Evolutionary methods for the approximation of the stability domain and frequency optimization of conservative maps

Y. G. Petalas, C. G. Antonopoulos, T. C. Bountis, M. N. Vrahatis

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2 Citations (Scopus)

Abstract

Two methodologies are presented for the numerical approximation of the "domain of stability" of nonlinear conservative maps: (a) the Evolutionary Estimation of the Domain of Stability (EEDS) and (b) the Evolutionary Frequency Optimization (EFO), optimizing certain frequency parameters of these maps so that the domain of stability encompasses the maximum possible "volume" of bounded motion, known in the accelerator literature as the dynamic aperture. The central components of the proposed approaches are: The Differential Evolution algorithm (DE) based on concepts of Computational Intelligence and the method of the Smaller ALignment Index (SALI) used for the determination of chaotic dynamics. Initially, we give a brief description of the two methodologies and then demonstrate their usefulness by applying them to some well-known examples of 2D and 4D Hénon maps. The proposed methodologies can be easily applied to "volume" preserving maps which are not necessarily symplectic as well as to continuous dynamical systems (flows) and can also be generalized to treat conservative dynamical systems of any dimension.

Original languageEnglish
Pages (from-to)2249-2264
Number of pages16
JournalInternational Journal of Bifurcation and Chaos
Volume18
Issue number8
DOIs
Publication statusPublished - Aug 2008

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Keywords

  • Accelerator maps
  • Chaotic regions
  • Conservative maps
  • Domain of stability
  • Evolutionary methods
  • The SALI method

ASJC Scopus subject areas

  • Modelling and Simulation
  • Engineering (miscellaneous)
  • General
  • Applied Mathematics

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