Dynamical Analysis and Offset Boosting in a 4-Dimensional Quintic Chaotic Oscillator with Circulant Connection of Space Variables

Abstract

In recent years, much energy has been devoted to the study of chaotic models with specific features particularly those with cyclic connection of the variables. Previous ones provide multistability, amplitude control, and so on. Concerning the first phenomenon, models with ring connection of variables presented a coexistence of up to twelve disconnected attractors. In order to emphasize the complexity of circulant chaotic oscillators and their use in the engineering domain, a quintic chaotic model with cyclic connection of variables is considered and studied, which has complex equilibria located on the line $x=y=z=w$ . Therefore, it experiences, amongst other, the phenomenon of offset boosting obtained by introducing four constants into the equations of the model, which has not be done in the past. Multistability is also revealed and the coexistence of eight and sixteen attractors is demonstrated using phase portraits. The system’s dynamics has been investigated considering its two parameters. Nonlinear dynamical tools such as bifurcation diagrams, phase portraits, time evolutions, two-parameter diagram, and Lyapunov exponents help to highlight the important phenomena encountered. The numerical results are confirmed using PSpice and particularly show the double-band chaotic attractor. Moreover, total amplitude control (TAC) is shown, proving that our oscillator can be used as an attenuator or amplifier in the engineering domain. The method of adaptive synchronization has been applied to the considered oscillator to emphasize the possible implication into the secure of communication systems.