Estimating the ultimate bound and positively invariant set for the hyperchaotic Lorenz–Haken system

Damei Li, Xiaoqun Wu and Jun-an Lu

Chaos, Solitons & Fractals, 2009, vol. 39, issue 3, 1290-1296

Abstract: To estimate the ultimate bound and positively invariant set for a dynamic system is an important but quite challenging task in general. In this paper, we attempt to investigate the ultimate bound and positively invariant set for the hyperchaotic Lorenz–Haken system using a technique combining the generalized Lyapunov function theory and optimization. For the Lorenz–Haken system, we derive a four-dimensional ellipsoidal ultimate bound and positively invariant set. Furthermore, the two-dimensional parabolic ultimate bound with respect to x–z is established. Finally, numerical results to estimate the ultimate bound are also presented for verification. The results obtained in this paper are important and useful in control, synchronization of hyperchaos and their applications.

Date: 2009
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Citations: View citations in EconPapers (9)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:39:y:2009:i:3:p:1290-1296

DOI: 10.1016/j.chaos.2007.06.038

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