Chaotic Phase Synchronization in Bursting-neuron Models Driven by a Weak Periodic Force

TL;DR

This paper explores how a chaotic neuron model with multiple time scales can synchronize with a weak periodic force, revealing complex phase locking behaviors and unique transition phenomena.

Contribution

It introduces a novel detection method for phase synchronization in systems with multiple time scales and characterizes the transition phenomena in chaotic bursting neurons.

Findings

Multiple phase locking types observed, including 1:1 and 1:l synchronization.

Power-law scaling of phase slip intervals near transition points.

Stepwise behavior of Kuramoto's order parameter before synchronization.

Abstract

We investigate the entrainment of a neuron model exhibiting a chaotic spiking-bursting behavior in response to a weak periodic force. This model exhibits two types of oscillations with different characteristic time scales, namely, long and short time scales. Several types of phase synchronization are observed, such as 1 : 1 phase locking between a single spike and one period of the force and 1 : l phase locking between the period of slow oscillation underlying bursts and l periods of the force. Moreover, spiking-bursting oscillations with chaotic firing patterns can be synchronized with the periodic force. Such a type of phase synchronization is detected from the position of a set of points on a unit circle, which is determined by the phase of the periodic force at each spiking time. We show that this detection method is effective for a system with multiple time scales. Owing to the existence of both the short and the long time scales, two characteristic phenomena are found around the transition point to chaotic phase synchronization. One phenomenon shows that the average time interval between successive phase slips exhibits a power-law scaling against the driving force strength and that the scaling exponent has an unsmooth dependence on the changes in the driving force strength. The other phenomenon shows that Kuramoto's order parameter before the transition exhibits stepwise behavior as a function of the driving force strength, contrary to the smooth transition in a model with a single time scale.