Leaky integrator

Leaky integrator

In mathematics, a leaky integrator equation is a specific differential equation, used to describe a component or system that takes an input but gradually leaks a small amount of input over time. It appears commonly in hydraulics, electronics, and neuroscience.

Equation

The equation is of the form

:dx/dt = -Ax + C ,

where C is the input and A is the rate of the 'leak.'

General solution

Its general solution is

:x(t) = ke^{-At} + C/A ,

where k is a constant.


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