摘要：

In this talk, I will report our recent works on the dynamics of the two-coupled reaction-diffusion Lengyel-Epstein system incorporating distributed-delay couplings in activators. For one hand, we are mainly concerned with the existence and stability of the non-constant steady state solutions for the one-layered diffusive Lengyel-Epsteinsystem. It is found that as the system parameter changes, the stability of the nonconstant steady state solutions of the one-layered system changes. This leads to the emergence of the periodic solutions via Hopf bifurcations. On the other hand, we are interested in studying Turing instability of the symmertric non-constant steady state solutions driven by inter-reactor diffusions.