The step size impact on the computational cost of spiking neuron simulation

Spiking neurons are mathematical models that simulate the generation of the electrical pulse at the neuron membrane. Most spiking neurons are expressed as a non-linear system of ordinary differential equations. Because these systems are hard to solve analytically, they must be solved using a numerical method through a discrete sequence of time steps. The step length is a factor affecting both the accuracy and computational cost of spiking neuron simulation. It is known the step size implications on the accuracy for some spiking neurons. However, it is unknown in which way the step size impacts the computational cost. We found that the computational cost as a function of the step length follows a power-law distribution. We reviewed the Leaky Integrate-and-Fire, Izhikevich, and Hodgkin-Huxley spiking neurons. Additionally, it was found that, with any step size, simulating the cerebral cortex in a sequential processing computer is prohibitive.