非线性微分系统的反射函数与周期解

Reflective Function and Periodic Solution of Nonlinear System

非线性微分系统解的几何性态在理论和应用中有着重要意义.利用反射函数理论,研究非线性微分系统具有满足特定关系式的反射函数的充要条件,并应用所得结论讨论周期非线性微分系统周期解的几何性态,建立该系统周期解存在及稳定的判定定理.所得结果为进一步解释一些物体的复杂运动规律,提供了新的理论依据和新的判定准则.

The geometric property of solution for the nonlinear system playes an important role in both theory and application. By using the reflective function theory, we discuss the necessay and sufficient conditions for the existence of reflective functions satisfying the special relation of nonlinear system. By applying the results we study the geometric property of the periodic solution for the periodic nonlinear system, and set up the decision theorems of the existence of the periodic solution and stability for the nonlinear system. All these resuhs provide some new theoretical basis and criteria for explaining the complicated law of motion of objects.