文件包括非线性方程数值计算时常用的lyapunov程序，以duffing方程为例，进行程序计算，可以稍微修改，计算其他方程。(The file includes the Lyapunov program commonly used in the numerical calculation of nonlinear equations. Taking Duffing equation as an example, the program can be modified slightly to calculate other equations.)