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How to study feedback? Which branch of Mathematics does it? 
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#1
Jun2514, 01:11 PM

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Hello,
I want to study a system, and I have realized that all variables in it are dependent. There is no independent variable. So everytime you modify the input, you get an output but at the same time that output modifies the input itself, there is an important feedback. So the system apparently is evolving searching a kind of equilibrium but it does it in several steps and I find it difficult to "isolate" one variable, or analyze what is the relationship between variables since they are affected by the rest of the system. I will try to put an example, hopefully it will show the main characteristics I am talking about. In the atmosphere if there is a raise in the amount of energy that arrives from the sun, the temperature raises. But that changes the amount of water the air can contain, and that modifies the amount of radiation that the atmosphere absorbs which is the factor we started analyzing. My question is, What is the best mathematical tool to understand systems where feedback between variables is key?  Another example: Would you use differential equations? Variational calculus? 


#3
Jun2514, 02:58 PM

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It has nothing to do with Chaos theory unless the system happens to be chaotic, and many systems as complex as the OP's picture are not.
Differential equations, signal processing (analog and digital), and control systems (stability analysis, etc) would be good topics to start learning. You may need some probability theory as well. 


#4
Jun2514, 03:09 PM

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How to study feedback? Which branch of Mathematics does it?
With 'feed back', this would be "nonlinear differential equations" or, more generally, "nonlinear analysis".



#5
Jun2514, 03:40 PM

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It's not 'chaos theory' you are looking for, but 'control theory' which deals with inputs to dynamical systems and the resulting feedback:
http://en.wikipedia.org/wiki/Control_theory It's not a branch of pure mathematics which deals with feedback, but a blend of math and engineering, an interdisciplinary effort. 


#6
Jun2514, 03:43 PM

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#7
Jun2514, 03:47 PM

P: 134

I mean, in mechanics you could go to a laboratory and analyze a pendulum. But the problem is that I can't do any experiment, it is like the atmosphere, you can't stop it and analyze any specific variable. Everything is mixed together and evolving constantly in time. The same problem you have in astrophysics, you can't stop the universe nor isolate a galaxy, I can just watch everything mixed and changing in time. Does that matter for control theory? 


#8
Jun2514, 04:27 PM

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You can't easily experiment with a system like the earth's atmosphere, but you can collect data and use it to estimate the parameters that control how the system behaves. That procedure is called "system identification". 


#9
Jun2514, 04:38 PM

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