Transition from amplitude to oscillation death under mean-field diffusive coupling.

Area of Science:

• Complex Systems
• Nonlinear Dynamics
• Network Science

Background:

• Amplitude death (AD) and oscillation death (OD) are distinct states in coupled oscillator systems.
• Understanding transitions between these states is crucial for characterizing complex oscillatory networks.

Purpose of the Study:

• To investigate the transition from amplitude death (AD) to oscillation death (OD) in limit-cycle oscillators.
• To analyze the role of mean-field diffusion coupling in inducing this transition.
• To identify and characterize novel states, such as nontrivial AD (NTAD).

Main Methods:

• Analysis of limit-cycle oscillators coupled via mean-field diffusion.
• Identification of parameter regions for state coexistence.
• Investigation of bifurcation mechanisms, specifically subcritical pitchfork bifurcation.
• Extension to network analysis of coupled oscillators.

Main Results:

• Mean-field diffusion coupling can induce a transition from AD to OD, even in identical oscillators.
• A parameter region exists where OD and a unique NTAD state coexist.
• The NTAD state arises from a subcritical pitchfork bifurcation and is sensitive to parameter mismatch.
• In oscillator networks, the transition scenario persists, leading to a two-cluster state.

Conclusions:

• Mean-field diffusion coupling provides a mechanism for state transitions in oscillatory systems.
• The discovery of the NTAD state and its properties offers new insights into oscillator dynamics.
• The findings are applicable to understanding collective behavior in large networks of coupled oscillators.