Subsystem Resetting of a Heterogeneous Network of Theta Neurons

TL;DR

This paper investigates how partial stochastic resetting of neurons in a heterogeneous theta network influences overall stability, revealing that high reset rates stabilize the network while finite rates induce complex, sometimes unpredictable dynamics.

Contribution

It introduces the concept of partial resetting in theta neuron networks and analyzes its effects on stability and dynamics, extending understanding of neural network control mechanisms.

Findings

High reset rates stabilize network to rest or spiking states

Finite reset rates cause stochastic fluctuations and complex behaviors

Partial resetting can effectively control neural stability

Abstract

Stochastic resetting has shown promise in enhancing the stability of dynamical systems. Here, we apply this concept to theta neuron networks with partial resetting, where only a fraction of neurons is intermittently reset. We examine both infinite and finite reset rates, using the averaged firing rate as an indicator of network stability. At infinite reset rates, a high proportion of resetting neurons drives the network to stable rest or spiking states, collapsing the bistable region at the Cusp bifurcation and producing smooth transitions. Finite resetting introduces stochastic fluctuations, leading to complex dynamics that sometimes deviate from theoretical predictions. These insights highlight the role of partial resetting in stabilizing neural dynamics, with applications in biological systems and neuromorphic computing.