二维Lotka-Volterra系统正周期解的全局稳定性

The Whole Stability of the Positive Periodic Solution to Two Dimensional Lotka-Volterra Systems

研究了时变条件下二维Lotka-Voltrra系统,对于具有周期系数的二维非自治Lotka-Voltrra系统,在其系数连续的情况下,得到了正周期解全局稳定的一个充分条件,为进一步研究Lotka-Voltrra系统解的性质提供了理论依据.同时利用构造Liapunov函数的方法对所得的结论进行了证明.

Two dimensional time-varying Lotka-Volterra systems are studied. We obtain a sufficient condition of the whole stability of the positive periodic solution to two dimensional non-autonomous Lotka - Volterra systems which have periodic coefficients and they are continuous, and provide a theoretic foundation to make further studying on the nature of the solution of Lotka-Volterra systems. At the same time, we prove the conclusion through constructing a Liapunov function.