Adjustable symmetry on the dynamics of a new chaotic system with cyclic symmetry: theoretical study, control and experimental investigation

Abstract

In this study, we propose a new chaotic autonomous system with adjustable cyclic and central symmetries. The new 3D system, with rich dynamics, is constructed based on the Thomas model. A detailed study of the nonlinear dynamics arising from the model allows us to reveal complex behaviors of different phenomena such as hysteresis dynamics, offset boosting, total amplitude control, and coexistence of several homogeneous and heterogeneous attractors in both regimes (symmetric and asymmetric). The control of multistability of the new cyclic system is studied by following the technique of linear augmentation. An analog electronic version of the model is designed and then simulated using the Pspice software. Moreover, a physical implementation using the Arduino microcontroller makes it possible to validate the results of the theoretical analysis.