This paper considers the combined effects of the nonlinear intra-specific regulation and maturation delays on the two-species competition model. Dynamical behaviors of the model are studied, and sharp global asymptoti...This paper considers the combined effects of the nonlinear intra-specific regulation and maturation delays on the two-species competition model. Dynamical behaviors of the model are studied, and sharp global asymptotical stability criteria for the coexistence equilibrium as well as the excluding equilibria are established. It is shown that increase of the maturation delay of one species has negative effect on its permanence and a sufficiently large maturation delay will directly lead to its extinction, and that variation of the intra-specific regulation parameter of one species may change the surviving or extinction behaviors of its competitor.展开更多
In this paper,we focus on the dynamic behaviors of the bistability for a two-species Lotka–Volterra competition model with stage structure.Using the theory of generalized saddle-point behaviors,it is shown that there...In this paper,we focus on the dynamic behaviors of the bistability for a two-species Lotka–Volterra competition model with stage structure.Using the theory of generalized saddle-point behaviors,it is shown that there exists a C1-separatrixΓon its state space such that Species 2 wins the competition whenever the initial distribution is aboveΓ,while Species 1 wins the competition whenever the initial distribution is belowΓ.Combining with the previous conclusions of the system,we give a complete classification for global competitive dynamics.Furthermore,we carefully analyze the changes of the competition outcome after introducing the stage structure.Finally,some numerical simulations are provided to illustrate the effectiveness of the theoretical results.展开更多
文摘This paper considers the combined effects of the nonlinear intra-specific regulation and maturation delays on the two-species competition model. Dynamical behaviors of the model are studied, and sharp global asymptotical stability criteria for the coexistence equilibrium as well as the excluding equilibria are established. It is shown that increase of the maturation delay of one species has negative effect on its permanence and a sufficiently large maturation delay will directly lead to its extinction, and that variation of the intra-specific regulation parameter of one species may change the surviving or extinction behaviors of its competitor.
基金This research was partially supported by tlie National Natural Science Foundation of China(11871231,11,526095).
文摘In this paper,we focus on the dynamic behaviors of the bistability for a two-species Lotka–Volterra competition model with stage structure.Using the theory of generalized saddle-point behaviors,it is shown that there exists a C1-separatrixΓon its state space such that Species 2 wins the competition whenever the initial distribution is aboveΓ,while Species 1 wins the competition whenever the initial distribution is belowΓ.Combining with the previous conclusions of the system,we give a complete classification for global competitive dynamics.Furthermore,we carefully analyze the changes of the competition outcome after introducing the stage structure.Finally,some numerical simulations are provided to illustrate the effectiveness of the theoretical results.
