Detecting the temporal structure of intermittent phase locking

TL;DR

This paper introduces a method to analyze the temporal structure of intermittent phase locking in oscillatory systems, focusing on the dynamics of synchronization and desynchronization episodes beyond traditional stability measures.

Contribution

It proposes a novel approach to characterize intermittent phase locking by examining phase relationships over cycles, applicable to various oscillatory systems including neural models.

Findings

The method quantifies timing and duration of phase locking loss and recovery.

It distinguishes differences in synchronization dynamics among similar systems.

Applicable to coupled maps, oscillators, and neural models.

Abstract

This study explores a method to characterize temporal structure of intermittent phase locking in oscillatory systems. When an oscillatory system is in a weakly synchronized regime away from a synchronization threshold, it spends most of the time in parts of its phase space away from synchronization state. Therefore characteristics of dynamics near this state (such as its stability properties/Lyapunov exponents or distributions of the durations of synchronized episodes) do not describe system's dynamics for most of the time. We consider an approach to characterize the system dynamics in this case, by exploring the relationship between the phases on each cycle of oscillations. If some overall level of phase locking is present, one can quantify when and for how long phase locking is lost, and how the system returns back to the phase-locked state. We consider several examples to illustrate this approach: coupled skewed tent maps, which stability can be evaluated analytically, coupled R\"{o}ssler and Lorenz oscillators, undergoing through different intermittencies on the way to phase synchronization, and a more complex example of coupled neurons. We show that the obtained measures can describe the differences in the dynamics and temporal structure of synchronization/desynchronization events for the systems with similar overall level of phase locking and similar stability of synchronized state.