一类平面和空间非线性自治系统的定性分析

The Qualitaliva Analyze of a Sort of Plane and Space Nonlinearity of Autonomous System

讨论一类平面和空间非线性自治系统的定性性质。首先证明关于两种群的Holling-Tanner模型如设其正平衡点为B,则当div(P,Q)|_B≤0时,相应的系统不存在闭轨;当div(P,Q)|_B>0,相应的系统在其平衡点B外围存在唯一稳定极限环。其次,我们较详细地讨论了一类空间非线性自治系统周期解的问题。

We in the article, discuss the qualitativa analyst of a sont of plane and space and space nonlinearty of autonomous system. First we prove about two kinds of Holling-Tanner model Assume it's positive equilibrium point being B, then when div(P,Q)\ B^0, system does not exist closed loop, then when div(P,Q)\ /,>0, the system exists the unique stable limit cycle in about Secondly, we detailed discuss the question about the periodic (al) solution of a sont of space nonlinearity autonomous system.