Leaky integrator
Appearance
![](http://upload.wikimedia.org/wikipedia/en/thumb/3/3d/Leakyintegrator.png/250px-Leakyintegrator.png)
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 where it can represent either a single neuron or a local population of neurons.[1]
Equation
[edit]The equation is of the form
where C is the input and A is the rate of the 'leak'.
General solution
[edit]The equation is a nonhomogeneous first-order linear differential equation. For constant C its solution is
where is a constant encoding the initial condition.
References
[edit]- ^ Eliasmith, Anderson, Chris, Charles (2003). Neural Engineering. Cambridge, Massachusetts: MIT Press. pp. 81. ISBN 9780262050715.
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