Forming and implementing a hyperchaotic system with rich dynamics

A simple three-dimensional （3D） autonomous chaotic system is extended to four-dimensions so as to generate richer nonlinear dynamics. The new system not only inherits the dynamical characteristics of its parental 3D system but also exhibits many new and complex dynamics, including assembled 1-scroll...

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Bibliographic Details
Published in:Chinese physics B 2011-09, Vol.20 (9), p.115-122
Main Author: 刘文波 邓榤生 陈关荣
Format: Article
Language:English
Subjects:
3D系统
Chaos theory
Computer simulation
Dynamical systems
Lyapunov
Lyapunov exponents
Mathematical models
Nonlinear dynamics
Three dimensional
Tuning
动态特性
数值模拟
混沌吸引子
电路实现
超混沌系统
非线性动力学
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Summary:A simple three-dimensional （3D） autonomous chaotic system is extended to four-dimensions so as to generate richer nonlinear dynamics. The new system not only inherits the dynamical characteristics of its parental 3D system but also exhibits many new and complex dynamics, including assembled 1-scroll, 2-scroll and 4-scroll attractors, as well as hyperchaotic attractors, by simply tuning a single system parameter. Lyapunov exponents and bifurcation diagrams are obtained via numerical simulations to further justify the existences of chaos and hyperchaos. Finally, an electronic circuit is constructed to implement the system, with experimental and simulation results presented and compared for demonstration and verification.
ISSN:1674-1056
2058-3834
DOI:10.1088/1674-1056/20/9/090510