In order to investigate the impact of periodically evolving domain on the mutualism interaction of two species,we study a mutualistic model on a periodically evolving domain.To overcome the difficulty caused by the ad...In order to investigate the impact of periodically evolving domain on the mutualism interaction of two species,we study a mutualistic model on a periodically evolving domain.To overcome the difficulty caused by the advection and dilution terms,we transform the model to a reaction-difusion problem in a fixed domain.By means of eigenvalue problems,the threshold parameters are introduced.The asymptotic profiles of the solutions on an evolving domain are studied by using the threshold parameters and the upper and lower solutions method.The impact of the domain evolution rate on the persistence or extinction of species is analyzed.Numerical simulations are performed to illustrate our analytical results.展开更多
To understand the impact of environmental heterogeneity and mutualistic interaction of species, we consider a mutualistic model with cross-diffusion in a heterogeneous environ- ment. Semi-coexistence states have been ...To understand the impact of environmental heterogeneity and mutualistic interaction of species, we consider a mutualistic model with cross-diffusion in a heterogeneous environ- ment. Semi-coexistence states have been studied by using the corresponding eigenvalue problems, and sufficient conditions for the existence and non-existence of coexistence states are given. Our results show that the model possesses at least one coexistence solution if the intrinsic populations growth rates are big or free-diffusion and cross-diffusion coefficients are weak. Otherwise, the model have no coexistence solution. The true solutions are obtained by utilizing the monotone iterative schemes. In order to illustrate our analytical results, some numerical simulations are given.展开更多
基金This work was partially supported by the National Natural Science Foundation of China(11771381 and 11911540464).
文摘In order to investigate the impact of periodically evolving domain on the mutualism interaction of two species,we study a mutualistic model on a periodically evolving domain.To overcome the difficulty caused by the advection and dilution terms,we transform the model to a reaction-difusion problem in a fixed domain.By means of eigenvalue problems,the threshold parameters are introduced.The asymptotic profiles of the solutions on an evolving domain are studied by using the threshold parameters and the upper and lower solutions method.The impact of the domain evolution rate on the persistence or extinction of species is analyzed.Numerical simulations are performed to illustrate our analytical results.
基金This work was partially supported by the National Natural Science Foundation of China （11771381） and Project funded by China Postdoctoral Science Foundation.
文摘To understand the impact of environmental heterogeneity and mutualistic interaction of species, we consider a mutualistic model with cross-diffusion in a heterogeneous environ- ment. Semi-coexistence states have been studied by using the corresponding eigenvalue problems, and sufficient conditions for the existence and non-existence of coexistence states are given. Our results show that the model possesses at least one coexistence solution if the intrinsic populations growth rates are big or free-diffusion and cross-diffusion coefficients are weak. Otherwise, the model have no coexistence solution. The true solutions are obtained by utilizing the monotone iterative schemes. In order to illustrate our analytical results, some numerical simulations are given.
