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:
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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*.



What mathematical field work with this kind of concept?
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.


