Dynamical Phase Transitions In Driven Integrate-And-Fire Neurons

TL;DR

This paper investigates the complex dynamics and phase transitions of an integrate-and-fire neuron under oscillatory input, revealing novel bifurcation types and scaling laws in neural firing patterns.

Contribution

It introduces a detailed analysis of phase locking and bifurcation phenomena in driven neurons, identifying new types of phase transitions and their scaling behaviors.

Findings

Identification of tangent and discontinuous bifurcations in neuron dynamics

Discovery of a new intermediate phase transition type

Characterization of scaling laws for different bifurcation types

Abstract

We explore the dynamics of an integrate-and-fire neuron with an oscillatory stimulus. The frustration due to the competition between the neuron's natural firing period and that of the oscillatory rhythm, leads to a rich structure of asymptotic phase locking patterns and ordering dynamics. The phase transitions between these states can be classified as either tangent or discontinuous bifurcations, each with its own characteristic scaling laws. The discontinuous bifurcations exhibit a new kind of phase transition that may be viewed as intermediate between continuous and first order, while tangent bifurcations behave like continuous transitions with a diverging coherence scale.