This paper reports the global asymptotic stability of a three-species predator-prey system involving the prey-taxis. With the assumptions, we establish the global asymptotic stability results of its equilibria, respec...This paper reports the global asymptotic stability of a three-species predator-prey system involving the prey-taxis. With the assumptions, we establish the global asymptotic stability results of its equilibria, respectively. Our results illustrate that 1) the global asymptotic stability of the semi-trivial equilibrium does not involve the prey-taxis coefficients χ, ξ;2) the global asymptotic stability of two boundary equilibria relies on a single prey-taxis coefficient χ and ξ, respectively;3) the global asymptotic stability of the unique positive equilibrium depends on two prey-taxis coefficients χ and ξ.展开更多
In this paper the author investigates the following predator-prey model with prey-taxis and rotational?ux terms■in a bounded domain with smooth boundary.He presents the global existence of generalized solutions to th...In this paper the author investigates the following predator-prey model with prey-taxis and rotational?ux terms■in a bounded domain with smooth boundary.He presents the global existence of generalized solutions to the model■in any dimension.展开更多
In this paper,we study a diffusive predator-prey model with hyperbolic mortality and prey-taxis under homogeneous Neumann boundary condition.We first analyze the influence of prey-taxis on the local stability of const...In this paper,we study a diffusive predator-prey model with hyperbolic mortality and prey-taxis under homogeneous Neumann boundary condition.We first analyze the influence of prey-taxis on the local stability of constant equilibria.It turns out that prey-taxis has influence on the stability of the unique positive constant equilibrium,but has no influence on the stability of the trivial equilibrium and the semi-trivial equilibrium.We then derive Hopf bifurcation and steady state bifurcation related to prey-taxis,which imply that the prey-taxis plays an important role in the dynamics.展开更多
文摘This paper reports the global asymptotic stability of a three-species predator-prey system involving the prey-taxis. With the assumptions, we establish the global asymptotic stability results of its equilibria, respectively. Our results illustrate that 1) the global asymptotic stability of the semi-trivial equilibrium does not involve the prey-taxis coefficients χ, ξ;2) the global asymptotic stability of two boundary equilibria relies on a single prey-taxis coefficient χ and ξ, respectively;3) the global asymptotic stability of the unique positive equilibrium depends on two prey-taxis coefficients χ and ξ.
基金supported by the National Natural Science Foundation of China(Nos.12001214,12231008)the Fundamental Research Funds for the Central Universities(No.3004011139)。
文摘In this paper the author investigates the following predator-prey model with prey-taxis and rotational?ux terms■in a bounded domain with smooth boundary.He presents the global existence of generalized solutions to the model■in any dimension.
基金supported by the Natural Science Foundation of Shandong Province,China(Nos.ZR2021MA028 and ZR2021MA025).
文摘In this paper,we study a diffusive predator-prey model with hyperbolic mortality and prey-taxis under homogeneous Neumann boundary condition.We first analyze the influence of prey-taxis on the local stability of constant equilibria.It turns out that prey-taxis has influence on the stability of the unique positive constant equilibrium,but has no influence on the stability of the trivial equilibrium and the semi-trivial equilibrium.We then derive Hopf bifurcation and steady state bifurcation related to prey-taxis,which imply that the prey-taxis plays an important role in the dynamics.
