一类含参数的二维非线性系统的全局稳定性研究

Study on Global Stability of a Class of Two-Dimensional Nonlinear Systems with Parameters

应用常微分定性理论,研究一类含参数的二维非线性系统的全局稳定性。首先分析系统随参数变化,其平衡点的个数和类型以及在平衡点处的稳定性发生什么样的改变,再研究该系统极限环的存在性、个数问题、稳定性及其位置,其次讨论了系统在无穷远点处的轨线情况,最后得到系统的全局相图。

The global stability of a class of two-dimensional nonlinear systems with parameters is studied by using the ordinary differential qualitative theory. Firstly, the variation of the system with param-eters is analyzed, the number and type of the equilibrium point and the stability at the equilibrium point of the system are analyzed. Then the existence, number, stability and position of limit cycles of the system are studied. Secondly, the trajectory of the system at infinity is discussed and the global phase diagram is obtained.