journal-title":"Neurobiol Aging"},{"key":"9485_CR5","doi-asserted-by":"publisher","first-page":"1022","DOI":"10.1038\/nn.3743","volume":"17","author":"P Calabresi","year":"2014","unstructured":"Calabresi P, Picconi B, Tozzi A et al (2014) Direct and indirect pathways of basal ganglia: a critical reappraisal. Nat Neurosci 17:1022\u20131030. https:\/\/doi.org\/10.1038\/nn.3743","journal-title":"Nat Neurosci"},{"key":"9485_CR6","unstructured":"Caron NS, Wright GEB, Hayden MR (1998) Huntington disease. In: Adam MP, Everman DB, Mirzaa GM, Pagon RA, Wallace SE, Bean LJH, Gripp KW, Amemiya A (eds) GeneReviews\u00ae. University of Washington, Seattle, pp 1993\u20132022 (updated 11 June 2020)"},{"key":"9485_CR7","doi-asserted-by":"publisher","unstructured":"Cartwright ML, Littlewood JE (1945) On non-linear differential equations of the second order: I. https:\/\/doi.org\/10.1112\/jlms\/s1-20.3.180","DOI":"10.1112\/jlms\/s1-20.3.180"},{"key":"9485_CR8","doi-asserted-by":"publisher","unstructured":"Cartwright ML, Littlewood JE (1947) On non-linear differential equations of the second order: I. https:\/\/doi.org\/10.1112\/jlms\/s1-20.3.180","DOI":"10.1112\/jlms\/s1-20.3.180"},{"key":"9485_CR9","doi-asserted-by":"publisher","DOI":"10.3389\/fpsyg.2019.01930","author":"AM Cebolla","year":"2019","unstructured":"Cebolla AM, Cheron G (2019) Understanding neural oscillations in the human brain: from movement to consciousness and vice versa. Front Psychol. https:\/\/doi.org\/10.3389\/fpsyg.2019.01930","journal-title":"Front Psychol"},{"key":"9485_CR10","doi-asserted-by":"publisher","first-page":"237","DOI":"10.1007\/s00422-010-0401-y","volume":"103","author":"VS Chakravarthy","year":"2010","unstructured":"Chakravarthy VS, Joseph D, Bapi RS (2010) What do the basal ganglia do? A modeling perspective. Biol Cybern 103:237\u2013253. https:\/\/doi.org\/10.1007\/s00422-010-0401-y","journal-title":"Biol Cybern"},{"key":"9485_CR11","doi-asserted-by":"publisher","unstructured":"Chakravarthy, Srinivasa V, Moustafa AA (2018) Computational neuroscience models of the basal ganglia. Springer, Singapore. https:\/\/doi.org\/10.1007\/978-981-10-8494-2","DOI":"10.1007\/978-981-10-8494-2"},{"key":"9485_CR12","volume-title":"Lectures on the diseases of the nervous system","author":"J Charcot","year":"1879","unstructured":"Charcot J, Sigerson G (1879) Lectures on the diseases of the nervous system, 2nd edn. Henry C. Lea, Philadelphia","edition":"2"},{"issue":"2","key":"9485_CR13","doi-asserted-by":"publisher","first-page":"415","DOI":"10.1080\/00036811.2023.2187789","volume":"103","author":"A Columbu","year":"2024","unstructured":"Columbu A, Frassu S, Viglialoro G (2024) Refined criteria toward boundedness in an attraction\u2013repulsion chemotaxis system with nonlinear productions. Appl Anal 103(2):415\u2013431. https:\/\/doi.org\/10.1080\/00036811.2023.2187789","journal-title":"Appl Anal"},{"key":"9485_CR14","doi-asserted-by":"publisher","DOI":"10.1016\/j.ncl.2014.09.003","author":"P Dayalu","year":"2015","unstructured":"Dayalu P, Albin RL (2015) Huntington disease: pathogenesis and treatment. Neurol Clin. https:\/\/doi.org\/10.1016\/j.ncl.2014.09.003","journal-title":"Neurol Clin"},{"key":"9485_CR15","doi-asserted-by":"publisher","first-page":"2925","DOI":"10.1038\/s41598-022-06911-3","volume":"12","author":"MA Elfouly","year":"2022","unstructured":"Elfouly MA, Sohaly MA (2022) Van der Pol model in two-delay differential equation representation. Sci Rep 