In this paper, we consider a discrete Lotka-Volterra competitive system with the effect of toxic substances and feedback controls. By using the method of discrete Lyapunov function and by developing a new analysis tec...In this paper, we consider a discrete Lotka-Volterra competitive system with the effect of toxic substances and feedback controls. By using the method of discrete Lyapunov function and by developing a new analysis technique, we obtain the sufficient conditions which guarantee that one of the two species will be driven to extinction while the other will be permanent. We improve the corresponding results of Li and Chen [Extinction in two-dimensional discrete Lotka Volterra competitive system with the effect of toxic substances, Dynam. Contin. Discrete Impuls. Syst. Ser. B Appl. Algorithms 15 （2008） 165-178]. Also, an example together with their numerical simulations shows the feasibility of our main results. It is shown that toxic substances and feedback control variables play an important role in the dynamics of the system.展开更多
We propose a modified discrete-time Leslie-Gower competition system of two popula- tions to study competition outcomes. Depending on the magnitude of a particular model parameter that measures intraspecific competitio...We propose a modified discrete-time Leslie-Gower competition system of two popula- tions to study competition outcomes. Depending on the magnitude of a particular model parameter that measures intraspecific competition between individuals within the same population, either one or both populations may be subject to Allee effects. The resulting system can have up to four coexisting steady states. Using the theory of planar compet- itive maps, it is shown that the model has only equilibrium dynamics. The competition outcomes then depend not only on the parameter regimes but may also depend on the initial population distributions.展开更多
基金The authors would like to thank the editor and the reviewers for their construcrive comments and suggestions which improved the quality of the paper. This work was supported by the National Natural Science Foundation of China under Grant 11401274, the National Natural Science Foundation of Fujian Province （2013J01010） and the Program for Science and Technology Development Foundation of Fuzhou University （2014-XQ-28）.
文摘In this paper, we consider a discrete Lotka-Volterra competitive system with the effect of toxic substances and feedback controls. By using the method of discrete Lyapunov function and by developing a new analysis technique, we obtain the sufficient conditions which guarantee that one of the two species will be driven to extinction while the other will be permanent. We improve the corresponding results of Li and Chen [Extinction in two-dimensional discrete Lotka Volterra competitive system with the effect of toxic substances, Dynam. Contin. Discrete Impuls. Syst. Ser. B Appl. Algorithms 15 （2008） 165-178]. Also, an example together with their numerical simulations shows the feasibility of our main results. It is shown that toxic substances and feedback control variables play an important role in the dynamics of the system.
文摘We propose a modified discrete-time Leslie-Gower competition system of two popula- tions to study competition outcomes. Depending on the magnitude of a particular model parameter that measures intraspecific competition between individuals within the same population, either one or both populations may be subject to Allee effects. The resulting system can have up to four coexisting steady states. Using the theory of planar compet- itive maps, it is shown that the model has only equilibrium dynamics. The competition outcomes then depend not only on the parameter regimes but may also depend on the initial population distributions.
