Summary
Chaotic systems are usually studied by numerical simulations. Due to rounding errors and sensitive dependence on initial conditions simulation results may be unreliable. It is shown that computations can be done in a way that ensures that rigorous results are obtained. A set of tools for rigorous studies of nonlinear systems is presented. This includes techniques for computing enclosures of trajectories, finding and proving the existence of symbolic dynamics and obtaining rigorous bounds for the topological entropy, methods for finding accurate enclosures of chaotic attractor, interval operators for proving the existence of fixed points and periodic orbits, and methods for finding all short cycles. As illustrative examples results of a rigorous numerical analysis of the Hénon map and the Chua’s circuit are presented.
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Galias, Z. (2009). Computational Methods for Rigorous Analysis of Chaotic Systems. In: Kocarev, L., Galias, Z., Lian, S. (eds) Intelligent Computing Based on Chaos. Studies in Computational Intelligence, vol 184. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-95972-4_2
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DOI: https://doi.org/10.1007/978-3-540-95972-4_2
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