Collective phase response curves for heterogeneous coupled oscillators

Area of Science:

• * Computational neuroscience
• * Systems biology
• * Nonlinear dynamics

Background:

• * Phase response curves (PRCs) are crucial for understanding biological oscillator entrainment and synchronization.
• * Real-world biological systems often involve large, heterogeneous ensembles of coupled oscillators.
• * The collective rhythm of these ensembles, rather than individual oscillations, is often physiologically significant.

Purpose of the Study:

• * To derive an analytic formula for the collective phase response curve (PRC) in large ensembles of globally coupled Sakaguchi-Kuramoto oscillators.
• * To investigate the scaling properties of amplitude and entrainment points for collective PRCs compared to individual oscillator PRCs.
• * To demonstrate the applicability of the derived theory to neuronal oscillator networks.

Main Methods:

• * Application of Ott-Antonsen theory to derive an asymptotically valid analytic formula for the collective PRC.
• * Analysis of phase resetting for the collective rhythm in large oscillator ensembles.
• * Numerical simulations to support analytical findings.

Main Results:

• * An analytic formula for the collective PRC of globally coupled Sakaguchi-Kuramoto oscillators was derived.
• * Characteristic scaling was identified for changes in amplitude and entrainment points in collective PRCs relative to individual PRCs.
• * The theoretical framework was validated using numerical evidence.

Conclusions:

• * The derived analytic formula provides a powerful tool for understanding collective rhythms in large oscillator systems.
• * The findings offer insights into the synchronization dynamics of coupled neuronal networks.
• * This work bridges the gap between individual oscillator behavior and emergent collective phenomena.