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Zbl 1222.37036
Wang, Pei; Li, Damei; Hu, Qianli
Bounds of the hyper-chaotic Lorenz-Stenflo system. (English)
[J] Commun. Nonlinear Sci. Numer. Simul. 15, No. 9, 2514-2520 (2010). ISSN 1007-5704

Summary: To estimate the ultimate bound and positively invariant set for a dynamical system is an important but quite challenging task in general. This paper attempts to investigate the ultimate bounds and positively invariant sets of the hyper-chaotic Lorenz-Stenflo (L-S) system, which is based on the optimization method and the comparison principle. A family of ellipsoidal bounds for all the positive parameters values $a$, $b$, $c$, $d$ and a cylindrical bound for $a>0$, $b>1$, $c >0$, $d>0$ are derived. Numerical results show the effectiveness and advantage of our methods.

MSC 2000:: *37D45 Strange attractors, chaotic dynamics
34C28 Other types of "recurrent" solutions of ODE

Keywords: hyper-chaotic system; ultimate bounds; positively invariant sets; optimization

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