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Dynamics of a delayed two-coupled oscillator with excitatory-to-excitatory connection
Authors:Ping Zhang  Shangjiang Guo  Yigang He
Institution:a College of Mathematics and Econometrics, Hunan University, Changsha, Hunan 410082, People’s Republic of China
b Sunshine College, Fuzhou University, Fuzhou, Fujian 350002, People’s Republic of China
c College of Electric and Information Engineering, Hunan University, Changsha, Hunan 410082, People’s Republic of China
Abstract:In this paper, we consider a neural network model consisting of two coupled oscillators with delayed feedback and excitatory-to-excitatory connection. We study how the strength of the connections between the oscillators affects the dynamics of the neural network. We give a full classification of all equilibria in the parameter space and obtain its linear stability by analyzing the characteristic equation of the linearized system. We also investigate the spatio-temporal patterns of bifurcated periodic oscillations by using the symmetric bifurcation theory of delay differential equations combined with representation theory of Lie groups. Moreover, the stability and bifurcation direction of the bifurcated periodic solutions are obtained by employing center manifold reduction and normal form theory. Some numerical simulations are provided to illustrate the theoretical results.
Keywords:Oscillator  Equilibria  Stability  Hopf bifurcation
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