Golden triangle (mathematics)

File:Leakyintegrator.png

A graph of a leaky integrator; the input changes at T=5.

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. Template:Clarify

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

$x(t)=ke^{-At}+Ct\,$

where k is a constant.

References

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