Propagation Dynamics Of A Nonlocal Diffusion Cooperative Irreducible System With Shifting Habitats

In recent years,nonlocal diffusion equations have attracted great interests in fields such as epidemiology,population dynamics,and materials science.Compared to classical random diffusion,nonlocal diffusion operators have prominent advantages in characterizing nonlocal spatial structures.The main dynamic problems of nonlocal diffusion equations are traveling wave solutions and asymptotic spreading speeds.In addition,a special type of heterogeneous environment has emerged in the study of population dynamics under the background of climate change,namely the shifting environment,which is characterized by equation coefficients depending on spatiotemporal variables in the form of a moving coordinate.To study the effects of shifting habitats on the survival of species,this thesis investigates the propagation dynamics of a nonlocal diffusion cooperative irreducible system with shifting habitats.Firstly,we considered the forced traveling waves of a nonlocal cooperative irreducible system with shifting habitats.By constructing suitable upper and lower solutions and applying the fixed point theorem,a nondecreasing forced waves connecting(0,0)and positive equilibrium point(u1*,u2*)is obtained for the system.For the aforementioned nondecreasing forced waves,it is proved to be unique by the sliding method.Additionally,using the dynamical system method,the specific discussion is carried out by defining relevant operators and semiflows,then by upper and lower solutions and comparison principle,we proved that the forced waves are globally asymptotically stable.Secondly,we studied the asymptotic spreading speed of the above system.Applying the theory of monotone semiflows and by studying the spreading properties of the upper and lower control systems,it was proved that there exists a critical speed c*,which depends on the diffusion ability and maximum linear growth rate of the species.It was ultimately concluded that the species will persist when the speed of the shifting habitat edge c<c*,while the species will eventually become extinct when the speed of the shifting habitat edge c>c*.Finally,specific applications and numerical simulations are presented.By studying a nonlocal diffusion fecal-oral transmission model with Holling-Ⅱ growth and a nonlocal diffusion two-species cooperative model with Logistic growth,the above results are specifically illustrated.The results of forced waves and asymptotic spreading speed for these two models are obtained,and more intuitive demonstrations are carried out through numerical simulations.