# A novel procedure for the identification of chaos in complex biological systems

## TL;DR

This paper presents a new method to identify chaos in complex biological systems using stochastic simulations, correlation length, and maxima density, demonstrated on ecological and other natural systems.

## Contribution

Introduces a novel quantitative approach to detect chaos in biological systems through the density of maxima and correlation length analysis.

## Key findings

- Chaos can be identified using the density of maxima in species evolution.
- A single experimental measurement can infer the correlation length of chaos.
- The method applies to ecological, differential equation, and ocean level systems.

## Abstract

We demonstrate the presence of chaos in stochastic simulations that are widely used to study biodiversity in nature. The investigation deals with a set of three distinct species that evolve according to the standard rules of mobility, reproduction and predation, with predation following the cyclic rules of the popular rock, paper and scissors game. The study uncovers the possibility to distinguish between time evolutions that start from slightly different initial states, guided by the Hamming distance which heuristically unveils the chaotic behavior. The finding opens up a quantitative approach that relates the correlation length to the average density of maxima of a typical species, and an ensemble of stochastic simulations is implemented to support the procedure. The main result of the work shows how a single and simple experimental realization that counts the density of maxima associated with the chaotic evolution of the species serves to infer its correlation length. We use the result to investigate others distinct complex systems, one dealing with a set of differential equations that can be used to model a diversity of natural and artificial chaotic systems, and another one, focusing on the ocean water level.