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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?

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Another example:

Would you use differential equations? Variational calculus?

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# How to study feedback? Which branch of Mathematics does it?

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