Phase Control of Chaotic Maps

  • Sijo K. JosephEmail author
  • Miguel A. F. Sanjuán
Part of the Nonlinear Systems and Complexity book series (NSCH, volume 12)


The phase control is a well-known control method that has been typically applied to periodically driven dynamical systems. Its application allows controlling them through the phase difference between the forcing term and another harmonic perturbation. In the current chapter, we focus on the application of this control method to maps. In particular, we analyze two paradigmatic maps: the bouncing ball map and the Hénon map. As a result, we observe that the application of the phase control can suppress or enhance the chaotic behavior on them. We also analyze the crisis induced intermittency in the bouncing ball map when the phase of the control signal is varied. Finally, the scaling behavior of the average Lyapunov exponents near the phase induced crisis is studied. Future applications of the phase control method are also discussed.


Lyapunov Exponent Bifurcation Diagram Chaotic Behavior Chaotic Attractor Large Lyapunov Exponent 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This work was supported by the Spanish Ministry of Science and Innovation under Project No. FIS2013-40653-P.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de FísicaUniversidad Rey Juan CarlosMóstolesSpain

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