In this paper, we consider a diffusive plant-herbivore system with the toxin-determined functional response and subject to the homogeneous Neumann boundary conditions on the bounded one-dimensional spatial domain. The...In this paper, we consider a diffusive plant-herbivore system with the toxin-determined functional response and subject to the homogeneous Neumann boundary conditions on the bounded one-dimensional spatial domain. The impacts of diffusion on the dynamical behaviors are investigated and it is found that although the appearance of diffusion does not affect the stability of constant steady states, it can lead to the occurrence of Hopf bifurcation of spatially inhomogeneous periodic solutions at the constant positive steady state. The conclusions show that the occurrence of spatial diffusion can induce more complex dynamical behaviors.展开更多
This paper is concerned with optimal harvesting control of a first order partial differential equation system representing a nonlinear n-dimensional competitive population model with age-structure. By the Ekeland＇s v...This paper is concerned with optimal harvesting control of a first order partial differential equation system representing a nonlinear n-dimensional competitive population model with age-structure. By the Ekeland＇s variational principle, the existence and unique char- acterization of the optimal control strategy are established. The optimality conditions for the control problem are obtained by the concept of the normal cone.展开更多
By the techniques of comparison argument and Lyapunov-like functionals, some criteria about persistence and extinction of the species are obtained. And then, with the help of constructing Lyapunov functionals and some...By the techniques of comparison argument and Lyapunov-like functionals, some criteria about persistence and extinction of the species are obtained. And then, with the help of constructing Lyapunov functionals and some new analysis method, sufficient conditions, provided with the form of average value of a function, to guarantee the stability of the system are derived. Finally, some examples together with their numerical simulations show the feasibility of these main results. Our conclusions are different from many existing forms for nonlinear competitive systems.展开更多
基金Acknowledgments The first author was supported by the Natural Science Foundation of Gansu Province （1212RJZA065）. The second author was supported by the National Natural Science Foundation of China （11261028） and Gansu Province National Natural Science Foundation （145RJZA216） and China Scholarship Council.
文摘In this paper, we consider a diffusive plant-herbivore system with the toxin-determined functional response and subject to the homogeneous Neumann boundary conditions on the bounded one-dimensional spatial domain. The impacts of diffusion on the dynamical behaviors are investigated and it is found that although the appearance of diffusion does not affect the stability of constant steady states, it can lead to the occurrence of Hopf bifurcation of spatially inhomogeneous periodic solutions at the constant positive steady state. The conclusions show that the occurrence of spatial diffusion can induce more complex dynamical behaviors.
文摘This paper is concerned with optimal harvesting control of a first order partial differential equation system representing a nonlinear n-dimensional competitive population model with age-structure. By the Ekeland＇s variational principle, the existence and unique char- acterization of the optimal control strategy are established. The optimality conditions for the control problem are obtained by the concept of the normal cone.
文摘By the techniques of comparison argument and Lyapunov-like functionals, some criteria about persistence and extinction of the species are obtained. And then, with the help of constructing Lyapunov functionals and some new analysis method, sufficient conditions, provided with the form of average value of a function, to guarantee the stability of the system are derived. Finally, some examples together with their numerical simulations show the feasibility of these main results. Our conclusions are different from many existing forms for nonlinear competitive systems.
