# Time Correlations in Mode Hopping of Coupled Oscillators

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## Abstract

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.

## Keywords

Coupled oscillators Mode hopping Arnold tongues Poincare sections Time correlations## Notes

### Acknowledgements

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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