Implementation of Izhikevich neuron model

[mstimberg]

Hi @shehnaz. This is a common reason for confusion, and we mention this issue briefly in our tutorial (Introduction to Brian part 1: Neurons — Brian 2 2.5.4 documentation). When describing physical systems, it is not meaningful to have a dimensionless right-hand-side for differential equations, even when all variables are dimensionless. An equation like \frac{dx}{dt} = -x does not make sense for a physical system: For a value of x=1, its value is to decrease by 1 , but should it decrease by this amount every second, every millisecond, every year, …? I explained this a bit in a post asking about the Van-der-Pol oscillator:

@mstimberg

Just to make the link to the mathematic formulation and e.g. the Wikipedia article more clear: By setting tau = 10*ms, you are defining your “unit of time” to be 10ms. This means when you simulate for 100ms, you simulate for “10 units of time”. If you want to plot something like https://en.wikipedia.org/wiki/Van_der_Pol_oscillator#/media/File:Vanderpol_mu=5.svg , you have to divide the time steps provided by Brian by 10ms to get the same time units on the x axis. Finally, note that Brian by default uses a simulation time step of 0.1ms (a reasonable time step for many neuron models), so with your definitions that means a simulation time step of 0.01 time units (often written as “h=0.01” in mathematical formulations).

In Izhikevich’s model, he states that all time constants are measured in ms (and similarly, membrane potentials are measured in mV, etc.), so this is the reason to divide everything by ms.

Hope that makes things clearer?