Correlation Analysis of Synchronization Type and Degree in Respiratory Neural Network.

Jieqiong Xu,Quan Yuan,Huiying Chen,Raşit Köker

doi:10.1155/2021/4475184

Jieqiong Xu, Quan Yuan + Show 2 more

Open Access

https://doi.org/10.1155/2021/4475184

Copy DOI

Abstract

Pre-Bötzinger complex (PBC) is a necessary condition for the generation of respiratory rhythm. Due to the existence of synaptic gaps, delay plays a key role in the synchronous operation of coupled neurons. In this study, the relationship between synchronization and correlation degree is established for the first time by using ISI bifurcation and correlation coefficient, and the relationship between synchronization and correlation degree is discussed under the conditions of no delay, symmetric delay, and asymmetric delay. The results show that the phase synchronization of two coupling PBCs is closely related to the weak correlation, that is, the weak phase synchronization may occur under the condition of incomplete synchronization. Moreover, the time delay and coupling strength are controlled in the modified PBC network model, which not only reveals the law of PBC firing transition but also reveals the complex synchronization behavior in the coupled chaotic neurons. Especially, when the two coupled neurons are nonidentical, the complete synchronization will disappear. These results fully reveal the dynamic behavior of the PBC neural system, which is helpful to explore the signal transmission and coding of PBC neurons and provide theoretical value for further understanding respiratory rhythm.

Highlights

Synchronous in the neuronal network, a complex population-firing pattern, is believed to play a critical role in many brain functions and many fundamental biological functions
By calculating the interspike interval (ISI), correlation coefficient, maximum synchronization difference, and similarity function of the coupled chaotic system, it is found that there is a complex synchronous transition behavior in the coupled Pre-Botzinger complex (PBC) network, including asynchronization, weak synchronization, and complete synchronization. e degree of synchronization between the two coupling neurons is judged by the correlation coefficient
It is found that when the coupling is negative, the two coupling neurons undergo fully synchronous period-3 bursting, and they get transit to approximate synchronization

Summary

Introduction

Synchronous in the neuronal network, a complex population-firing pattern, is believed to play a critical role in many brain functions and many fundamental biological functions. Duan et al studied the bursting dynamics of the two-coupled PBC complex neurons and explored the possible forms of dynamics that the model network could produce as well the transitions of in- and anti-phase bursting, respectively [47]. Ey observed a new type of mixed burst similar to a depolarization block bursting (DBbursting) in the model of PBC neurons and studied the types of mixed burst and their transition mechanisms by using the multi-time-scale dynamics and one- and two-parameter bifurcation analysis, as well as investigated the effects of persistent sodium conductance on the anti-phase synchronization pattern in coupled PBC neurons [48].

Single Compartment PBC Neuron Model

Lag Synchronization under Nonidentical Coupling

Conclusion