Hopf bifurcation in a general n-neuron ring network with n time delays

Document Type : Research Article

Authors

• E. Javidmanesh
• M. Khorshidi

Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran.

10.22067/ijnao.v4i2.40227

Abstract

In this paper, we consider a general ring network consisting of n neurons and n time delays. By analyzing the associated characteristic equation, a classification according to n is presented. It is investigated that Hopf bifur-cation occurs when the sum of the n delays passes through a critical value.In fact, a family of periodic solutions bifurcate from the origin, while the zero solution loses its asymptotically stability. To illustrate our theoretical results, numerical simulation is given.

Keywords

• Ring network
• Stability
• Periodic solution
• Hopf bifurcation
• Time delay

20.1001.1.24236977.2014.4.2.2.2

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