A Verified Optimization Technique to Locate Chaotic Regions of Hénon Systems |
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Authors: | Tibor Csendes Barnabás M. Garay Balázs Bánhelyi |
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Affiliation: | (1) Institute of Informatics, University of Szeged, H-6701 Szeged, P.O. Box 652, Hungary;(2) Institute of Mathematics, Budapest University of Technology, H-1521 Budapest, Hungary |
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Abstract: | We present a new verified optimization method to find regions for Hénon systems where the conditions of chaotic behaviour hold. The present paper provides a methodology to verify chaos for certain mappings and regions. We discuss first how to check the set theoretical conditions of a respective theorem in a reliable way by computer programs. Then we introduce optimization problems that provide a model to locate chaotic regions. We prove the correctness of the underlying checking algorithms and the optimization model. We have verified an earlier published chaotic region, and we also give new chaotic places located by the new technique. |
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Keywords: | chaos global optimization Hénon-map verified optimization method |
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