Golden triangle (mathematics): Difference between revisions
en>Helpful Pixie Bot m ISBNs (Build KE) |
en>David Eppstein |
||
| Line 1: | Line 1: | ||
[[Image:Leakyintegrator.png|thumb|right|250px|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.<ref>{{cite book|last=Eliasmith, Anderson|first=Chris, Charles|title=Neural Engineering|year=2003|publisher=MIT Press|location=Cambridge, Massachusetts|pages=81}}</ref> {{Clarify|date=July 2009}} | |||
==Equation== | |||
The equation is of the form | |||
:<math>dx/dt = -Ax + C \,</math> | |||
where C is the input and A is the [[Time constant|rate of the 'leak']]. | |||
===General solution=== | |||
Its general solution is | |||
:<math>x(t) = ke^{-At} + Ct \,</math> | |||
where k is a constant. | |||
==References== | |||
{{reflist}} | |||
{{DEFAULTSORT:Leaky Integrator}} | |||
[[Category:Differential equations]] | |||
{{mathanalysis-stub}} | |||
{{mathapplied-stub}} | |||
Revision as of 00:04, 16 December 2013
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] Template:Clarify
Equation
The equation is of the form
where C is the input and A is the rate of the 'leak'.
General solution
Its general solution is
where k is a constant.
References
43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.
Template:Mathanalysis-stub Template:Mathapplied-stub
- ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534