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

• Published in: Archives of control sciences 2024-01, Vol.34 (2), p.301-322
• Main Authors: VaidyanathaN, Sundarapandian, Hannachi, Fareh, Moroz, Irene M., Aruna, Chittineni, Mohamed, Mohamad Afendee, Sambas, Aceng
• Format: Article
• Language: English
• Subjects: backstepping control; bifurcation analysis; Bifurcation theory; chaos; Chaos theory; chaotic systems; Circuit design; Computer engineering; Control systems; Design parameters; Dynamical systems; Eigenvalues; Electronic circuits; Engineers; Equilibrium; Field programmable gate arrays; jerk systems; Mathematical models; mechanical systems; Nonlinear control; Nonlinearity; Poincare spheres; Sine waves; Synchronism; synchronization; Three dimensional analysis; Unstable equilibrium point
• ISSN: 1230-2384; 2300-2611
• DOI: 10.24425/acs.2024.149662

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 -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.