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Cross-frequency synchronization of oscillators with time-delayed coupling.

Vladimir V Klinshov1, Dmitry S Shchapin1, Vladimir I Nekorkin1

  • 1Institute of Applied Physics of the Russian Academy of Sciences, 46 Ul'yanov Street, 603950, Nizhny Novgorod, Russia and University of Nizhny Novgorod, 23 Prospekt Gagarina, 603950, Nizhny Novgorod, Russia.

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This study explores cross-frequency synchronization in coupled pulse oscillators. Theoretical models accurately predict experimental results for synchronization zones and system dynamics.

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Area of Science:

  • Nonlinear dynamics
  • Complex systems
  • Oscillator networks

Background:

  • Coupled oscillators are fundamental in various scientific fields.
  • Understanding synchronization phenomena is crucial for analyzing complex systems.
  • Time-delayed coupling introduces complex dynamics in oscillator networks.

Purpose of the Study:

  • To investigate cross-frequency synchronization between two pulse oscillators with time-delayed coupling.
  • To develop a theoretical framework for predicting synchronization behavior.
  • To experimentally validate the theoretical findings using an electronic circuit.

Main Methods:

  • Theoretical analysis using phase resetting curves and Poincaré maps.
  • Analysis of system dynamics under weak coupling conditions.
  • Experimental implementation and study of an electronic circuit with coupled pulse oscillators.

Main Results:

  • Synchronization zones for m:n synchronization were identified in the parameter space.
  • The theoretical model accurately predicted the location of synchronization zones.
  • Experimental results confirmed the theoretical predictions, including bifurcations within synchronization zones.

Conclusions:

  • The developed theory effectively describes the dynamics of coupled pulse oscillators with time-delayed coupling.
  • Experimental validation confirms the predictive power of the theoretical models.
  • This work provides insights into synchronization phenomena in realistic coupled oscillator systems.