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

Published on Aug 1, 2021in International Journal of Electrical and Computer Engineering
· DOI :10.11591/IJECE.V11I4.PP%P
Aceng Sambas12
Estimated H-index: 12
,
Sundarapandian Vaidyanathan81
Estimated H-index: 81
+ 4 AuthorsW. S. Mada Sanjaya5
Estimated H-index: 5
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Abstract
This paper announces a new three-dimensional multistable chaotic jerk system with two saddle-foci equilibrium points and gives a dynamic analysis of the properties of the jerk system such as Lyapunov exponents, phase portraits, equilibrium points and bifurcation analysis. Chaotic jerk systems have a nice triangular structure in their dynamics and they have many engineering applications. Our new jerk system is obtained by modifying the dynamics of the Genesio-Tesi chaotic jerk system (1992), and our jerk system has two quadratic nonlinearities in total. The new jerk system has multistability with coexisting attractors. Also, the new jerk system is dissipative and has high complexity. As an engineering application, new synchronization results based on active backstepping control are also derived for the new jerk system. In addition, an electronic circuit implementation of the new jerk system is designed and implemented in MultiSIM. A good qualitative agreement has been shown between the MATLAB simulations of the theoretical chaotic jerk model and the MultiSIM results
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