Universal behavior in populations composed of excitable and self-oscillatory elements

Area of Science:

• Dynamical systems theory
• Nonlinear dynamics
• Statistical physics

Background:

• Globally coupled ensembles of excitable and oscillatory units can exhibit complex collective behaviors.
• Understanding the conditions for robust self-sustained oscillations is crucial in various scientific fields.
• The
• aging transition
• framework describes phenomena in systems with evolving properties.

Purpose of the Study:

• To analyze the robustness of self-sustained oscillatory activity in globally coupled systems.
• To determine the critical balance required for collective self-sustained oscillations.
• To extend the existing
• aging transition
• theory to a broader range of dynamical systems.

Main Methods:

• Analytical investigation of coupled excitable and oscillatory units.
• Mathematical derivation of critical conditions for collective oscillations.
• Development of a universal scaling function for ensemble mean frequency.

Main Results:

• The critical balance for achieving collective self-sustained oscillations was analytically established.
• A universal scaling function describing the ensemble's mean frequency was identified.
• The findings extend the applicability of the
• aging transition
• framework.

Conclusions:

• Self-sustained oscillations in globally coupled systems exhibit robust collective behavior under specific conditions.
• The identified universal scaling law provides a predictive tool for ensemble frequency.
• This research broadens the scope of dynamical systems explained by the
• aging transition
• theory, with potential biological applications.