The emergence of multi-scroll chaotic rotating waves in a ring of threshold controller based coupled non-autonomous chaotic oscillators

Abstract

This paper introduces a novel ring of three identical second-order non-autonomous oscillators, a unique configuration, that are coupled unidirectionally via threshold controllers. This configuration, with threshold controllers employed both within the oscillators and for coupling, facilitates the generation of multi-scroll chaotic rotating waves. The system demonstrates various dynamics, including periodic, quasi-periodic, and chaotic regimes, as control parameters are varied. It is delved into the transition from constant phase difference to phase synchronization using Hilbert transform analysis and investigated the underlying mechanisms driving these behaviours. The research is further validated through a rigorous process, including real-time analog simulation and numerical studies such as bifurcation diagrams and Lyapunov exponent analysis, ensuring the reliability of our findings.