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]
The equation is of the form
dx/dt=-Ax+C
where C is the input and A is the rate of the 'leak'.
The equation is a nonhomogeneous first-order linear differential equation. For constant C its solution is
x(t)=ke-At+
| C | |
| A |
where
k