一类具有S型功能性反应系统的稳定性

The Stability for a Class of Systems with S-type Functional Response

考虑S型功能性反应模型的捕食-被捕食系统的动力性态,应用规范形理论和平面系统的定性理论研究了生物模型的定性性质,得到了平衡点在各种不同参数下的局部性质;在不同的参数下,它们可以为鞍点、稳定结点、鞍-结点、不稳定结点、弱中心等;利用计算第一系数的方法,研究了弱中心附近的超临界Hopf分岔,并在弱中心附近分支出唯一的极限环.

This paper considers the dynamitic property of predator-prey system of S-type functional response model,uses normal form theory and qualitative theory of planner system to study the qualitative property of biological model,obtains local property of the balanced point under all kinds of parameters,indicates that under different parameters,they can be saddle point,stable node,saddle-node,unstable node,weak center and so on,uses the method to calculate the first coefficient to study the supercritical Hopf bifurcation near weak center and branches an only limit loop near the weak center.