In the Izhikevich numerical model, the inputs to a neuron are represented by the term $I$ in the dynamical equation for $v$. In the example code provided, "purely random inputs" to a neuron (called "thalamic input", given the analogy of cortical neuron modeling) are drawn from a Gaussian random variable at each time step. If the amplitude of the Gaussian random variable is held constant, the number of spikes induced by the random input is highly dependent on the time step of integration.
(I observed this phenomenon as I was trying to use decreasing time steps in integration, to show that the simulated traces would converge to a stationary value.)
I think a reasonable way to handle the unwanted variation in the strength of the random input effect is to pre-synthesize the random input traces at the beginning, and interpolate the result for a specified integration time.
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