Chaos and Hopf Bifurcation Analysis of the Delayed Local Lengyel-Epstein System - Qingsong Liu; Yiping Lin; Jingnan Cao; Jinde Cao (Discrete Dynamics in Nature and Society)
The local reaction-diffusion Lengyel-Epstein system with delay is investigated. By choosing τ as bifurcating parameter, we show that Hopf bifurcations occur when time delay crosses a critical value. Moreover, we derive the equation describing the flow on the center manifold; then we give the formula for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions. Finally, numerical simulations are performed to support the analytical results and the chaotic behaviors are observed.