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Bounds of the hyper-chaotic Lorenz-Stenflo system. (English) Zbl 1222.37036
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:
 37D45 Strange attractors, chaotic dynamics 34C28 Complex behavior, chaotic systems (ODE)
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##### References:
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