Synchronization for two coupled oscillators with inhibitory connection

In this paper we present an oscillatory neural network composed of two coupled neural oscillators with inhibitory connections. Each of the oscillators describes the dynamics of average activities of excitatory and inhibitory populations of neurons. Regarding time delays τ as the bifurcation parameter, we not only obtain the existence of Hopf bifurcations but also investigate the bifurcation direction and stability of bifurcated periodic solutions by employing normal form theory and center manifold reduction. Finally, numerical simulations are provided to illustrate the theoretical results. Copyright © 2009 John Wiley & Sons, Ltd.