Frequency domain approach to computational analysis of bifurcation and periodic solution in a two-neuron network model with distributed delays and self-feedbacks

Authors:
Min Xiao;Wei Xing Zheng;Jinde Cao
Affiliations:
School of Mathematics and Information Technology, Nanjing Xiaozhuang University, Nanjing 210017, PR China and School of Computing, Engineering and Mathematics, University of Western Sydney, Penrit ...;School of Computing, Engineering and Mathematics, University of Western Sydney, Penrith NSW 2751, Australia;Department of Mathematics, Southeast University, Nanjing 210096, PR China
Venue:
Neurocomputing
Year:
2013

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Abstract

In this paper, a general two-neuron model with distributed delays, self-feedbacks and a weak kernel is studied. It is shown that the Hopf bifurcation occurs as the bifurcation parameter, the mean delay, passes a critical value where a family of periodic solutions emanate from the equilibrium. By applying the frequency domain approach and analyzing the associated characteristic equation, the existence of the bifurcation critical point of the mean delay is determined. The direction and the stability of bifurcating periodic solutions are determined by the Nyquist criterion and the graphical Hopf bifurcation theorem. Numerical simulation results supporting the theoretical analysis are also given.