LIF Neuron Equation Solution for arbitrary time-dependent current (Neural Dynamics)

In summary, the "LIF Neuron Equation Solution for arbitrary time-dependent current (Neural Dynamics)" discusses the mathematical modeling of leaky integrate-and-fire (LIF) neurons in response to varying input currents over time. The paper presents a solution that allows for the analysis of neuron dynamics under complex stimuli, enabling predictions of neuronal behavior. By deriving equations that account for both the leaky behavior of the membrane and the integration of input current, the study enhances the understanding of neural response patterns and their implications in computational neuroscience.
  • #1
gigorina
1
0
In the book Neural Dynamics: https://neuronaldynamics.epfl.ch/online/Ch1.S3.html

There is a solution to the following differential equation (LIF Neuron) for arbitrary time-dependent current. I was trying to figure out the steps the author took to get to the solution.

Original Equation:
Screenshot 2024-01-07 at 21.49.10.png

Solution:
Screenshot 2024-01-07 at 21.49.02.png
 

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