Hopf-like bifurcation and mixed mode oscillation in a fractional-order fitzHugh-nagumo model
Küçük Resim Yok
Tarih
2019
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Maltepe Üniversitesi
Erişim Hakkı
CC0 1.0 Universal
info:eu-repo/semantics/openAccess
info:eu-repo/semantics/openAccess
Özet
In 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.
Açıklama
Anahtar Kelimeler
Fitzhugh-nagumo model, Canard explosion, Fractional-order system, Mixed-mode oscillation, Chaos
Kaynak
International Conference of Mathematical Sciences (ICMS 2019)
WoS Q Değeri
Scopus Q Değeri
Cilt
Sayı
Künye
Abdelouahab, 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.
