Looking for the closest example of life forms similar to some mathematical patterns
For the second subquestion (papers or references of similar models), it could be useful for you to look at the books by J.D Murray for inspiration; Mathematical Biology, vol I &amp; II. A pdf of volume 1 can be found here, and the second volume here. Even if they are a complete of years old (last edition from 2002 I think) they provide a really nice background to the field of Mathematical biology, and he has quite many examples on pattern formation of different kinds. I don’t remember if dynamics systems are included per se though.

However, several chapters include reaction diffusion systems and wave models, to model e.g. coat/fur patterns and wound healing. It is also packed with references, so you should be able to find lots of classic citations that might be useful.

Some chapters you might find interesting:


Reaction Diffusion, Chemotaxis and Non-local Mechanisms
Travelling Waves in Reaction Diffusion Systems with Weak Diffusion: Analytical Techniques and Results
Animal Coat Patterns and Other Practical Applications of Reaction Diffusion Mechanisms
Mechanical Theory for Generating Pattern and Form in Development
Bacterial Patterns and Chemotaxis


I've mostly looked at population modeling in his books, so I'm not very familier with these topics myself.