A new chaotic jerk system with a sinusoidal nonlinearity, its bifurcation analysis, multistability, circuit design and complete synchronization design via backstepping control

Journal article

In this research work, we investigate a new three-dimensional jerk system with three parameters in which one of the nonlinear terms is a sinusoidal nonlinearity. We show that the new jerk system has two unstable equilibrium points on the 𝑥-axis. Numerical integrations show the existence of periodic and chaotic states, as well as unbounded solutions. Consideration of the Poincaré sphere at infinity found no periodic states. We show that the new jerk system exhibits multistability with coexisting attractors. We also present results for the offset boosting of the proposed chaotic jerk system. Using MultiSim version 14.1, we design an electronic circuit for the new jerk system with a sinusoidal nonlinearity. As a control application, we design complete synchronization for the master-slave jerk systems using backstepping control technique. Simulations are presented to illustrate the main results of this research work. Go to article

Authors: Vaidyanathan, S; Hannachi, F; Moroz, IM; Aruna, C; Mohamed, MA

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Committee of Automatic Control and Robotics PAS
• Journal: Archives of Control Sciences
• Volume: 34
• Issue: 2
• Pages: 301-322
• Publication date: 2024-02-13
• Acceptance date: 2024-02-06
• DOI: 10.24425/acs.2024.149662
• ISSN: 1230-2384
• Language: English
• Keywords: chaos; chaotic systems; jerk systems; backstepping control synchronization; bifurcation analysis; mechanical systems; circuit design