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I am looking for a mathematical field that deal with this concept, I don't have a very formal definition of this and I'll have to count on these naive definitions I provided:

  1. It's about the idea of an adaptative live system;

  2. The system evolves with time cycles;

  3. This system has $n$ properties;

    • I am expressing a naive understanding of the meaning of properties, but it should be something like a function that would alter the output at some time cycles.
  4. The system has a smaller number $p$ of properties to keep itself alive;

    • It will work with any properties, as long as $n\geq p$;

    • For every subset of properties, this system is going to yield different outputs.

Considering such a thing exist, what mathematical field would deal with it? I've had some naive readings about some fields such as mathematical biology, mathematical modeling, automata and perhaps game theory. Could you point me to something more specific?

Motivation:

It's more a philosophical issue: In my entire life, I've heard arguments such as "without $y$, makind could not exist" (where $x$ is a aribtrary property). But I always felt that there's something wrong with such class of arguments, if I can demonstrate the existence of such a system, I could suggest the hypothesis that the system we're in could exist with or without some properties that are considered essential. I guess there are probably a lot of works that adress the issue I'm having but for me it seems that showing such scenario could be a feasible speculation of other possible worlds.

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I think in order to get a good answer, you have to try to explain what sort of thing you would regard as interesting. –  Johan Wästlund May 17 '13 at 8:05
    
I've introduced my motivation and what I would consider as interesting. –  Vÿska May 17 '13 at 9:28

2 Answers 2

up vote 2 down vote accepted

I think you are looking for dynamical systems theory.

In particular (especially discrete) cases you might be interested in automata theory, modal logic and game theory. But your “definition” sounds more like a general notion from dynamical systems theory.

Mathematical biology and modeling are “just” applications.

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Thanks for your answer. –  Vÿska May 17 '13 at 9:28

It also sound a bit like neural networks; these are "trained" (adapted) to yield certain output for certain input.

Maybe you will also be interested in Markov processes, (which can also be trained to give certain output for some given input).

Both these concepts are related to something called genetic programming, where a large parameter space is sampled, evaluated, and mutated, so that the next iteration performs "better" than the previous.

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Thanks for your answer. –  Vÿska May 17 '13 at 9:28

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