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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 of systems with hyperbolic behavior 34C28 Complex behavior and chaotic systems of ordinary differential equations
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References:
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