Beat Frequency Induced Transitions in Synchronization Dynamics

TL;DR

This study uses neuronal network simulations to explore how beat frequency interactions influence synchronization transitions, revealing characteristic timing and frequency mode emergence relevant for understanding neural dynamics.

Contribution

It introduces a novel analysis of beat frequency effects on synchronization transitions in neuronal networks, highlighting the role of frequency bifurcations and intermittent dynamics.

Findings

Frequency mode emergence at bifurcation points.

Transitions between synchronization states follow beat frequency statistics.

Frequency differences by multiples of a gap influence transition times.

Abstract

In neurosciences, the brain processes information via the firing patterns of connected neurons operating across a spectrum of frequencies. To better understand the effects of these frequencies in the neuron dynamics, we have simulated a neuronal network of Izhikevich neurons to examine the interaction between frequency allocation and intermittent phase synchronization dynamics. As the synchronized population of neurons passes through a bifurcation, an additional frequency mode emerges, enabling a match in the mean frequency while retaining distinct most probable frequencies among neurons. Subsequently, the network intermittently transits between two patterns, one partially synchronized and the other unsynchronized. Through our analysis, we demonstrate that the frequency changes on the network lead to characteristic transition times between synchronization states. Moreover, these transitions adhere to beat frequency statistics when the neurons' frequencies differ by multiples of a frequency gap. Finally, our results can improve the performance in predicting transitions on problems where the beat frequency strongly influences the dynamics.