Stability and Bifurcation Analysis on a Ring of Five Neurons with Discrete Delays

Authors:
Changjin Xu;Xianhua Tang;Maoxin Liao
Affiliations:
Guizhou Key Laboratory of Economics System Simulation, Guizhou University of Finance and Economics, Guizhou, China 550004;School of Mathematical Science and Computing Technology, Central South University, Hunan, China 410083;School of Mathematics and Physics, Nanhua University, Hengyang, China 421001
Venue:
Journal of Dynamical and Control Systems
Year:
2013

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Abstract

In this paper, a five-neuron model with discrete delays is considered, where the time delays are regarded as parameters. Its dynamics is studied in terms of local analysis and Hopf bifurcation analysis. By analyzing the associated characteristic transcendental equation, it is found that Hopf bifurcation occurs when these delays pass through a sequence of critical value. Some explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using the normal form theory and center manifold theory. Finally, numerical simulations supporting the theoretical analysis are presented.