Hopf bifurcation analysis of a BAM neural network with multiple time delays and diffusion

Xiaohong Tian, Rui Xu and Qintao Gan

Applied Mathematics and Computation, 2015, vol. 266, issue C, 909-926

Abstract: In this paper, a BAM neural network with multiple time delays and diffusion under homogeneous Neumann boundary conditions is investigated. By analyzing the corresponding characteristic equations, the local stability of the trivial uniform steady state and the existence of Hopf bifurcation under two different cases are established, respectively. By using the normal form theory and the center manifold reduction of partial functional differential equations (PFDEs), explicit formulae are obtained to determine the direction of bifurcations and the stability of bifurcating periodic solutions. Numerical simulations are carried out to illustrate the main results.

Keywords: BAM neural network; Multiple time delays; Diffusion; Hopf bifurcation (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:266:y:2015:i:c:p:909-926

DOI: 10.1016/j.amc.2015.06.009

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