Chaos detection and control of a fractional piecewise-smooth system with nonlinear damping

Chaotic response is a robust effect in natural systems, and it is usually unfavorable for applications owing to uncertainty. In this paper, we propose several control strategies to stabilize the chaotic rhythm of a fractional piecewise-smooth oscillator. First, the Melnikov analysis is applied to the system, and the critical condition for the occurrence of homoclinic chaos is scrupulously established. Then, by applying appropriate control mechanisms, including delayed feedback control and periodic excitations, to the system, we can eliminate the zeros in the original Melnikov function, which serve as sufficient criteria for chaos suppression. Numerical simulations further demonstrate the accuracy of the theoretical results and the validity of the control schemes. Finally, the effects of parameter variations on the efficiency of control strategies are investigated. Note that we use the complex Simpson formula to calculate the complicated Melnikov functions presented in this paper. The current work may open a new innovative path to detect and control the chaotic dynamics of fractional non-smooth models.