STABILITY AND HOPF BIFURCATION ANALYSIS IN COUPLED LIMIT CYCLE OSCILLATORS WITH TIME DELAY

The amplitude death in coupled systems gets great concern. We investigate the stability and Hopf bifurcation at zero equilibrium point. The amplitude death region is obtained. Based on the existence of Hopf bifurcation, the nominal form method and center manifold theorem are used to determine the direction of the Hopf bifurcation and the stability of the bifurcating periodic solution. Furthermore, the existence of degenerate double Hopf bifurcation is studied. Quasi-periodicity and chaos are seen at the critical values of degenerate double Hopf bifurcation by numerical simulations. We affirm that chaos really occurs by the largest Liapunov exponent.