DYNAMICS IN TIME-DELAY RECURRENTLY COUPLED OSCILLATORS

A model of time-delay recurrently coupled spatially segregated neural oscillators is proposed. Each of the oscillators describes the dynamics of average activities of excitatory and inhibitory populations of neurons. Bifurcation analysis shows the richness of the dynamical behaviors in a biophysically plausible parameter region. We find oscillatory multi-stability, hysteresis, and stability switches of the rest state provoked by the time delay as well as the strength of the connections between the oscillators. Then we derive the equation describing the flow on the center manifold that enables us to determine the bifurcation direction and stability of bifurcated periodic solutions and equilibria. We also give some numerical simulations to support our main results.