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Global stabilization of periodic orbits using a proportional feedback control with pulses

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Abstract

We investigate the stabilization of periodic orbits of one-dimensional discrete maps by using a proportional feedback method applied in the form of pulses. We determine a range of the parameter μ values representing the strength of the feedback for which all positive solutions of the controlled equation converge to a periodic orbit.

An important feature of our approach is that the required assumptions for which our results hold are met by a general class of maps, improving in this way some previous results. We discuss the applicability of our scheme to some models of population dynamics, and give numerical simulations to illustrate our analytical results.

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Authors and Affiliations

  1. Department of Mathematics, University of Calgary, 2500 University Drive N.W., Calgary, AB, T2N 1N4, Canada

    Elena Braverman

  2. Departamento de Matemática Aplicada II, E.T.S.E. Telecomunicación, Universidade de Vigo, Campus Marcosende, 36310, Vigo, Spain

    Eduardo Liz

Authors
  1. Elena Braverman
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  2. Eduardo Liz
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Correspondence to Eduardo Liz.

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Braverman, E., Liz, E. Global stabilization of periodic orbits using a proportional feedback control with pulses. Nonlinear Dyn 67, 2467–2475 (2012). https://doi.org/10.1007/s11071-011-0160-x

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  • DOI: https://doi.org/10.1007/s11071-011-0160-x

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