给出了判定微分动力系统平衡点类型的一种方法.该方法通过Dulac 函数将平衡点类型的判定转化为多项式方程组实根求解,后者可由符号计算来完成.通过结合Bendixson-Dulac定理、积分因子法、李雅普诺夫方法,给出最终判定结论.

In this paper, a new method for determining the type of equilibrium point of differential dynamical systems is given. This method by Dulac function translates the problem into solving the real roots of polynomial equations, which can be done by symbolic computation. By playing other criterions like the Bendixson-Dulac theorem, integral-factor method and Lyapunov method, we draw the final conclusion.