The #Izhikevichmodel is a powerful tool for simulating the #spiking and bursting behavior of #neurons with a remarkable balance between biological relevance and computational efficiency Here is a short introduction along with a #Python implementation to simulate various types of #cortical neurons, including regular spiking, fast spiking, and bursting neurons:
https://www.fabriziomusacchio.com/blog/2024-04-29-izhikevich_model/
Feel free to share and experiment with it
Unfortunately, I wasn’t able to replicate one type of neuron from the original publication (https://www.izhikevich.org/publications/spikes.pdf): Resonator neurons (RZ) I tried different values and different input currents, without success. If you have any suggestions on how to simulate the resonator behavior, please let me know
@pixeltracker Without knowing what you tried and taking in account that I haven't done those in particular, I would bet that the intensity kick needs to happen in a very particular way. The neurons resonate to inputs of certain frequency, so I'm quite sure it will be phase dependent (and the kick duration might need some fine-tuning).
The neuron will only change its state in a certain region of its phase space, and you need to perturb it at that moment.
@pixeltracker It's a cute article, seems informative for people learning these kind of models. A small personal battle I have with Izhikevich's model: I would not say that parameters are "dimensionless" , because you are measuring voltage all the time in mV, time is measured in ms, so things have an appropiate dimension. Actually, Izhikevich fitted the model (that's why there are "magic numbers" in it) to match actual neurons with actual dimensions, so the model is all but dimensionless.
@vbuendiar I fully agree with you. Due to the fit to real-world data, the initially simplified parameters and variables align with units like mV for membrane potential and ms for time. I appreciate you pointing this out! Such details are crucial for understanding the model's practical relevance and accuracy. I just checked it twice, and fortunately, I didn't forget to mention this aspect in the post. It’s always good to emphasize the significance of these 'magic numbers'. Thanks
@vbuendiar That’s a valid point, thanks. This time, I didn’t take a look at the phase plane plots, but I guess it would have been helpful here