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A new technique to generate independent periodic attractors in the state space of nonlinear dynamic systems

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Abstract

This paper proposes a method to generate several independent periodic attractors, in continuous-time nonchaotic systems (with an equilibrium point or a limit cycle), based on a switching piecewise-constant controller. We demonstrate here that the state space equidistant repartition of these attractors is on a precise zone of a precise curve that depends on the parameters of the system. We determine the state space domains where the attractors are generated from different initial conditions. A mathematical formula giving their maximal number in function of the controller piecewise-constant values is then deduced. Throughout this study, the proposed methodology is illustrated with several examples.

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Authors and Affiliations

  1. École Supérieure d’Électronique de l’Ouest—ESEO, 4, rue Merlet de la Boulaye, 49009, Angers, France

    Cristina Morel & Eric Chauveau

  2. Technical University of Cluj-Napoca, 103-105, Bd. Muncii, 400641, Cluj-Napoca, Romania

    Radu Vlad

Authors
  1. Cristina Morel
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  2. Radu Vlad
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  3. Eric Chauveau
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Correspondence to Cristina Morel.

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Morel, C., Vlad, R. & Chauveau, E. A new technique to generate independent periodic attractors in the state space of nonlinear dynamic systems. Nonlinear Dyn 59, 45–60 (2010). https://doi.org/10.1007/s11071-009-9519-7

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  • DOI: https://doi.org/10.1007/s11071-009-9519-7

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