Wave Analysis of a Diffusive Modified Leslie-Gower Predator-prey System with Holling Type IV Schemes

A diffusive predator-prey model with modified Leslie-Gower and Holling type IV schemes is investigated analytically and numerically. Mathematical theoretical works mainly focus on the existence of traveling wave solutions. Numerical simulations are performed to confirm the feasibility of traveling wave solutions. All these results are significant in exploration of the dynamic complexity of ecosystems. Introduction Predator-prey interactions have attracted considerable attention in mathematical biology. In the classical Lotka-Volterra predator-prey models, the growth rate of population is assumed to be proportional to its size. However, Leslie and Gower [1,2] initiated a predator-prey model where the carrying capacity of predator is proportional to the number of prey. Recently, the non-monotonic Holling type IV functional response has been widely used to describe the process of predation with self-selection and the inhibitory effect of prey [3,4,5]. On the other hand, all organisms interact with each other in a limited space. Meanwhile, the spatial value has been regarded as a pivotal role on how ecological communities are shaped [6,7,8]. From above, we can study the following equations: