报告题目：The diffusion-driven instability and complexity for a single-handed discrete Fisher equation
内容摘要：It seems to be a necessary condition that the diffusion coefficient of the inhibitor must be larger than that of the activator when the Turing instability is considered. However, the diffusion-driven instability/Turing instability for a single-handed discrete Fisher equation with the Neumann boundary conditions may occur and a series of 2-periodic patterns have be observed. Motivated by these pattern formations, the existence of 2-periodic solutions is also established by using the inverse function theorem. Naturally, the periodic double and the chaos phenomenon should be considered. To this end, a simplest two elements system will be further discussed, the flip bifurcation theorem will be obtained by computing the center manifold, and the bifurcation diagrams will be simulated by using the shooting method. Thus, the Turing instability and the complexity of dynamical behaviors can be completely driven by the diffusion term. Additionally, those effective methods of numerical simulations are also valid for experiments of other patterns, thus, are beneficial for some application scientists.