带有避难项的扩散捕食模型的稳定性及Hopf分岔

Stability and Hopf Bifurcation for a Diffusive Predator-Prey Model with Refuge

探讨了一类在齐次留曼边界条件下带有避难项的扩散捕食模型的稳定性及Hopf分岔,其避难项给食饵提供了避难保护.证明了当避难常数充分小时,正常数解是全局渐近稳定的;当避难常数在某两正常数之间时,半零解是全局渐近稳定的.进一步证明了该系统有周期解分支.

A diffusive predator-prey model is considered with a constant prey refuge which provides a condition for protecting of prey from predation under homogeneous Neumann boundary condition. The stability of equilibrium points and Hopf bifurcation are investigated. It is obtained that the positive constant solution is globally asymptotically stable when the constant refuge is sufficiently small and the semi-trivial equilibrium point is globally asymptotically stable when the constant refuge is between two positive constants. Furthermore, it is proved that this system has the periodic bifurcation.