The European Physical Journal Special Topics

, Volume 164, Issue 1, pp 35–44 | Cite as

Phase synchronization in unidirectionally coupled Ikeda time-delay systems

  • D.V. SenthilkumarEmail author
  • M. Lakshmanan
  • J. Kurths


Phase synchronization in unidirectionally coupled Ikeda time-delay systems exhibiting non-phase-coherent hyperchaotic attractors of complex topology with highly interwoven trajectories is studied. It is shown that in this set of coupled systems phase synchronization (PS)does exist in a range of the coupling strength which is preceded by a transition regime (approximate PS)and a nonsynchronous regime. However, exact generalized synchronization does not seem to occur in the coupled Ikeda systems (for the range of parameters we have studied)even for large coupling strength, in contrast to our earlier studies in coupled piecewise-linear and Mackey-Glass systems [27,28]. The above transitions are characterized in terms of recurrence based indices, namely generalized autocorrelation function P(t), correlation of probability of recurrence (CPR), joint probability of recurrence (JPR)and similarity of probability of recurrence (SPR). The existence of phase synchronization is also further confirmed by typical transitions in the Lyapunov exponents of the coupled Ikeda time-delay systems and also using the concept of localized sets.


Lyapunov Exponent Coupling Strength European Physical Journal Special Topic Chaotic Attractor Phase Synchronization 
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© EDP Sciences and Springer 2008

Authors and Affiliations

  1. 1.Centre for Nonlinear Dynamics, Department of PhysicsBharathidasan UniversityTiruchirapalliIndia
  2. 2.Interdisciplinary Centre for Dynamics of Complex Systems, University of PotsdamPotsdamGermany
  3. 3.Humboldt University, Berlin and Potsdam Institute for Climate Impact ResearchPotsdamGermany

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