Common stochastic inputs induce neuronal transient synchronization with partial reset

Abstract

Neuronal synchronization plays important roles in information encoding and transmission in the brain. Mathematical models of neurons have been widely used to simulate synchronization behavior and analyze its mechanisms. Common stochastic inputs are considered to be effective in facilitating synchronization. However, the mechanisms of how partial reset affects neuronal synchronization are still not well understood. In this paper, the synchronization of Stein’s model neurons with partial reset is studied. The differences in synchronization mechanisms between neurons with full reset and those with partial reset are analyzed, and the findings lead to the novel concept of transient synchronization. Furthermore, it is proven analytically that due to common stochastic inputs, Stein’s model neurons with different initial membrane potentials and partial reset achieve transient synchronization with probability 1. Additionally, a systematic numerical analysis is performed to explore the similarities and differences between full reset and partial reset regarding model parameters, synchronization time, and desynchronization behavior. Thus, partial reset is a powerful and flexible tool that facilitates neuronal synchronization while reserving the possibility of desynchronization. Our analysis also provides an alternative approach to analyze neurons of the integrate-and-fire family and a theoretical complement implying possible information encoding mechanisms in the brain.