Leaky integrator
In mathematics, a leaky integrator equation is a specific differential equation, used to describe a component or system that takes the integral of an input, but gradually leaks a small amount of input over time. It appears commonly in hydraulics, electronics, and neuroscience in single-neuron models.[1]
Equation
The equation is of the form
where C is the input and A is the rate of the 'leak.'
General solution
Its general solution is
where k is a constant.
References
- ^ Eliasmith, Anderson, Chris, Charles (2003). Neural Engineering. Cambridge, Massachusetts: MIT Press. pp. 81.
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