Similarly, the post-spike current arises from past spikes through a response kernel (k_{h}(t)) by (H t)=int_{-infty}^{t}k_{h} t-s mathbb{I} t-s mathbb{
The drift term (b cdot)) contains three currents: the leak current (-gamma(X t -mu)), where γ is the decay rate and μ is the reversal potential, the stimulus-driven current (I(t)), and the post-spike current (H(t)).
More biophysical realism can be obtained by allowing for post-spike currents generated by past spikes [22].
The membrane currents consist of a fast sodium current, I Na, a potassium current, I K, and a leak current, I L, collectively referred to as the spiking currents, and a slow muscarinic potassium M-current, I M.
The process was then reset to (x_{0}) and started again, while the stimulus continued without any interruption, and the previously recorded spike times entered in the calculation of the post-spike currents.
The presence of a supercritical Hopf bifurcation (magenta curve, labeled HB), introduced by the spiking currents, converts the branch of saddle nodes at the top of the Z into a limit point branch instead (blue curve, labeled LP).
Here we use post-spike currents generated via three types of kernels [23, 24]: bursting, decaying, and delaying kernel, all modeled by the difference between two decaying exponentials, but any kernel could be used.
(Because spiking currents have been removed in the derivation of Equations 1 and 2, these oscillations are interpreted as burst envelopes, i.e. neuron i is assumed to be spiking when V i is high and quiescent when V i is low).
This method has also proved quite useful for incorporating additional processing modules, such as neuronal refractoriness and after-spike currents (Paninski et al. 2004; Pillow et al. 2005).
