The Study Of Hybrid Ecological Models With Intermittent Diffusion

Species dispersal is one of the most ubiquitous prevalent phenomena in nature, it is important for us to know the ecosystem and nature, there are a large number of mathe-matical models focus on the dynamical behaviors of the system with diffusion, which help us to more deeply learn the ecosystem. Based on these study, we also give some intensive research for some population dispersal problem:A class of nonautonomous almost peri-odic single species system with intermittent diffusion and time delays and analysis for a delayed predator-prey system with dissymmetric impulse dispersal between two patches.The main contents in this paper can be summarized as follows:In section1, we introduce the ecological background of our study. Then, we introduce some current research situation and some research results about the diffusion model. We give the main research system finally.In section2, we propose a class of nonautonomous almost periodic single species sys-tem with intermittent diffusion and time delays between two patches. By using Liapunov-Razumikhin type technology and comparison theorem, we obtain sufficient conditions for the permanence of the system. By constructing a suitable Liapunov functional to give the sufficient condition for the global asymptotical stability of the system. Using almost periodic functional hull theory, sufficient conditions on the existence, uniqueness and glob-ally asymptotical stability for an almost periodic solution of this system are established. Finally, numerical simulations are presented to illustrate our theoretical results.In section3, we study a delayed predator-prey system with dissymmetric impulse dispersal between two patches, by using a comparison theorem of impulsive differential equation and some analysis skills, the sufficient conditions ensuring the global attrac-tivity of predator-extinction positive periodic solution and the permanence of a delayed predator-prey system with dissymmetric impulse dispersal are established. In section4, we have a summary.