Dynamics Of Multi-species Competitive Systems

The multi-species competition model plays an important role in the development of differential equations and is widely used in the biological field.In this paper,we study the dynamics of the competitive reaction-diffusion system.First,the initial boundary value problem of the three-species competition reaction diffusion with Nemann boundary conditions is considered,and it is proved that the coexistence equilibrium point is locally asymptotically stable in the case of weak competition and unstable in the case of strong competition.Next,in actual problems,there are some complex spatiotemporal phenomena in competing populations.In order to better reveal this phenomenon,we next consider the effects of non-local intra-species competition.The scale of the region is the branch parameter.The stability of the positive equilibrium solution,the existence of Hopf branch and the Turing branch and the nature of the branch are studied.Further,the non-local expansion from intra-species competition to inter-species competition,considering the non-local terms with convolution integral of overall density and kernel function,found the same results as the local diffusion competition model.The above results indicate that the Hopf branch is more likely to appear in a non-local diffusion competition model.Finally,we demonstrate these results using numerical simulations.