A neuron is composed of three main parts; the soma (cell body), the dendrites, and the axon. The soma contains the nucleus, the dendrites receive synaptic input (neurotransmitters), and the axon releases the neurotransmitters. The large branching structure of the dendrites and axon terminal allow each neuron to have connections to thousands of other neurons, forming a massive communication web.
A neuron communicates via action potentials. An action potential is an electric pulse that travels down the axon until it reaches the synapses, where it then causes the release of neurotransmitters. These action potentials are known as neuron firing or neuron spiking (1). Spiking neural networks (SNNs) fall into the third generation of neural network models, increasing the level of realism in a neural simulation. SNNs have become widely used in a variety of biological and engineering applications, and to date there have been a large number of neuron models that have been proposed in the scientific literature. The idea is that neurons in the SNN do not fire at each propagation cycle (as it happens with typical multi-layer perceptron networks), but rather fire only when an action potential reaches a specific value (2). This paper seeks to better understand the neuron models that are used in such endeavors, and to propose recommendations for which models should be used in certain circumstances and the computational costs of the different neuron models used to construct these spiking networks. It is important to simulate the behavior of individual neurons exactly. To these ends, this paper not only examines the cost of implementing different solution methods on different neuron models, but also studies how different time resolutions affect a neuron model’s accuracy.
The Hodgkin–Huxley model is one of the most biophysically meaningful models of neuron spiking. Designed from the study of a squid giant axon, this model was proposed to describe the response of a neuron to external current stimulation, and included the effects of different ionic channels and leakage currents. The Hodgkin–Huxley model involves a system of nonlinear ordinary differential equations. From these equations, it is easy to obtain the impression that the Hodgkin–Huxley model is a very computationally expensive system, inherently complex, and only viable for small neural networks. However, if coded correctly, those impressions can be implemented in a manner that is more computationally efficient than most competing models (2, 3).
One alternative to the biologically realistic Hodgkin–Huxley model is the Izhikevich model, introduced for its computational efficiency. This model of neuron spiking involves less than half the equations of the Hodgkin–Huxley model, yet seems to replicate most of the neuron-spiking behaviors. The tradeoff, then, was that this model was not biologically realistic, but rather phenomenological. The Izhikevich model has become one...