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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

2024

Vol. 34, No. 4

697--713

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.