Dynamics, control and symmetry-breaking aspects of a new chaotic Jerk system and its circuit implementation

L. Kamdjeu Kengne; H. T. Kamdem Tagne; J. R. Mboupda Pone; J. Kengne

doi:10.1140/epjp/s13360-020-00338-3

2023 Impact factor 2.8

EPJ PLUS - Condensed Matter and Complex Systems

Eur. Phys. J. Plus (2020) 135: 340
https://doi.org/10.1140/epjp/s13360-020-00338-3

Regular Article

Dynamics, control and symmetry-breaking aspects of a new chaotic Jerk system and its circuit implementation

L. Kamdjeu Kengne¹^,2^*, H. T. Kamdem Tagne³, J. R. Mboupda Pone¹ and J. Kengne¹

¹ Unité de Recherche d’Automatique et Informatique Appliquée (UR-AIA), Department of Electrical Engineering, IUT-FV Bandjoun, University of Dschang, Dschang, Cameroon
² Unité de Recherche de Mécanique et de Modélisation des Systèmes Physiques (UR-2MSP), Department of Physics, University of Dschang, P.O. Box 67, Dschang, Cameroon
³ Unité de Recherche de Matière Condensée, d’Electronique et de Traitement du Signal (UR-MACETS), Department of Physics, University of Dschang, P.O. Box 67, Dschang, Cameroon

^* e-mail: lkamdjeu@gmail.com

Received: 26 November 2019
Accepted: 17 March 2020
Published online: 30 March 2020

Abstract

The study of chaotic systems with symmetry is very well documented. However, very little is known unfortunately about the dynamics of such systems when their symmetry is perturbed or broken. This paper introduces a new chaotic jerk system with quadratic-cubic nonlinearity $\varphi _{k} \left( x \right) =-x+kx^{2}+x^{3}$ where k denotes a symmetry perturbation parameter. We consider the mechanism of chaos generation both for the symmetric ( $$k=0$$ ) and the asymmetric ( $k\ne 0$ ) modes of operation. The model has three fixed points one of which is located at the origin of the state space. Oscillations are excited from the origin, giving rise to a mono-scroll chaotic attractor. We demonstrate that the presence of the quadratic terms breaks the odd symmetry of the model and engenders a plethora of new nonlinear dynamics patterns such as critical transitions, coexisting asymmetric bubbles of bifurcation, coexisting asymmetric attractors, and parallel bifurcation branches. These interesting features are rarely reported, at least in a 3D autonomous system having the simplicity of the one studied in this work. By exploiting the method of linear augmentation, a simple control strategy is developed that help to convert the multistable system from the state of six coexisting attractors to a monostable state when simply adjusting the coupling parameter. Experimental results based on an appropriate electronic realization of the system are consistent with the theoretical investigations.