The neuron is the most common component in our brain, we have nearly 86 billion neurons and 1000 trillion synaptic connections, estimates to a computer with a 1 trillion bit per seconds processor
Is the field of study in which we measure and simulate the neurons process. Our brain is a complex machine and its behavior is non-linear.
We need previous knowledge of electronics, ODE’s, neurobiology, chemistry, and programming.
We start with the easiest model that tries to interpret the neuronal behavior.
We can consider the neuron an electronic circuit:
Passive Membrane Model:
We solve the linear differential equation:
In absence of (Green’s Function):
where is an input current.
Add threshold :
Let be the removing charge, every
time we hit the threshold.
the reset corresponds to a short current pulse.
Here we have the simulation of a neuron using a heavystep current input first equation and Leaky-integrate and fire (LIF)
The image below shows the different Leaky-integrate and fire methods and the input current gived for the neuron.
Given an aleatory input for the neuron, we obtain the next simulation for voltage potential (, time-scale constant, , ):