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

被引：1

作者：

Zhou, Leilei ^{[1
]}

Chen, Zengqiang ^{[1
,2
]}

Wang, Jiezhi ^{[2
]}

Zhang, Qing ^{[2
]}

机构：

[1] Nankai Univ, Coll Comp & Control Engn, Key Lab Intelligent Robot Tianjin, Tianjin 300353, Peoples R China

[2] Civil Aviat Univ China, Coll Sci, Tianjin 300300, Peoples R China

来源：

NONLINEAR ANALYSIS-MODELLING AND CONTROL | 2017年 / 22卷 / 05期

关键词：

hyper-chaotic system; ultimate bound; positively invariant set; globally exponentially attractive set; topological horseshoe; COMPUTER-ASSISTED VERIFICATION; LORENZ-SYSTEM; SECURE-COMMUNICATION; LYAPUNOV EXPONENTS; DYNAMICAL-SYSTEMS; SYNCHRONIZATION; ATTRACTOR; SETS;

D O I：

10.15388/NA.2017.5.1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 Omega(1) and globally exponentially attractive set Omega(2) 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.

引用

页码：579 / 597

页数：19

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