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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:
37D45Strange attractors, chaotic dynamics
34C28Complex behavior, chaotic systems (ODE)
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