摘要
In this paper,we study a difusive toxic-phytoplankton-zooplankton model with prey-taxis under Neumann boundary condition.By analyzing the characteristic equation,we discuss the local stability of the positive constant solutions and show the repulsive prey-taxis is the key factor that destabilizes the solutions.By means of the abstract bifurcation theorem,we investigate the existence of non-constant positive steady-state solutions bifurcating from the constant coexistence equilibrium.Furthermore,we obtain the criterion for the stability of the branching solutions near the bifurcation point.Numerical simulations support our theoretical results,together with some interesting phenomena,stable heterogeneous periodic solutions emerge when prey-tactic sensitivity coefficient is well below the critical value,and zooplankton populations present extinction and continued transitions as habitat size increases.
基金
supported by the National Natural Science Foundation of China(No.12171193)
the project of the Distinguished Professor of colleges and universities of Henan province in 2019 and Project of Foreign expert in Henan(HNGD2023074)
the Natural Science Foundation of Henan(No.232300420127)
the Science and Technology Key Project of Henan Province of China(No.222102110028).
