Locally asymptotic stability of 2-dimension nonlinear analytic dynamic systems in critical cases
二维非线性临界解析动态系统的局部渐近稳定性

The locally asymptotic stability of a 2-dimension nonlinear analytic dynamic system with a pair of conjugated imaginary eigenvalues is studied. The system is firstly simplified to a standard form by using the non-singular linear coordinate transformation and the time scale transformation. Next, based on the idea of formal progression, a method is developed to determine the Lyapunov function for this standard form by constructing several sets of linear equations. Finally, a sufficient condition of locally asymptotic stability for the system is obtained. The validity is shown by two examples at the end of this paper.