Effects of depth potential on the dynamics of Duffing system and chaos control: numerical and electronic implementation

Abstract

Numerical and experimental results concerning the control of chaos in the double-well Duffing system with one external force are presented in this paper. Lyapunov exponent is used as the identifier of chaos in the nonlinear system. As the expression of the potential function depends on the damping coefficient, it is found that the depth of the potential well increases with damping. Thus, this paper presents a physical insight into control damping (or coefficient of damping of a system) to quench, and also to prevent chaotic situations, which are considered disturbances and are harmful for operations. It is found that when the depth of the double-well potential increases, it becomes more difficult for the state to switch from one equilibrium to other, and thus, the chaos is suppressed. The new feedback control method based on damping coefficient and Lyapunov exponent is proposed. The experimental investigation using electronic components shows that the results obtained are similar to those observed from numerical investigation.