一类捕食系统的非负定态解及其稳定性

应用渐近展开的方法构造生物学里提出的一类具有反应扩散项的捕食者─食饵系统的非平凡非负定态解，并应用固有值的解析摄动理论对所获得的非平凡非负定态解进行了稳定性分析．

The Nonnegative Steady-State Solution and Stability of a Predator-Prey System

he existence and stability of the nontrivial and nonnegative steady-state solution of an ecological predator-prey system with the reaction-diffusion term are discussed. Based on the asymptotic expansion method, the semi-trivial and nonnegative steady-state solution bifurcated from the trivial one is obtained by taking the birth rate of the prey as a bifurcation parameter. Then the nontrivial and nonnegative steady-state solution bifurcated from the semi-trivial one is obtained by assuming the death rate of the predator to be a bifurcation parameter. The solutions in series form obtained are convergent owing to the fact that the bifurcations occur near the simple eigenvalues. All the solutions obtained are found to be stable after an analysis with the theory of the analytic perturbation of the eigenvalues is made.