Research and Simulation of Lyapunov's Exponents
Dong Qing-tian · Jisuanji fangzhen · 2005
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.