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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.

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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.

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  • $\begingroup$ So this could in a way be thought of as a cell receiving stimulus over a period of time (as the integrator) and the decay (leak) due to other chemical activity? $\endgroup$
    – Synex
    Oct 27 '13 at 13:56
  • $\begingroup$ That's what I imagined when you mentioned neuroscience. Though my understanding is that neurons themselves don't obey nice smooth equations like that one. Perhaps a neuron is a leak integrate as long is it remains below threshold "use it or loose it". $\endgroup$ Oct 27 '13 at 14:12

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