一类具有捕食者与食饵依赖功能性反应的种群模型的全局稳定性

Global Stability for A Population Model with Predator-Prey-Dependent Functional Response

本文研究了一类具有Neumann边界条件的捕食者与食饵依赖模型.通过构造新的Lyapunov函数,得到了保证系统的唯一正平衡点是全局渐近稳定的充分条件.该充分条件比前人得到的条件更弱,更简洁.所得结论表明构造一个适当的Lyapunov函数对证明全局渐近稳定性是至关重要的.

A predator-prey-dependent model with reaction-diffusion and Neumann boundary conditions is reconsidered in this paper.By constructing a new Lyapunov function,sufficient condition which ensures the global asymptotical stability of the unique positive equilibrium of the system is obtained.It is shown that our condition is weaker and simpler than the earlier one given in earlier paper.Therefore,constructing a suitable Lyapunov function is crucial to prove global asymptotic stability result.