Amplitude death induced by dynamic coupling.

Area of Science:

• Physics
• Nonlinear Dynamics
• Chaos Theory

Background:

• Coupled oscillators are fundamental in various scientific fields.
• Amplitude death, a phenomenon where oscillations cease, can occur in coupled systems.
• Delayed-feedback control is a technique used in chaos management.

Purpose of the Study:

• To investigate the conditions under which dynamic coupling induces amplitude death in identical oscillators.
• To establish the necessary and sufficient conditions for amplitude death in a simple limit-cycle oscillator.
• To determine if amplitude death can be prevented using specific properties of delayed-feedback control.

Main Methods:

• Theoretical analysis of coupled identical limit-cycle oscillators.
• Derivation of the condition for amplitude death.
• Investigation of the role of the odd number property in delayed-feedback control.

Main Results:

• Dynamic coupling is shown to induce amplitude death in coupled identical oscillators.
• A precise condition for amplitude death in a simple limit-cycle oscillator has been identified.
• It is proven that amplitude death never occurs if oscillators possess the odd number property.

Conclusions:

• Dynamic coupling can lead to the cessation of oscillations (amplitude death) in identical coupled systems.
• The presence of the odd number property in delayed-feedback control guarantees the persistence of oscillations, preventing amplitude death.