Analysis of Lyapunov exponents in class of nonlinear electrical oscillator

This paper is an effort to probe into the complex dynamics behaviors of a class of nonlinear electrical oscillator described by Duffing equation. The influence on the global dynamics behaviors by the change of the parameters of Duffing equation with force excitation was investigated. The very rich and multiplex nonlinear dynamics of the Duffing equation was investigated by theoretical and numerical simulation with the tiny change of the system parameters. the periodic bubble in the bifurcation diagram, which follows the sequence of P-1→P-2→P-1. could be observed.The characteristics of chaos attractors of the systems were analyzed by the Poincare map. periodic and chaos motions under the presented parameters were demonstrated exactly by simulating the bifurcation diagrams. The chaos characteristics of the systems were analyzed by computing time series’ Lyapunov exponents and Lyapunov dimensions of Duffing equation. Routes from doubling-periodic bifurcation of periodic motion to chaos and the complex dynamics behaviors of the systems were discussed. In addition, the paper justifies the conformity of the Lyapunov exponents and Lyapunov dimensions and bifurcation diagrams of the systems. By studying the theoretical and numerical simulation, it is possible to provide reliable theory and effective numerical method for other systems. In addition, the methods and conclusions would be useful for electrical designers.