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

Iranian Journal of Numerical Analysis and Optimization

مقاله 1، دوره 4، شماره 2 - شماره پیاپی 6، بهمن 2014، صفحه 15-30   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.v4i2.40227

نویسندگان

E. Javidmanesh؛ M. Khorshidi^*

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

چکیده

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.

کلیدواژه‌ها

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

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