Nonlinear Dynamics

, Volume 67, Issue 4, pp 2467–2475 | Cite as

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

  • Elena Braverman
  • Eduardo Liz
Original Paper


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.


Chaos control Proportional feedback Population model Periodic orbit Global attractor 


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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of CalgaryCalgaryCanada
  2. 2.Departamento de Matemática Aplicada II, E.T.S.E. TelecomunicaciónUniversidade de VigoVigoSpain

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