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Nonlinear Dynamics

, Volume 67, Issue 4, pp 2317–2342 | Cite as

Finding attractors of continuous-time systems by parameter switching

  • Marius-F. Danca
  • Miguel Romera
  • Gerardo Pastor
  • Fausto Montoya
Review

Abstract

The review presents a parameter switching algorithm and his applications which allows numerical approximation of any attractor of a class of continuous-time dynamical systems depending linearly on a real parameter. The considered classes of systems are modeled by a general initial value problem which embeds dynamical systems continuous and discontinuous with respect to the state variable, of integer, and fractional order. The numerous results, presented in several papers, are systematized here on four representative known examples representing the four classes. The analytical proof of the algorithm convergence for the systems belonging to the continuous class is presented briefly, while for the other categories of systems, the convergence is numerically verified via computational tools. The utilized numerical tools necessary to apply the algorithm are contained in Appendices A, B, C, D and E.

Keywords

Parameter switching Global attractors Local attractors Fractional systems Discontinuous systems Filippov regularization 

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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Marius-F. Danca
    • 1
    • 2
  • Miguel Romera
    • 3
  • Gerardo Pastor
    • 3
  • Fausto Montoya
    • 3
  1. 1.Department of Mathematics and Computer ScienceAvram Iancu UniversityCluj-NapocaRomania
  2. 2.Romanian Institute of Science and TechnologyCluj-NapocaRomania
  3. 3.Instituto de Física AplicadaConsejo Superior de Investigaciones CientíficasMadridSpain

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