Aging transition in systems of oscillators with global distributed-delay coupling

Area of Science:

• Complex systems
• Nonlinear dynamics
• Network science

Background:

• Globally coupled networks of oscillators are fundamental in various scientific fields.
• Understanding transitions to complex network states, like aging, is crucial for predicting system behavior.
• The influence of distributed delays on network dynamics, particularly oscillation suppression, requires further investigation.

Purpose of the Study:

• To derive conditions for aging transition in a network of active and inactive oscillators with distributed-delay coupling.
• To analyze the impact of uniform and gamma delay distributions on aging transition.
• To determine the role of coupling parameters and the proportion of inactive oscillators in achieving aging transition.

Main Methods:

• Mathematical derivation of conditions for aging transition.
• Analysis of uniform delay distribution properties.
• Analysis of gamma delay distribution properties.
• Investigation of coupling strength and proportion of inactive elements.

Main Results:

• Conditions for aging transition were derived for both uniform and gamma delay distributions.
• For uniform delays, increasing distribution width (for constant mean delay) lowers the required coupling strength and inactive proportion for aging.
• For gamma delays, aging transition is achievable for any proportion of inactive oscillators within a specific coupling strength range, especially with large mean delays.

Conclusions:

• The characteristics of delay distributions significantly influence the conditions for aging transition in coupled oscillator networks.
• Network aging, characterized by oscillation suppression, can be controlled by tuning delay distribution parameters and coupling strength.
• These findings offer insights into designing and controlling complex oscillatory systems.