Synchronization of Excitatory Neurons with Strongly Heterogeneous Phase Responses

TL;DR

This paper introduces a new theoretical framework for analyzing heterogeneous oscillator networks, specifically addressing the complex phase response curves of neurons, and discovers a novel state transition in cortical neuron networks.

Contribution

The paper develops a novel method using complex phase variables to solve self-consistent equations for heterogeneous oscillator networks, advancing understanding of neural synchronization.

Findings

Identifies a new state transition in heterogeneous neuron networks.

Demonstrates the applicability of the theory to cortical neuron data.

Provides a framework for analyzing systems with diverse phase responses.

Abstract

In many real-world oscillator systems, the phase response curves are highly heterogeneous. However, dynamics of heterogeneous oscillator networks has not been seriously addressed. We propose a theoretical framework to analyze such a system by dealing explicitly with the heterogeneous phase response curves. We develop a novel method to solve the self-consistent equations for order parameters by using formal complex-valued phase variables, and apply our theory to networks of in vitro cortical neurons. We find a novel state transition that is not observed in previous oscillator network models.