Double Hopf bifurcation in a bidirectionally linearly coupled identical Ikeda model with time delay

【摘要】：In this paper, we consider a coupled Ikeda system with a single delay. By regarding the time delay τ and laser intensity m as the bifurcation parameters, some non-resonant double Hopf bifurcation point is discovered. The dynamical equations on the center manifold are obtained by the center manifold theory. Then, the normal form for the non-resonant double Hopf bifurcation is deduced by the normal form method. The local dynamical behaviors near the double Hopf bifurcation point are also classified in details. Finally, numerical simulations supporting our theoretical results are also presented.