具Ⅱ型Hlling功能性反应捕食系统解的性质

Behaviors of solutions to a predate-prey model with Hlling type Ⅱ functional response

研究一个齐次Neumann边界条件弱耦合的反应扩散系统.利用Lyapunov函数及局部稳定性给出了正常数解全局渐近稳定的充分条件,并由此说明,只要食饵的出生率足够大、或者捕食者的捕获率足够小、或者捕食者的内部竞争充分强,正常数解就是全局渐近稳定的.另外,还证明了只要一个物种的扩散率足够大,则稳态系统不存在非常数解.

The weakly coupled reaction-diffusion system with homogeneous Neumann boundary conditions is studied in this paper. A sufficient condition for the global asymptotical stability is given by Lyapunov function and the local asymptotical stability. It is revealed that if the intrinsic growth rate of prey is fast, or the capturing rate of predator is slow, or the intra-specific competition of predator is strong enough, the positive constant solution is globally asymptotically stable. It is also shows that the steady state has no non-constant positive solution if one of the diffusion rates is large enough.