【摘要】 李雅普诺夫指数在研究动力系统的分岔、混沌运动特征中起着重要的作用。该文介绍了李雅普诺夫指数的定义、计算原理及数值计算的实现方法,应用Matlab软件,编制了计算李雅普诺夫指数的程序,分析了一维、二维和三维非线性动力系统中分岔和混沌与李雅普诺夫指数之间的关系。绘制了逻辑斯蒂映射、埃农映射和洛仑兹方程的分岔图,并计算了相应的李雅普诺夫指数。实例的计算机仿真表明李雅普诺夫指数是研究分岔、混沌运动,解决工程实际问题的有效方法之一。更多还原

【Abstract】 Lyapunov’s exponents plays an important role in researching the characters of bifurcation and chaos motion of dynamics. In the paper the definition, calculation principle and the method of numerical calculation of Lyapunov exponents are introduced. The programs for calculating the Lyapunov’s exponents are compiled by the MATLAB software. The relationship between the bifurcation, chaos and Lyapunov’s exponents are analyzed in nonlinear dynamical system of one , two and three dimensions. Then as examples, the bifurcation charts for Logistic mapping, Henon mapping and Lorenz system are protracted and the Lyapunov’s exponents corresponding to these systems are calculated numerically. The examples of computer simulation indicate that Lyapunov’s exponent is one of the efficient methods for researching the bifurcation and chaos, as well as for solving the practical engineering problems.更多还原