A verified optimization technique to locate chaotic regions of hénon systems

Tibor Csendes, Barnabás M. Garay, Balázs Bánhelyi

Research output: Contribution to journalArticle

21 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)145-160
Number of pages16
JournalJournal of Global Optimization
Volume35
Issue number1
DOIs
Publication statusPublished - May 1 2006

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Keywords

  • Chaos
  • Global optimization
  • Hénon-map
  • Verified optimization method

ASJC Scopus subject areas

  • Computer Science Applications
  • Management Science and Operations Research
  • Control and Optimization
  • Applied Mathematics

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