A hyperchaotic system from a chaotic system with one saddle and two stable node-foci

This paper presents a 4D new hyperchaotic system which is constructed by a linear controller to a 3D new chaotic system with one saddle and two stable node-foci. Some complex dynamical behaviors such as ultimate boundedness, chaos and hyperchaos of the simple 4D autonomous system are investigated an...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 360; no. 1; pp. 293 - 306
Main Authors Yang, Qigui, Liu, Yongjian
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier Inc 01.12.2009
Elsevier
Subjects
Bifurcation
Chaos
Exact sciences and technology
Global analysis, analysis on manifolds
Hyperchaos
Lyapunov exponents
Mathematical analysis
Mathematics
Operator theory
Ordinary differential equations
Sciences and techniques of general use
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Ultimate boundedness
Chaos
Bifurcation
Hyperchaos
Lyapunov exponents
Ultimate boundedness
Autonomous system
Mathematical analysis
Lyapunov exponent
Hopf bifurcation
Application
Attractor
Chaotic systems
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Summary:This paper presents a 4D new hyperchaotic system which is constructed by a linear controller to a 3D new chaotic system with one saddle and two stable node-foci. Some complex dynamical behaviors such as ultimate boundedness, chaos and hyperchaos of the simple 4D autonomous system are investigated and analyzed. The corresponding bounded hyperchaotic and chaotic attractor is first numerically verified through investigating phase trajectories, Lyapunove exponents, bifurcation path, analysis of power spectrum and Poincaré projections. Finally, two complete mathematical characterizations for 4D Hopf bifurcation are rigorous derived and studied.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2009.06.051