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 where it can represent either a single neuron or a local population of neurons.[1]
![](../I/m/Leakyintegrator.png)
A graph of a solution to a leaky integrator; the input changes at T=5.
This is equivalent to a 1st-order lowpass filter with cutoff frequency far below the frequencies of interest.
Equation
The equation is of the form
where C is the input and A is the rate of the 'leak'.
General solution
As the equation is a nonhomogeneous first-order linear differential equation, its general solution is
where is a constant, and is an arbitrary solution of the equation.
gollark: Also FPGAs.
gollark: Also, they now make GPUs and optical networking gear and WiFi chips and a bunch of other random nonsense.
gollark: You DO realize that they are massively bigger than AMD and make up basically the entire server market still?
gollark: What? No.
gollark: IIRC their Atoms from the time were pretty competitive with ARM. But they never took off because... I'm not actually sure.
References
- Eliasmith, Anderson, Chris, Charles (2003). Neural Engineering. Cambridge, Massachusetts: MIT Press. pp. 81.
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