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Finding attractors of continuous-time systems by parameter switching

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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.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Avram Iancu University, 400380, Cluj-Napoca, Romania

    Marius-F. Danca

  2. Romanian Institute of Science and Technology, 400487, Cluj-Napoca, Romania

    Marius-F. Danca

  3. Instituto de Física Aplicada, Consejo Superior de Investigaciones Científicas, Serrano 144, 28006, Madrid, Spain

    Miguel Romera, Gerardo Pastor & Fausto Montoya

Authors
  1. Marius-F. Danca
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  2. Miguel Romera
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  3. Gerardo Pastor
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  4. Fausto Montoya
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Correspondence to Marius-F. Danca.

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Danca, MF., Romera, M., Pastor, G. et al. Finding attractors of continuous-time systems by parameter switching. Nonlinear Dyn 67, 2317–2342 (2012). https://doi.org/10.1007/s11071-011-0172-6

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  • DOI: https://doi.org/10.1007/s11071-011-0172-6

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