Mechanisms for bump state localization in two-dimensional networks of leaky Integrate-and-Fire neurons

TL;DR

This paper investigates mechanisms to stabilize bump states in two-dimensional networks of leaky Integrate-and-Fire neurons, highlighting the roles of refractory periods and node inactivation in controlling asynchronous domain movement.

Contribution

It introduces novel insights into stabilizing bump states using refractory periods and node inactivation, with an analytical approach for stationary bump states in large networks.

Findings

Refractory periods can anchor asynchronous domains.

Inactivating nodes stabilizes domain positions and halts oscillations.

Large networks with many inactive nodes reach a frozen, non-oscillatory state.

Abstract

Networks of nonlocally coupled leaky Integrate-and-Fire neurons exhibit a variety of complex collective behaviors, such as partial synchronization, frequency or amplitude chimeras, solitary states and bump states. In particular, the bump states consist of one or many regions of asynchronous elements within a sea of subthreshold (quiescent) elements. The asynchronous domains travel in the network in a direction predetermined by the initial conditions. In the present study we investigate the occurrence of bump states in networks of leaky Integrate-and-Fire neurons in two-dimensions using nonlocal toroidal connectivity and we explore possible mechanisms for stabilizing the moving asynchronous domains. Our findings indicate that I) incorporating a refractory period can effectively anchor the position of these domains in the network, and II) the switching off of some randomly preselected nodes (i.e., making them permanently idle/inactive) can likewise contribute to stabilizing the positions of the asynchronous domains. In particular, in case II for large values of the coupling strength and a large percentage of idle elements, all nodes acquire different fixed (frozen) values in the quiescent region and oscillations cease throughout the network due to self-organization. For the special case of stationary bump states, we propose an analytical approach to predict their properties. This approach is based on the self-consistency argument and is valid for infinitely large networks. Case I is of particular biomedical interest in view of the importance of refractoriness for biological neurons, while case II can be biomedically relevant when designing therapeutic methods for stabilizing moving signals in the brain.