Subharmonic oscillations in stochastic systems under periodic driving.

Area of Science:

• Nonlinear dynamics
• Stochastic processes
• Statistical physics

Background:

• Subharmonic response is a known phenomenon in deterministic nonlinear systems.
• Open systems with stochastic dynamics are influenced by thermal fluctuations.
• Coherent oscillations in stochastic autonomous systems are limited by network states.

Purpose of the Study:

• Investigate conditions for persistent subharmonic oscillations in open stochastic systems.
• Explore the behavior of subharmonic oscillations in periodically driven systems.
• Analyze the thermodynamic cost and period scaling of persistent subharmonic responses.

Main Methods:

• Analysis of stochastic nonlinear dynamical systems.
• Theoretical modeling of periodically driven open systems.
• Model calculations for thermodynamic cost and period scaling.

Main Results:

• Subharmonic oscillations can persist indefinitely in periodically driven systems, irrespective of network size.
• Thermodynamic cost of persistent oscillations scales logarithmically with the number of coherent oscillations.
• Periods of persistent subharmonic response scale linearly with the number of network states.

Conclusions:

• Periodic driving enables sustained subharmonic oscillations in open stochastic systems.
• Findings are relevant for biochemical oscillations and stochastic models of time crystals.
• Demonstrates a mechanism for long-lived coherent behavior in small, open networks.