Codimension two bifurcation in a coupled FitzHugh–Nagumo system with multiple delays

Houssem Achouri, Chaouki Aouiti and Bassem Ben Hamed

Chaos, Solitons & Fractals, 2022, vol. 156, issue C

Abstract: In this paper, a coupled FitzHugh–Nagumo system with multiple delays is considered. In a first step, the critical point at which a zero root of multiplicity two occurs in the characteristic equation is constructed. In a second step, in order to ensure that all the roots of the characteristic equation except for the double zero root have negative real parts, the zeros of a third and a fourth degree exponential polynomial are studied. Moreover, the critical values where the Bogdanov–Takens bifurcation occurs are derived. By using the normal form theory and reduction on the centre manifold, the truncated normal form is obtained, and throughout the bifurcation diagram, its dynamical behaviours are studied. Finally, a numerical example is given to demonstrate our results.

Keywords: Coupled FitzHugh–Nagumo system; Time delay; Bogdanov–Takens bifurcation (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:156:y:2022:i:c:s0960077922000352

DOI: 10.1016/j.chaos.2022.111824

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