Article Dans Une Revue Nonlinear Dynamics Année : 2010

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

Cristina Morel
  • Fonction : Auteur
Radu Vlad
  • Fonction : Auteur
Eric Chauveau

Résumé

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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hal-01202707 , version 1 (23-02-2018)

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Cristina Morel, Radu Vlad, Eric Chauveau. A new technique to generate independent periodic attractors in the state space of nonlinear dynamic systems. Nonlinear Dynamics, 2010, 59 (1-2), pp.45-60. ⟨10.1007/s11071-009-9519-7⟩. ⟨hal-01202707⟩
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