Journal of Statistical Physics

, Volume 167, Issue 3–4, pp 792–805 | Cite as

Time Correlations in Mode Hopping of Coupled Oscillators

  • Mathias L. Heltberg
  • Sandeep Krishna
  • Mogens H. Jensen


We study the dynamics in a system of coupled oscillators when Arnold Tongues overlap. By varying the initial conditions, the deterministic system can be attracted to different limit cycles. Adding noise, the mode hopping between different states become a dominating part of the dynamics. We simplify the system through a Poincare section, and derive a 1D model to describe the dynamics. We explain that for some parameter values of the external oscillator, the time distribution of occupancy in a state is exponential and thus memoryless. In the general case, on the other hand, it is a sum of exponential distributions characteristic of a system with time correlations.


Coupled oscillators Mode hopping Arnold tongues Poincare sections Time correlations 



SK thanks the Simons Foundation for funding. MLH and MHJ acknowledge support from the Danish Council for Independent Research and Danish National Research Foundation through StemPhys Center of Excellence, grant number DNRF116.


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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • Mathias L. Heltberg
    • 1
    • 2
  • Sandeep Krishna
    • 1
    • 2
  • Mogens H. Jensen
    • 1
    • 2
  1. 1.The Niels Bohr InstituteUniversity of CopenhagenKøbenhavnDenmark
  2. 2.Simons Centre for the Study of Living MachinesNational Centre for Biological SciencesBangaloreIndia

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