We present a systematic approach to identify the similarities and differences between a chaotic system with delayed feedback and two mutually delay-coupled systems. We consider the general case in which the coupled systems are either unsynchronized or in a generally synchronized state, in contrast to the mostly studied case of identical synchronization. We construct a new time-series for each of the two coupling schemes, respectively, and present analytic evidence and numerical confirmation that these two constructed time-series are statistically equivalent. From the construction, it then follows that the distribution of time-series segments that are small compared to the overall delay in the system is independent of the value of the delay and of the coupling scheme. By focusing on numerical simulations of delay-coupled chaotic lasers, we present a practical example of our findings.
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December 2013
Research Article|
December 13 2013
Relation between delayed feedback and delay-coupled systems and its application to chaotic lasers
Miguel C. Soriano;
Miguel C. Soriano
a)
Instituto de Física Interdisciplinar y Sistemas Complejos, IFISC (CSIC-UIB)
, Campus Universitat Illes Balears, E-07122 Palma de Mallorca, Spain
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Valentin Flunkert;
Valentin Flunkert
Instituto de Física Interdisciplinar y Sistemas Complejos, IFISC (CSIC-UIB)
, Campus Universitat Illes Balears, E-07122 Palma de Mallorca, Spain
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Ingo Fischer
Ingo Fischer
Instituto de Física Interdisciplinar y Sistemas Complejos, IFISC (CSIC-UIB)
, Campus Universitat Illes Balears, E-07122 Palma de Mallorca, Spain
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Miguel C. Soriano
a)
Valentin Flunkert
Ingo Fischer
Instituto de Física Interdisciplinar y Sistemas Complejos, IFISC (CSIC-UIB)
, Campus Universitat Illes Balears, E-07122 Palma de Mallorca, Spain
a)
Electronic mail: [email protected].
Chaos 23, 043133 (2013)
Article history
Received:
March 22 2013
Accepted:
November 26 2013
Citation
Miguel C. Soriano, Valentin Flunkert, Ingo Fischer; Relation between delayed feedback and delay-coupled systems and its application to chaotic lasers. Chaos 1 December 2013; 23 (4): 043133. https://doi.org/10.1063/1.4844335
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