12:2925. https:\/\/doi.org\/10.1038\/s41598-022-06911-3","journal-title":"Sci Rep"},{"key":"9485_CR16","doi-asserted-by":"publisher","DOI":"10.1016\/S0006-3495(61)86902-6","author":"R FitzHugh","year":"1961","unstructured":"FitzHugh R (1961) Impulses and physiological states in theoretical models of nerve membrane. Biophys J. https:\/\/doi.org\/10.1016\/S0006-3495(61)86902-6","journal-title":"Biophys J"},{"key":"9485_CR17","doi-asserted-by":"publisher","first-page":"153","DOI":"10.1007\/s13311-013-0244-z","volume":"11","author":"S Frank","year":"2014","unstructured":"Frank S (2014) Treatment of Huntington\u2019s disease. Neurotherapeutics 11:153\u2013160. https:\/\/doi.org\/10.1007\/s13311-013-0244-z","journal-title":"Neurotherapeutics"},{"issue":"4","key":"9485_CR21","first-page":"485","volume":"77","author":"JF G\u00f3mez-Aguilar","year":"2010","unstructured":"G\u00f3mez-Aguilar JF, Mor\u00e1n-L\u00f3pez JL (2010) Van der Pol oscillator controlled by the stochastic resonance phenomenon. Eur Phys J B 77(4):485\u2013489","journal-title":"Eur Phys J B"},{"key":"9485_CR18","doi-asserted-by":"publisher","unstructured":"Gopalsamy K (2013) Stability and oscillations in delay differential equations of population dynamics. Kluwer Academic Publishers, Springer. https:\/\/doi.org\/10.1007\/978-94-015-7920-9","DOI":"10.1007\/978-94-015-7920-9"},{"key":"9485_CR19","doi-asserted-by":"publisher","unstructured":"Groenewegen HJ, Voorn P, Berendse HW, Mulder AB, Cools AR (eds) (2009) The basal ganglia IX. Springer. https:\/\/doi.org\/10.1007\/978-1-4419-0340-2","DOI":"10.1007\/978-1-4419-0340-2"},{"issue":"27","key":"9485_CR22","doi-asserted-by":"publisher","first-page":"7476","DOI":"10.1523\/JNEUROSCI.5200-07.2008","volume":"28","author":"C G\u00fcnay","year":"2008","unstructured":"G\u00fcnay C, Edgerton JR, Jaeger D (2008) Channel density distributions explain spiking variability in the globus pallidus: a combined physiology and computer simulation database approach. J Neurosci 28(27):7476\u20137491. https:\/\/doi.org\/10.1523\/JNEUROSCI.5200-07.2008","journal-title":"J Neurosci"},{"key":"9485_CR20","doi-asserted-by":"publisher","DOI":"10.1002\/mds.26714","author":"J Guridi","year":"2017","unstructured":"Guridi J, Alegre M (2017) Oscillatory activity in the basal ganglia and deep brain stimulation. Mov Disord. https:\/\/doi.org\/10.1002\/mds.26714","journal-title":"Mov Disord"},{"issue":"1","key":"9485_CR26","first-page":"57","volume":"37","author":"L H\u00e9liot","year":"2015","unstructured":"H\u00e9liot L (2015) Van der Pol and the history of relaxation oscillations: toward the emergence of a conceptual framework. Hist Philos Life Sci 37(1):57\u201381","journal-title":"Hist Philos Life Sci"},{"key":"9485_CR23","doi-asserted-by":"publisher","first-page":"386","DOI":"10.1007\/s00381-002-0604-1","volume":"18","author":"MT Herrero","year":"2002","unstructured":"Herrero MT, Barcia C, Navarro J (2002) Functional anatomy of thalamus and basal ganglia. Childs Nerv Syst 18:386\u2013404. https:\/\/doi.org\/10.1007\/s00381-002-0604-1","journal-title":"Childs Nerv Syst"},{"issue":"1","key":"9485_CR24","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1186\/s13408-018-0062-z","volume":"8","author":"AR Houweling","year":"2018","unstructured":"Houweling AR, Bretonnet L, Fairhurst MT, L\u0151rincz A (2018) Hopf bifurcation analysis of a computational model for the subthalamic nucleus\u2013globus pallidus network. J Math Neurosci 