A simple multi-stable chaotic jerk system with two saddle-foci equilibrium points: analysis, synchronization via backstepping technique and MultiSim circuit design

Aceng Sambas (Universitas Muhammadiyah Tasikmalaya)
Sundarapandian Vaidyanathan (Vel Tech University)
Irene M. Moroz (University of Oxford,)
Babatunde Idowu (Lagos State University)
Mohamad Afendee Mohamed (Universiti Sultan Zainal Abidin)
Mustafa Mamat (Universiti Sultan Zainal Abidin)
W. S. Mada Sanjaya (Universitas Islam Negeri Sunan Gunung Djati Bandung)

International Journal of Electrical and Computer Engineering
Vol 11, No 4: August 2021

This paper announces a new three-dimensional chaotic jerk system with two saddle-focus equilibrium points and gives a dynamic analysis of the properties of the jerk system such as Lyapunov exponents, phase portraits, Kaplan-Yorke dimension and equilibrium points. By modifying the Genesio-Tesi jerk dynamics (1992), a new jerk system is derived in this research study. The new jerk model is equipped with multistability and dissipative chaos with two saddle-foci equilibrium points. By invoking backstepping technique, new results for synchronizing chaos between the proposed jerk models are successfully yielded. MultiSim software is used to implement a circuit model for the new jerk dynamics. A good qualitative agreement has been shown between the MATLAB simulations of the theoretical chaotic jerk model and the MultiSIM results