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Multiscroll Chaotic Sea Obtained from a Simple 3D System Without Equilibrium

Biomedical Engineering Department, Amirkabir University of Technology, Tehran 15875-4413, Iran

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School of Electronics and Telecommunications, Hanoi University of Science and Technology, 01 Dai Co Viet, Hanoi, Vietnam

E-mail Address: pvt3010@gmail.com

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Tomasz Kapitaniak

Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90-924 Lodz, Poland

E-mail Address: tomasz.kapitaniak@p.lodz.pl

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https://doi.org/10.1142/S0218127416500310Cited by:158 (Source: Crossref)

Abstract

Recently, many rare chaotic systems have been found including chaotic systems with no equilibria. However, it is surprising that such a system can exhibit multiscroll chaotic sea. In this paper, a novel no-equilibrium system with multiscroll hidden chaotic sea is introduced. Besides having multiscroll chaotic sea, this system has two more interesting properties. Firstly, it is conservative (which is a rare feature in three-dimensional chaotic flows) but not Hamiltonian. Secondly, it has a coexisting set of nested tori. There is a hidden torus which coexists with the chaotic sea. This new system is investigated through numerical simulations such as phase portraits, Lyapunov exponents, Poincaré map, and frequency spectra. Furthermore, the feasibility of such a system is verified through circuital implementation.

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