Chaos Controlling in a Class of Nonlinear Electrical Oscillator

This paper probed into the complex dynamics behaviors of a class of nonlinear electrical oscillator described by Duffing equation.We investigated the influence on the global dynamics behaviors by the change of the parameters of Duffing equation with force excitation.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 characteristics of chaos attractors of the systems were illustrated on the Poincare maps.By simulating the bifurcation diagrams,we demonstrated exactly periodic and chaos motions under the presented parameters.By computing time series′ Lyapunov exponents and Lyapunov dimensions of Duffing equation,we analyzed the chaos characteristics of the systems.Routes from doubling-periodic bifurcation of periodic motion to chaos and the complex dynamics behaviors of the systems were discussed.In addition,the paper proved the conformity of the Lyapunov exponents and Lyapunov dimensions and bifurcation diagrams of the systems.By selecting proper controlling parameters according to bifurcation graph,the chaotic motions of the system can be successfully converted to the stable periodic orbits under two kinds of feedback control methods.