Ultimate boundary estimations and topological horseshoe analysis of a new 4D hyper-chaotic system | Zendy

Leilei Zhou | Zendy; Zengqiang Chen | Zendy; Jiezhi Wang | Zendy; Qing Zhang | Zendy

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Ultimate boundary estimations and topological horseshoe analysis of a new 4D hyper-chaotic system

Author(s) -

Leilei Zhou,

Zengqiang Chen,

Jiezhi Wang,

Qing Zhang

Publication year - 2017

Publication title -

nonlinear analysis modelling and control

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.734

H-Index - 32

eISSN - 2335-8963

pISSN - 1392-5113

DOI - 10.15388/na.2017.5.1

Subject(s) - chaotic , boundary (topology) , mathematics , stability (learning theory) , nonlinear system , computation , set (abstract data type) , lyapunov stability , topology (electrical circuits) , computer science , statistical physics , mathematical analysis , physics , algorithm , artificial intelligence , quantum mechanics , machine learning , combinatorics , programming language

. In this paper, we first estimate the boundedness of a new proposed 4-dimensional (4D) hyper-chaotic system with complex dynamical behaviors. For this system, the ultimate bound set Ω1 and globally exponentially attractive set Ω2 are derived based on the optimization method, Lyapunov stability theory, and comparison principle. Numerical simulations are presented to show the effectiveness of the method and the boundary regions. Then, to prove the existence of hyper-chaos, the hyper-chaotic dynamics of the 4D nonlinear system is investigated by means of topological horseshoe theory and numerical computation. Based on the algorithm for finding horseshoes in three-dimensional hyper-chaotic maps, we finally find a horseshoe with two-directional expansions in the 4D hyper-chaotic system, which can rigorously prove the existence of the hyper-chaos in theory.

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