8(1):7","journal-title":"J Math Neurosci"},{"issue":"50","key":"9485_CR25","doi-asserted-by":"publisher","first-page":"12921","DOI":"10.1523\/jneurosci.3486-06.2006","volume":"26","author":"MD Humphries","year":"2006","unstructured":"Humphries MD, Stewart RD, Gurney KN (2006) A physiologically plausible model of action selection and oscillatory activity in the basal ganglia. J Neurosci 26(50):12921\u201312942. https:\/\/doi.org\/10.1523\/jneurosci.3486-06.2006","journal-title":"J Neurosci"},{"issue":"4","key":"9485_CR27","doi-asserted-by":"publisher","first-page":"368","DOI":"10.1136\/jnnp.2007.131045","volume":"79","author":"J Jankovic","year":"2008","unstructured":"Jankovic J (2008) Parkinson\u2019s disease: clinical features and diagnosis. J Neurol Neurosurg Psychiatry 79(4):368\u2013376","journal-title":"J Neurol Neurosurg Psychiatry"},{"issue":"10","key":"9485_CR28","doi-asserted-by":"publisher","first-page":"1611","DOI":"10.1001\/archneur.58.10.1611","volume":"58","author":"J Jankovic","year":"2001","unstructured":"Jankovic J, Kapadia AS (2001) Functional decline in Parkinson disease. Arch Neurol 58(10):1611\u20131615","journal-title":"Arch Neurol"},{"key":"9485_CR29","doi-asserted-by":"publisher","DOI":"10.3934\/dcdsb.2024021","author":"Z Jiao","year":"2024","unstructured":"Jiao Z, Jadlovsk\u00e1 I, Li T (2024) Analysis of an SIS reaction\u2013diffusion\u2013chemotaxis epidemic model with gradient-dependent flux limitation and standard incidence. Discrete Continuous Dyn Syst B. https:\/\/doi.org\/10.3934\/dcdsb.2024021","journal-title":"Discrete Continuous Dyn Syst B"},{"issue":"4","key":"9485_CR30","doi-asserted-by":"publisher","first-page":"787","DOI":"10.1113\/jphysiol.2012.239590","volume":"591","author":"P Jiruska","year":"2013","unstructured":"Jiruska P, de Curtis M, Jefferys JG, Schevon CA (2013) Synchronization and desynchronization in epilepsy: controversies and hypotheses. J Physiol 591(4):787\u2013797","journal-title":"J Physiol"},{"issue":"12","key":"9485_CR31","doi-asserted-by":"publisher","DOI":"10.1101\/cshperspect.a009621","volume":"2","author":"JL Lanciego","year":"2012","unstructured":"Lanciego JL, Luquin N, Obeso JA (2012) Functional neuroanatomy of the basal ganglia. Cold Spring Harb Perspect Med 2(12):a009621. https:\/\/doi.org\/10.1101\/cshperspect.a009621","journal-title":"Cold Spring Harb Perspect Med"},{"key":"9485_CR32","doi-asserted-by":"publisher","first-page":"16336","DOI":"10.1038\/s41598-020-73269-9","volume":"10","author":"M Lodi","year":"2020","unstructured":"Lodi M, Della Rossa F, Sorrentino F et al (2020) Analyzing synchronized clusters in neuron networks. Sci Rep 10:16336. https:\/\/doi.org\/10.1038\/s41598-020-73269-9","journal-title":"Sci Rep"},{"key":"9485_CR33","doi-asserted-by":"publisher","unstructured":"Lytton WW (2002) Neural circuits. In: From computer to brain. Springer, New York. https:\/\/doi.org\/10.1007\/0-387-22733-4_15","DOI":"10.1007\/0-387-22733-4_15"},{"issue":"6","key":"9485_CR34","doi-asserted-by":"publisher","first-page":"1042","DOI":"10.1016\/j.neuron.2019.02.010","volume":"101","author":"MM McGregor","year":"2019","unstructured":"McGregor MM, Nelson AB (2019) Circuit mechanisms of Parkinson\u2019s disease. Neuron 101(6):1042\u20131056. https:\/\/doi.org\/10.1016\/j.neuron.2019.02.010","journal-title":"Neuron"},{"issue":"10","key":"9485_CR35","doi-asserted-by":"publisher","first-page":"2061","DOI":"10.1109\/JRPROC.1962.288235","volume":"50","author":"J