Analysis and Backstepping Control of a Novel 4D Fractional Chaotic Oscillator

Source abstract

ABSTRACT In this study, we introduce a new 4D fractional model to extract the chaotic attractors of a biological oscillator. The proposed description includes a recently developed ‐Caputo fractional derivative. To explore the model, we employ the time domain analysis and the phase plane method, both of which exhibit the chaotic attractors for some fractional orders. Furthermore, we implement a robust approximation scheme based on a sequential substitution rule and investigate its convergence. The last step is to design a stabilizing backstepping controller to eliminate undesired chaotic behaviors. We then show that the closed‐loop system is globally asymptotically stable, as stated in Theorem 5.1, and use experiments to confirm that it works.