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A new chaotic hyperjerk system with a half-line of equilibrium points, its dynamic analysis, multistability, circuit simulation and anti-synchronization via backstepping control

Vaidyanathan Sundarapandian, Hannachi Fareh, Mohamed Mohamad Afendee, Sambas Aceng, Aruna Chittineni, Ramesh Repud

Archives of Control Sciences

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2025

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Vol. 35, No. 1

123--143

EN

In this work, we present a new four-dimensional chaotic hyperjerk system with a half-line of equilibrium points. In the chaos literature, it is well-known that chaotic systems with an infinite number of equilibrium points exhibit hidden attractors. Thus, we deduce in this research work that the new chaotic hyperjerk system has hidden attractors. We next study the new chaotic hyperjerk system for a dynamic analysis using bifurcation plots and Lyapunov Exponents (LE) diagrams.We exhibit that the new hyperjerk system has a special property of multistability with coexisting attractors. Using Multisim version 14.2, we carry out an electronic circuit simulation for the proposed 4-D chaotic hyperjerk system with a half-line of equilibrium points. Finally, as an application in control engineering, we apply backstepping control for achieving antisynchronization of a pair of new chaotic hyperjerk systems taken as master-slave systems, which has important applications in communication systems.

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

Vaidyanathan Sundarapandian, Hannachi Fareh, Moroz Irene M., Aruna Chittineni, Mohamed Mohamad Afendee, Sambas Aceng

Archives of Control Sciences

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2024

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Vol. 34, No. 2

301--322

EN

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.

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A new chaotic hyperjerk system with four quadratic nonlinearities, its bifurcation analysis, multistability, circuit design and complete synchronization design via active backstepping control

Vaidyanathan Sundarapandian, Sambas Aceng, Moroz Irene M., Aruna Chittineni, Mohamed Mohamad Afendee, Sundaram Arun

Archives of Control Sciences

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2024

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Vol. 34, No. 4

697--713

EN

In this research work, we propose a new four-dimensional chaotic hyperjerk system with four quadratic nonlinearities. We carry out a detailed bifurcation analysis and derive conditions for the existence of a Hopf bifurcation for the new hyperjerk system. A linear analysis shows that there is only a unique trivial equilibrium state, whose stability depends solely on the parameter p. The only bifurcation possible is a Hopf bifurcation when p = 2. This is verified from bifurcation transition diagrams. We derive new results showing multistability and the existence of coexisting attractors for the new chaotic hyperjerk system. Using MultiSim, a new electronic circuit is designed for the new chaotic hyperjerk system with four quadratic nonlinearities. Finally, we present a control application for the proposed chaotic hyperjerk system with four quadratic nonlinearities. Using active backstepping control, we design a new controller that achieves complete synchronization for the master-slave chaotic hyperjerk systems with four quadratic nonlinearities.