Article ID Journal Published Year Pages File Type
838646 Nonlinear Analysis: Real World Applications 2015 15 Pages PDF
Abstract

We consider the dynamical behavior of a delayed two-coupled oscillator with excitatory-to-inhibitory connection. Some parameter regions are given for linear stability, absolute synchronization, and Hopf bifurcations by using the theory of functional differential equations. Conditions ensuring the stability and direction of the Hopf bifurcation are determined by applying the normal form theory and the center manifold theorem. We also investigate the spatio-temporal patterns of bifurcating periodic oscillations by using the symmetric bifurcation theory of delay differential equations combined with representation theory of Lie groups. Finally, numerical simulations are given to illustrate the results obtained.

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