Dynamics of a Large-Scale Spiking Neural Network with Quadratic Integrate-and-Fire Neurons

Abstract

Since the high dimension and complexity of the large-scale spiking neural network, it is difficult to research the network dynamics. In recent decades, the mean-field approximation has been a useful method to reduce the dimension of the network. In this study, we construct a large-scale spiking neural network with quadratic integrate-and-fire neurons and reduce it to a mean-field model to research the network dynamics. We find that the activity of the mean-field model is consistent with the network activity. Based on this agreement, a two-parameter bifurcation analysis is performed on the mean-field model to understand the network dynamics. The bifurcation scenario indicates that the network model has the quiescence state, the steady state with a relatively high firing rate, and the synchronization state which correspond to the stable node, stable focus, and stable limit cycle of the system, respectively. There exist several stable limit cycles with different periods, so we can observe the synchronization states with different periods. Additionally, the model shows bistability in some regions of the bifurcation diagram which suggests that two different activities coexist in the network. The mechanisms that how these states switch are also indicated by the bifurcation curves.

Neurochip3: An Autonomous Multichannel Bidirectional Brain-Computer Interface for Closed-Loop Activity-Dependent Stimulation

“…The advantage of optogenetic stimulation for closed-loop applications is the absence of an electrical artifact, the ability to deliver brief activity-dependent inhibitory events and to target stimulation to specific cell types. Neural network simulations predict that spike-triggered inhibitory stimulation could lead to decreases in the strength of synaptic connections ( Shupe and Fetz, 2021 ).…”

“…The NC3 can run an integrate-and-fire spiking neural network (SNN) on the FPGA in parallel with its other operations. Details of the SSN are described elsewhere ( Shupe and Fetz, 2021 ). This feature can be used to process multiple inputs and generate events to trigger stimuli.…”

“…If Vj(t) reaches threshold it is reset to 0 and the unit sends a spike to all of its target units, which will cause a Post Synaptic Potential proportional to Wij. These PSPs may be excitatory or inhibitory, depending on the sign of Wij (for more details see Shupe and Fetz, 2021 ).…”