🧠 Spiking Neural Network

It is a simplified neuron model where a single variable, the membrane potential V, decays toward a resting value over time (the "leak") while also integrating incoming current from external drive and synaptic input. When V crosses a fixed threshold, the neuron emits a spike, V resets, and the neuron becomes briefly unresponsive during a refractory period. It captures the essential spiking behaviour of real neurons without modelling detailed ion-channel biophysics.

K sets how many random directed synapses each neuron sends to other neurons in the network, controlling how densely connected the population is. Excitatory fraction sets what percentage of neurons add positive current to their targets when they spike, versus the remainder, which are inhibitory and subtract current, taming runaway activity.

It compares how evenly spikes are spread over time against how clumped they are. Spike times are grouped into short 20-millisecond bins across the last second, and the variance of spike counts across those bins is normalised by the mean. A low value means neurons fire fairly independently and evenly over time; a high value means many neurons tend to spike together in tight bursts.

When excitatory coupling is strong relative to inhibition, a few neurons firing together deliver enough extra current to push many of their neighbours over threshold at once, and that burst cascades through the network. This runaway effect is reduced by increasing the inhibitory fraction or lowering coupling strength and external drive, which is exactly what the Inhibition-dominated and Sparse presets demonstrate.

It captures core principles of spiking dynamics — thresholds, refractory periods, excitation/inhibition balance, and network-driven synchrony — but it is a simplified model, not a biophysically detailed simulation. It uses arbitrary units and a random directed-graph connectivity rather than realistic axon delays, dendritic geometry, or ion-channel kinetics, so it is best used to build intuition about network-level spiking behaviour rather than to reproduce quantitative experimental data.