Open AccessA simple multi-stable chaotic jerk system with two saddle-foci equilibrium points: analysis, synchronization via backstepping technique and MultiSim circuit design
Author(s) -
Aceng Sambas,
Sundarapandian Vaidyanathan,
Irene M. Moroz,
Babatunde A. Idowu,
Mohamad Afendee Mohamed,
Mustafa Mamat,
W. S. Mada Sanjaya
Publication year - 2021
Publication title -
international journal of power electronics and drive systems/international journal of electrical and computer engineering
Language(s) - English
Resource type - Journals
eISSN - 2722-2578
pISSN - 2722-256X
DOI - 10.11591/ijece.v11i4.pp2941-2952
Subject(s) - jerk , control theory (sociology) , chaotic , equilibrium point , lyapunov exponent , saddle , computer science , dissipative system , multistability , backstepping , mathematics , physics , mathematical analysis , nonlinear system , classical mechanics , artificial intelligence , mathematical optimization , differential equation , acceleration , control (management) , quantum mechanics , adaptive control
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