Bogdanov–Takens singularity in the Hindmarsh–Rose neuron with time delay

Yingying Li, Zhouchao Wei, Wei Zhang, Matjaž Perc and Robert Repnik

Applied Mathematics and Computation, 2019, vol. 354, issue C, 180-188

Abstract: In this paper, we study the Bogdanov–Takens singularity in the Hindmarsh–Rose neuron model with time delay. We use the center manifold reduction and the normal form method, by means of which the dynamics near this nonhyperbolic equilibrium can be reduced to the study of the dynamics of the corresponding normal form restricted to the associated two-dimensional center manifold. We show that changes in the time delay length can lead to the saddle-node bifurcation, to the Hopf bifurcation, and to the homoclinic bifurcation.

Keywords: Hindmarsh–Rose model; Bogdanov–Takens Bifurcation; Center manifold; Normal form method; Time delay (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:354:y:2019:i:c:p:180-188

DOI: 10.1016/j.amc.2019.02.046

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