Occasional coupling enhances amplitude death in delay-coupled oscillators

Area of Science:

• Nonlinear Dynamics
• Complex Systems
• Control Theory

Background:

• Oscillatory states can be detrimental in systems like thermoacoustic combustors, where a stable, non-oscillatory state (amplitude death) is preferred.
• Time delay coupled oscillators are common in various physical and biological systems.
• Intermittent interactions, or occasional coupling, offer a novel approach to controlling oscillator dynamics.

Purpose of the Study:

• To investigate the effectiveness of an occasional coupling scheme in enhancing amplitude death regions in time delay coupled oscillators.
• To analyze the impact of intermittent interactions on coupled limit cycle, chaotic, and thermoacoustic systems.
• To explore the role of control parameters like coupling strength, frequency ratio, and time delay in conjunction with occasional coupling.

Main Methods:

• Utilized coupled limit cycle (Stuart-Landau) and chaotic (Rössler) oscillators.
• Applied occasional coupling schemes, including on-off (square wave) and half-wave rectified sinusoidal functions.
• Performed linear stability analysis to understand the mechanisms behind the enhanced amplitude death regions.

Main Results:

• Occasional coupling significantly enhances amplitude death regions compared to continuous coupling across different oscillator types.
• The intermittent interaction expands the parameter space for achieving amplitude death.
• Similar enhancements were observed when using frequency ratio and time delay as control parameters with occasional coupling.

Conclusions:

• Occasional coupling is a viable and effective strategy for achieving and enhancing amplitude death in time delay coupled systems.
• This method offers a practical approach to suppress undesirable oscillations in sensitive systems, such as thermoacoustic devices.
• The findings provide valuable insights for designing and controlling complex oscillatory networks.