Chaotic behavior in Lotka-Volterra and May-Leonard models of biodiversity

TL;DR

This paper investigates chaos in biodiversity models using Hamming distance and spatial autocorrelation, revealing how chaos varies with species number and model parameters.

Contribution

It introduces a novel approach to quantify chaos in ecological models through Hamming distance and autocorrelation analysis, linking chaos to species diversity.

Findings

Chaotic behavior identified in different scenarios.

Characteristic length correlates with species number.

Hamming distance effectively detects chaos.

Abstract

Quantification of chaos is a challenging issue in complex dynamical systems. In this paper, we discuss the chaotic properties of generalized Lotka-Volterra and May-Leonard models of biodiversity, via the Hamming distance density. We identified chaotic behavior for different scenarios via the specific features of the Hamming distance and the method of q-exponential fitting. We also investigated the spatial autocorrelation length to find the corresponding characteristic length in terms of the number of species in each system. In particular, the results concerning the characteristic length are in good accordance with the study of the chaotic behavior implemented in this work.