Hopf-like bifurcation and mixed mode oscillation in a fractional-order fitzHugh-nagumo model

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dc.authorid0000-0003-0451-4255en_US
dc.contributor.authorAbdelouahab, Mohammed Salah
dc.contributor.authorLozi, Rene
dc.date.accessioned2024-07-12T20:55:47Z
dc.date.available2024-07-12T20:55:47Z
dc.date.issued2019en_US
dc.departmentMaltepe Üniversitesi, İnsan ve Toplum Bilimleri Fakültesien_US
dc.description.abstractIn this work we investigate the emergence of mixed-mode oscillations and canard explosion, in a planar fractional-order FitzHugh-Nagumo model(FFHN). An algorithm, called Global-Local Canard Explosion Search Algorithm (GLCESA) is developed and used to investigate the existence of canard oscillations in the neighbourhoods of Hopf-like bifurcation points. the appearance of various patterns of solutions is revealed, with an increasing number of small-amplitude oscillations when two key parameters of the FFHN model are varied. The numbers of such oscillations versus the two parameters, respectively, are perfectly fitted using exponential functions. Finally, it is conjectured that chaos could occur in a 2-dimensional fractional-order autonomous dynamical system, with a fractional order close to one. After all, the article demonstrates that the FFHN Model is a very simple 2-dimensional model with an incredible ability to present the complex dynamics of neurons.en_US
dc.identifier.citationAbdelouahab, M. S. ve Lozi, R. (2019). Hopf-like bifurcation and mixed mode oscillation in a fractional-order fitzHugh-nagumo model. International Conference of Mathematical Sciences (ICMS 2019). s. 183.en_US
dc.identifier.endpage184en_US
dc.identifier.isbn978-605-2124-29-1
dc.identifier.startpage183en_US
dc.identifier.urihttps://hdl.handle.net/20.500.12415/2894
dc.language.isoenen_US
dc.publisherMaltepe Üniversitesien_US
dc.relation.ispartofInternational Conference of Mathematical Sciences (ICMS 2019)en_US
dc.relation.publicationcategoryUluslararası Konferans Öğesi - Başka Kurum Yazarıen_US
dc.rightsCC0 1.0 Universal*
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.rights.urihttp://creativecommons.org/publicdomain/zero/1.0/*
dc.snmzKY01401
dc.subjectFitzhugh-nagumo modelen_US
dc.subjectCanard explosionen_US
dc.subjectFractional-order systemen_US
dc.subjectMixed-mode oscillationen_US
dc.subjectChaosen_US
dc.titleHopf-like bifurcation and mixed mode oscillation in a fractional-order fitzHugh-nagumo modelen_US
dc.typeArticle
dspace.entity.typePublication

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