Nagumo","year":"1962","unstructured":"Nagumo J, Arimoto S, Yoshizawa S (1962) An active pulse transmission line simulating nerve axon. Proc IRE 50(10):2061\u20132070. https:\/\/doi.org\/10.1109\/JRPROC.1962.288235","journal-title":"Proc IRE"},{"key":"9485_CR38","doi-asserted-by":"publisher","unstructured":"No Author (2002) Neural circuits. In: From computer to brain. Springer, New York. https:\/\/doi.org\/10.1007\/0-387-22733-4_15","DOI":"10.1007\/0-387-22733-4_15"},{"key":"9485_CR37","doi-asserted-by":"publisher","unstructured":"No Author (2006) Antiparkinsonians vs deep-brain stimulation for PD. Inpharma Wkly 1554:12. https:\/\/doi.org\/10.2165\/00128413-200615540-00037","DOI":"10.2165\/00128413-200615540-00037"},{"key":"9485_CR36","doi-asserted-by":"publisher","unstructured":"No Author (2016) Deep brain stimulation for PD not cost effective at 1 year. PharmacoEcon Outcomes News 746:19. https:\/\/doi.org\/10.1007\/s40274-016-2797-7","DOI":"10.1007\/s40274-016-2797-7"},{"issue":"S1","key":"9485_CR39","doi-asserted-by":"publisher","first-page":"S28","DOI":"10.1002\/mds.21620","volume":"23","author":"JA Obeso","year":"2008","unstructured":"Obeso JA, Rodriguez-Oroz MC, Rodriguez M, DeLong MR (2008) Pathophysiology of Parkinson\u2019s disease: from clinical neurology to basic neuroscience and back. Mov Disord 23(S1):S28\u2013S40. https:\/\/doi.org\/10.1002\/mds.21620","journal-title":"Mov Disord"},{"issue":"4968","key":"9485_CR40","doi-asserted-by":"publisher","first-page":"499","DOI":"10.1172\/JCI117111","volume":"249","author":"LF Olsen","year":"1990","unstructured":"Olsen LF, Schaffer WM (1990) Chaos versus noisy periodicity: alternative hypotheses for childhood epidemics. Science 249(4968):499\u2013504. https:\/\/doi.org\/10.1172\/JCI117111","journal-title":"Science"},{"issue":"12","key":"9485_CR45","doi-asserted-by":"publisher","first-page":"1591","DOI":"10.1002\/mds.26424","volume":"30","author":"RB Postuma","year":"2015","unstructured":"Postuma RB, Berg D, Stern M, Poewe W, Olanow CW, Oertel W et al (2015) MDS clinical diagnostic criteria for Parkinson\u2019s disease. Mov Disord 30(12):1591\u20131601","journal-title":"Mov Disord"},{"key":"9485_CR46","doi-asserted-by":"publisher","first-page":"4584389","DOI":"10.1155\/2018\/4584389","volume":"2018","author":"FA Rihan","year":"2018","unstructured":"Rihan FA, Tunc C, Saker SH, Lakshmanan S, Rakkiyappan R (2018) Applications of delay differential equations in biological systems. Complexity 2018:4584389. https:\/\/doi.org\/10.1155\/2018\/4584389","journal-title":"Complexity"},{"issue":"3","key":"9485_CR47","doi-asserted-by":"publisher","first-page":"823","DOI":"10.1111\/j.1471-4159.1990.tb02325.x","volume":"54","author":"AHV Schapira","year":"1990","unstructured":"Schapira AHV, Cooper JM, Dexter D, Jenner P, Clark JB, Marsden CD (1990) Mitochondrial complex I deficiency in Parkinson\u2019s disease. J Neurochem 54(3):823\u2013827. https:\/\/doi.org\/10.1111\/j.1471-4159.1990.tb02325.x","journal-title":"J Neurochem"},{"key":"9485_CR48","first-page":"415","volume":"8","author":"S Shen","year":"2018","unstructured":"Shen S, Jiang Q, Zhu H, Chen Y, Yu J, Tang Y (2018) Artificial neural networks for automated diagnosis of Parkinson\u2019s disease: a systematic review. Neurol Res Ther 8:415\u2013425","journal-title":"Neurol Res Ther"},{"issue":"12 Suppl 4","key":"9485_CR49","doi-asserted-by":"publisher","first-page":"S70","DOI":"10.1212\/01.wnl.0000238411.60781.85","volume":"66","author":"AZ Sherzai","year":"2006","unstructured":"Sherzai AZ, Thompson PD, Schneider JS (2006) Can selegiline and tocopherol protect against MPTP induced Parkinsonism? Neurology 66(12 Suppl 4):S70\u2013S78. https:\/\/doi.org\/10.1212\/01.wnl.0000238411.60781.85","journal-title":"Neurology"},{"issue":"2","key":"9485_CR50","doi-asserted-by":"publisher","first-page":"353","DOI":"10.1016\/s0306-4522(98)00004-9","volume":"86","author":"Y Smith","year":"1998","unstructured":"Smith Y, Bevan MD, Shink E, Bolam JP (1998) Microcircuitry of the direct and indirect pathways of the basal ganglia. Neuroscience 86(2):353\u2013387. https:\/\/doi.org\/10.1016\/s0306-4522(98)00004-9","journal-title":"Neuroscience"},{"issue":"9","key":"9485_CR51","doi-asserted-by":"publisher","first-page":"520","DOI":"10.1016\/j.tins.2004.07.004","volume":"27","author":"Y Smith","year":"2004","unstructured":"Smith Y, Raju DV, Pare JF, Sidibe M (2004) The thalamostriatal system: a highly specific network of the basal ganglia circuitry. Trends Neurosci 27(9):520\u2013527","journal-title":"Trends Neurosci"},{"key":"9485_CR52","volume-title":"Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering","author":"SH Strogatz","year":"1994","unstructured":"Strogatz SH (1994) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering. Perseus Books Publishing, New York"},{"issue":"7","key":"9485_CR53","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 J, 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"},{"key":"9485_CR54","unstructured":"The Editors of Encyclopaedia Britannica (2022) Chaos theory. Encyclopedia Britannica. https:\/\/www.britannica.com\/science\/chaos-theory. Accessed 27 July 2022"},{"key":"9485_CR55","doi-asserted-by":"publisher","first-page":"tre-5-296","DOI":"10.5334\/tohm.275","volume":"5","author":"TC Vale","year":"2015","unstructured":"Vale TC, Cardoso F (2015) Chorea: a journey through history. Tremor Other Hyperkinet Mov 5:tre-5-296. https:\/\/doi.org\/10.5334\/tohm.275","journal-title":"Tremor Other Hyperkinet Mov"},{"key":"9485_CR41","first-page":"701","volume":"1","author":"B Van der Pol","year":"1920","unstructured":"Van der Pol B (1920) Theory of the amplitude of free and forced triode vibrations. Radio Rev 1:701\u2013710","journal-title":"Radio Rev"},{"key":"9485_CR42","doi-asserted-by":"publisher","DOI":"10.1080\/14786442608564127","author":"B Van der Pol","year":"1926","unstructured":"Van der Pol B (1926) On, \u201crelaxation-oscillations.\u201d Lond Edinb Dublin Philos Mag J Sci. https:\/\/doi.org\/10.1080\/14786442608564127","journal-title":"Lond Edinb Dublin Philos Mag J Sci"},{"key":"9485_CR43","doi-asserted-by":"publisher","first-page":"363","DOI":"10.1038\/120363a0","volume":"120","author":"B Van der Pol","year":"1927","unstructured":"Van der Pol B, Van der Mark J (1927) Frequency demultiplication. Nature 120:363\u2013364. https:\/\/doi.org\/10.1038\/120363a0","journal-title":"Nature"},{"issue":"6","key":"9485_CR44","doi-asserted-by":"publisher","first-page":"763","DOI":"10.1080\/14786441108564652","volume":"7","author":"B van der Pol","year":"1928","unstructured":"van der Pol B, van der Mark J (1928) The heartbeat considered as a relaxation oscillation, and an electrical model of the heart. Lond Edinb Dublin Philos Mag J Sci 7(6):763\u2013775. https:\/\/doi.org\/10.1080\/14786441108564652","journal-title":"Lond Edinb Dublin Philos Mag J Sci"},{"issue":"2","key":"9485_CR56","doi-asserted-by":"crossref","first-page":"154","DOI":"10.1002\/asjc.91","volume":"11","author":"HJ Wang","year":"2009","unstructured":"Wang HJ, Zhang XG (2009) Modelling and control of automotive powertrain with rubber belt CVT using Van der Pol oscillator. Asian J Control 11(2):154\u2013166","journal-title":"Asian J Control"},{"key":"9485_CR57","doi-asserted-by":"publisher","DOI":"10.1172\/JCI117111","author":"JN Weiss","year":"1994","unstructured":"Weiss JN, Garfinkel A, Spano ML, Ditto WL (1994) Chaos and chaos control in biology. J Clin Investig. https:\/\/doi.org\/10.1172\/JCI117111","journal-title":"J Clin Investig"},{"issue":"6","key":"9485_CR58","doi-asserted-by":"publisher","first-page":"899","DOI":"10.1016\/j.neuron.2019.08.026","volume":"103","author":"T Wichmann","year":"2019","unstructured":"Wichmann T, DeLong MR (2019) Deep brain stimulation for movement disorders of basal ganglia origin: restoring function or functionality? Neuron 103(6):899\u2013900. https:\/\/doi.org\/10.1016\/j.neuron.2019.08.026","journal-title":"Neuron"},{"issue":"4","key":"9485_CR59","doi-asserted-by":"publisher","first-page":"2120","DOI":"10.1152\/jn.00822.2005","volume":"95","author":"T Wichmann","year":"2006","unstructured":"Wichmann T, Soares J (2006) Neuronal firing before and after burst discharges in the monkey basal ganglia is predictably patterned in the normal state and altered in Parkinsonism. J Neurophysiol 95(4):2120\u20132133. https:\/\/doi.org\/10.1152\/jn.00822.2005","journal-title":"J Neurophysiol"},{"key":"9485_CR60","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.77.061921","volume":"77","author":"Y Xie","year":"2008","unstructured":"Xie Y et al (2008) Controlling the onset of Hopf bifurcation in the Hodgkin-Huxley model. Phys Rev E 77:061921","journal-title":"Phys Rev E"},{"key":"9485_CR61","unstructured":"Young CB, Reddy V, Sonne J (2022) Neuroanatomy, basal ganglia. In: StatPearls. StatPearls Publishing, Treasure Island. https:\/\/www.ncbi.nlm.nih.gov\/books\/NBK537141\/ (updated 31 July 2021)"}],"container-title":["Acta Biotheoretica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10441-024-09485-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10441-024-09485-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10441-024-09485-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,10,1]],"date-time":"2024-10-01T13:04:47Z","timestamp":1727787887000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10441-024-09485-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,9]]},"references-count":61,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2024,9]]}},"alternative-id":["9485"],"URL":"https:\/\/doi.org\/10.1007\/s10441-024-09485-x","relation":{},"ISSN":["0001-5342","1572-8358"],"issn-type":[{"value":"0001-5342","type":"print"},{"value":"1572-8358","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,9]]},"assertion":[{"value":"9 July 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 July 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 September 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The author declare no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"Not applicable; there are no clinical data for human or animal experiments. The data in the manuscript were suggestions by the author to clarify the behaviour of the model and to explain different symptoms of Parkinson's disease or Huntington's disease.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical Approval"}}],"article-number":"11"}}