Leaky integrator in novice terms I have read few article on the leaky integrator including the Wikipedia. They all give the same equation and the graph and say it is applicable in areas such as neuroscience etc. But I still cannot understand how this works in practice. So I would like to know an example scenario how a leaky integrator works in real world. I do not want equations just a plain scenario would do to make it clear in my mind.

An example might be a resistor-capacitor filter in electronics. The charge on the capacitor will be the integral of the current you pour into it (and the voltage across it proportional to the charge). However if the capacitor is in parallel with a resistor, it will discharge ("leak") through that resistor. Thus it's equation of motion will be

$$ I = C{dV\over dt} + V/R $$

which you can re-arrange to get the ODE shown on the Wikipedia.