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. The equation is of the form 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 where is a constant encoding the initial condition.