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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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