Subject to the homogeneous Neumann boundary condition, a ratio-dependent predator-prey reaction diffusion model is discussed. An improved result for the model is derived, that is, the unique positive constant steady s...Subject to the homogeneous Neumann boundary condition, a ratio-dependent predator-prey reaction diffusion model is discussed. An improved result for the model is derived, that is, the unique positive constant steady state is the global stability. This is done using the comparison principle and establishing iteration schemes involving positive solutions supremum and infimum. The result indicates that the two species will ultimately distribute homogeneously in space. In fact, the comparison argument and iteration technique to be used in this paper can be applied to some other models. This method deals with the not-existence of a non-constant positive steady state for some reaction diffusion systems, which is rather simple but sufficiently effective.展开更多
In order to enhance the efficiency of spectrum utilization and reduce communication overhead in spectrum sharing process, we propose a two-stage dynamic spectrum sharing scheme in which cooperative and noncooperative ...In order to enhance the efficiency of spectrum utilization and reduce communication overhead in spectrum sharing process, we propose a two-stage dynamic spectrum sharing scheme in which cooperative and noncooperative modes are analyzed in both stages. In particular, the existence and the uniqueness of Nash Equilibrium(NE) strategies for noncooperative mode are proved. In addition, a distributed iterative algorithm is proposed to obtain the optimal solutions of the scheme. Simulation studies are carried out to show the performance comparison between two modes as well as the system revenue improvement of the proposed scheme compared with a conventional scheme without a virtual price control factor.展开更多
This paper investigates the maximal and minimal solutions of initial value problem for n-th order nonlinear integro-differential equations of Volterra type on an infinite interval in a Banach space by establishing a c...This paper investigates the maximal and minimal solutions of initial value problem for n-th order nonlinear integro-differential equations of Volterra type on an infinite interval in a Banach space by establishing a comparison result and using the monotone iterative technique.展开更多
文摘Subject to the homogeneous Neumann boundary condition, a ratio-dependent predator-prey reaction diffusion model is discussed. An improved result for the model is derived, that is, the unique positive constant steady state is the global stability. This is done using the comparison principle and establishing iteration schemes involving positive solutions supremum and infimum. The result indicates that the two species will ultimately distribute homogeneously in space. In fact, the comparison argument and iteration technique to be used in this paper can be applied to some other models. This method deals with the not-existence of a non-constant positive steady state for some reaction diffusion systems, which is rather simple but sufficiently effective.
基金supported in part by the National Natural Science Foundation of China(61471115)the National Science and Technology Major Project of the Ministry of Science and Technology of China(2014ZX03003010-002)+1 种基金the General Program of Natural Science Foundation of Jiangsu Province(BK20131299)the 2016 Science and Technology joint research and innovation foundation of Jiangsu province(SBY2016020323)
文摘In order to enhance the efficiency of spectrum utilization and reduce communication overhead in spectrum sharing process, we propose a two-stage dynamic spectrum sharing scheme in which cooperative and noncooperative modes are analyzed in both stages. In particular, the existence and the uniqueness of Nash Equilibrium(NE) strategies for noncooperative mode are proved. In addition, a distributed iterative algorithm is proposed to obtain the optimal solutions of the scheme. Simulation studies are carried out to show the performance comparison between two modes as well as the system revenue improvement of the proposed scheme compared with a conventional scheme without a virtual price control factor.
文摘This paper investigates the maximal and minimal solutions of initial value problem for n-th order nonlinear integro-differential equations of Volterra type on an infinite interval in a Banach space by establishing a comparison result and using the monotone iterative technique.
