Analysis, Synchronization and Microcontroller Implementation of a New Quasiperiodically Forced Chaotic Oscillator with Megastability

Periodically and quasiperiodically forced nonlinear oscillators are in the group of systems which can exhibit chaotic behavior. Chaotic systems could be characterized by their strange attractor’s properties into one or more subtypes, e.g., chaotic systems with hidden attractors, megastability or extreme multistability. In this article, we propose a new quasiperiodically forced chaotic system, which has megastability. The statistical properties, bifurcation diagram, Lyapunov exponents and entropy analysis are considered to study this new system. Furthermore, for the first time, the bidirectional and unidirectional coupling schemes between two quasiperiodically forced chaotic systems with megastability have been studied. As it is observed, when the value of the coupling coefficient is increased in both coupling schemes, the coupled systems undergo a transition from desynchronization mode to complete synchronization. Also, the simulation results reveal the richness of the coupled system’s dynamical behavior. In particular, in the bidirectional coupling case, interesting nonlinear dynamics, such as a transition from a chaotic to quasiperiodic desynchronization and finally to a complete synchronization via an intermittent phenomenon, are observed. Furthermore, in the unidirectional coupling case, in which the system passes from the desynchronization to complete synchronization through a region where the chaotic attractor of the second coupled system is shifted and decreased, is also observed. Finally, the system’s realization has been done by using a microcontroller.