Dynamical Analysis and Chaos Control of a Driven System with One Cubic Nonlinearity: Numerical and Experimental Investigations
The dynamics of a non-autonomous chaotic system with one cubic nonlinearity is studied through numerical and experimental investigations in this paper. A method for calculating Lyapunov exponents (LEs), Lyapunov dimension (LD) from time series is presented. Furthermore, some complex dynamic behaviors such as periodic, quasi-periodic motion and chaos which occurred in the system are analyzed, and a route to chaos, phase portraits, Poincare sections, bifurcation diagrams are observed. Finally, a first order differential controller for the non-autonomous system is designed. Also some dynamics such as Poincare sections, bifurcation diagrams for specific control parameter values of the controlled system are showed using numerical and experimental simulations.
Z. Wang et al., "Dynamical Analysis and Chaos Control of a Driven System with One Cubic Nonlinearity: Numerical and Experimental Investigations", Advanced Materials Research, Vol. 486, pp. 204-210, 2012