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Time-delayed Duffing oscillator in an active bath
Antonio A Valido1, Mattia Coccolo1, Miguel A F Sanjuán1
1Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid, Spain.
Physical Review. E
|January 20, 2024
Summary
Active particles, modeled by stochastic processes, exhibit complex dynamics in forced, time-delayed Duffing oscillators. Noise and time delay interplay to alter oscillation amplitude and frequency, revealing stochastic resonance effects.
Area of Science:
- Nonlinear dynamics
- Statistical physics
- Active matter physics
Background:
- Active particles are ubiquitous in natural and artificial systems.
- Their dynamics are often modeled using stochastic processes with Gaussian white and Ornstein-Uhlenbeck noises.
- Time-delayed systems introduce complex behaviors not seen in non-delayed counterparts.
Purpose of the Study:
- Investigate the nonlinear dynamics of a forced, time-delayed Duffing oscillator under different noise types.
- Analyze the impact of time delay, noise strength, and driving force on oscillation amplitude and frequency.
- Explore the interplay between noise, forcing, and time delay in shaping system dynamics.
Main Methods:
- Numerical simulation of the forced, time-delayed Duffing oscillator.
- Analysis of steady-state oscillation amplitude and characteristic frequency.
- Systematic variation of noise strength, driving force amplitude, and time delay values.
Main Results:
- Time delay significantly modifies the system's response to noise compared to non-delayed systems.
- Oscillation amplitude can increase with noise strength when time delay acts as damping.
- Trajectories transition from periodic to aperiodic, influenced by the competition between noise and driving force.
- Stochastic resonance can promote interwell motion under specific noise and forcing conditions.
Conclusions:
- The interplay of noise, forcing, and time delay creates rich and complex dynamics in the Duffing oscillator.
- Time delay's role is context-dependent, capable of both damping and sustaining oscillations.
- Noise can either disrupt or restore regular motion, depending on the system parameters and time delay effects.
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