Dynamics and Robust Synchronization of an Oscillator With Cubic and Signum Terms

In recent years, there has been a marked surge in research focused on nonlinear oscillators. Among these, a particular emphasis has been placed on a class of oscillators distinguished by their concealed attractors, drawing considerable attention due to their unique characteristics. This paper delves into the exploration of an elegant oscillator belonging to this distinctive class. Despite comprising five terms and lacking equilibrium points, this oscillator displays remarkably intricate dynamics. The study covers various aspects such as chaos, hidden attractors, offset boosting, and notably, different strange attractors exhibited by this oscillator. Additionally, approaches involving synchronization for such oscillators are introduced. Apart from the presentation of the novel chaotic oscillator, the synchronization of a nominal and uncertain chaotic system is evinced by the sliding mode technique (super-twisting algorithm) in the first case, and a robust controller is synthesized, respectively. The appropriate Lyapunov functions are implemented in the two synchronization strategies leading to obtain suitable control strategies to achieve fast and accurate control laws. The respective simulations are performed along with the conclusions of this work.