Field theory of birhythmicity

Area of Science:

• Statistical Physics
• Complex Systems Dynamics
• Theoretical Physics

Background:

• Nonequilibrium dynamics are crucial in diverse systems, from physics to neuroscience.
• Key characteristics include broken fluctuation-dissipation relations and stable, non-static phases.
• Limit cycles and birhythmicity (coexisting stable cycles) represent fundamental dynamical phases.

Purpose of the Study:

• To investigate phase transitions in nonequilibrium systems using a field-theoretic approach.
• To model a single limit cycle phase with phase-amplitude coupling and its transition to a two-cycle phase.
• To analyze the impact of nonequilibrium coupling on fluctuation spectra and critical phenomena.

Main Methods:

• Development of a simple linear model for a single limit cycle phase.
• Extension of the model to incorporate a continuous transition to a two-cycle phase.
• Application of field-theoretic tools to analyze fluctuation spectra and critical behavior.
• Qualitative numerical demonstrations of theoretical predictions.

Main Results:

• Demonstrated the effect of nonequilibrium phase-amplitude coupling on fluctuation spectra.
• Identified the emergence of a critical exceptional point during the transition.
• Observed the destruction of the transition and enhanced phase noise.
• Revealed the presence of Kardar-Parisi-Zhang (KPZ) dynamics.

Conclusions:

• The study provides a theoretical framework for understanding transitions between single and double limit cycle phases in nonequilibrium systems.
• The findings highlight the significant role of phase-amplitude coupling in shaping system dynamics and critical behavior.
• The results offer insights into the complex dynamics and phase transitions relevant to various scientific fields.