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Oscillation quenching induced by time-varying coupling functions.
Dushko Stavrov1, Aneta Koseska2, Tomislav Stankovski3,4
1Faculty of Electrical Engineering and Information Technologies, Ss. Cyril and Methodius University, Skopje, North Macedonia.
Chaos (Woodbury, N.Y.)
|December 4, 2025
Summary
We developed a framework to analyze and control oscillation quenching in systems with time-varying interactions. This method identifies novel states and uses a controller to maintain oscillations, preventing quenching.
Area of Science:
- Nonlinear Dynamics
- Complex Systems Analysis
Background:
- Time-varying interactions can disrupt oscillatory dynamics in natural and man-made systems.
- This disruption leads to oscillation quenching, where oscillations are suppressed.
Purpose of the Study:
- To introduce a framework for analyzing, assessing, and controlling oscillation quenching.
- To investigate bifurcations and dynamical transitions induced by time-varying coupling functions.
Main Methods:
- Analysis of limit-cycle oscillators with time-varying diffusive and periodic coupling functions.
- Investigation of transitions between oscillation quenching states with invariant coupling strength.
- Application of dynamical Bayesian inference to develop a controller.
Main Results:
- Identified novel, non-trivial inhomogeneous states using time-varying periodic coupling functions.
- Developed a Proportional Integral controller to maintain oscillations and prevent quenching.
- Demonstrated a framework for controlling oscillation quenching in systems with time-varying interactions.
Conclusions:
- The proposed framework effectively analyzes and controls oscillation quenching.
- Novel dynamical states can emerge from time-varying periodic coupling.
- The framework has broad implications for controlling oscillations in various systems.
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