Effect Of Population Behavior On The Spatiotemporal Dynamics Of A Modified Leslie-gower Predator-prey System

Population dynamics has been one of the current research hotpots in theecological field. Many scholars at home and abroad have paid more and moreattention on the predator-prey due to its wide real existence of the predator-preyinteraction in nature and great practical value in society and economics.This paper mainly studies the influence of population behavior on thespatiotemporal dynamics of a modified Leslie-Gower predator-prey model withdiffusion. In section1, the research background and research situation of theLeslie-Gower predator-prey are introduced and the commonly used comparisontheorems are also presented. In section2, the dynamics of a diffusivepredator-prey with modified Leslie-Gower and Holling type IV schemes areconsidered analytically and numerically. Mathematical theoretical works havebeen pursuing the existence of global solutions, positive steady solutions andtraveling wave solutions, as well as the stability of equilibrium points andpopulation persistence, which in turn display the critical expression of somecritical parameters. Numerical simulations indicate that the system has atraveling wave solution, which further confirms the feasibility of theoreticalresults. In section3, the spatiotemporal dynamics of a diffusive Leslie-Gowerpredator-prey model with prey refuge are investigated analytically andnumerically. Mathematical theoretical works have considered the stability ofequilibrium points, which depict the threshold expression of some criticalparameters. Numerical simulations are performed to explore the patternformation of species. In section4, a diffusive predator-prey system with preyrefuge is studied analytically and numerically. The Turing bifurcation isanalyzed in detail, which in turn provides a theoretical basis for the numericalsimulation. The influence of prey refuge and group defense on the equilibriumdensity and patterns of species under the condition of Turing instability isexplored by numerical simulations and this shows that the prey refuge and group defense have a important effect on the equilibrium density and patterns ofspecies. Moreover, it can be obtained that the distributions of species are moresensitive to group defense than prey refuge. All these results are expected to beof significance in the exploration of the dynamical richness and complexity ofecosystems. Finally, we summarizes the full text, and points out the researchdirection in the future.