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.


37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
34C28 Complex behavior and chaotic systems of ordinary differential equations
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