Nonlinear Dynamics

, Volume 67, Issue 4, pp 2455–2465 | Cite as

A novel bounded 4D chaotic system

Original Paper


This paper presents a novel bounded four-dimensional (4D) chaotic system which can display hyperchaos, chaos, quasiperiodic and periodic behaviors, and may have a unique equilibrium, three equilibria and five equilibria for the different system parameters. Numerical simulation shows that the chaotic attractors of the new system exhibit very strange shapes which are distinctly different from those of the existing chaotic attractors. In addition, we investigate the ultimate bound and positively invariant set for the new system based on the Lyapunov function method, and obtain a hyperelliptic estimate of it for the system with certain parameters.


Hyperchaos Ultimate bound Positively invariant set Lyapunov function 


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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Institute of Systems EngineeringTianjin UniversityTianjinChina

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