Modeling symbiosis by interactions through species carrying capacities

TL;DR

This paper presents a comprehensive mathematical model of symbiosis that accounts for how species influence each other's carrying capacities, revealing diverse dynamical regimes including growth, extinction, and singularities.

Contribution

It introduces a novel, versatile model capturing various symbiotic interactions and classifies all possible dynamical behaviors in ecological and social contexts.

Findings

Four distinct dynamical regimes identified

Model applicable to biological and social systems

Complete classification of system behaviors

Abstract

We introduce a mathematical model of symbiosis between different species by taking into account the influence of each species on the carrying capacities of the others. The modeled entities can pertain to biological and ecological societies or to social, economic and financial societies. Our model includes three basic types: symbiosis with direct mutual interactions, symbiosis with asymmetric interactions, and symbiosis without direct interactions. In all cases, we provide a complete classification of all admissible dynamical regimes. The proposed model of symbiosis turned out to be very rich, as it exhibits four qualitatively different regimes: convergence to stationary states, unbounded exponential growth, finite-time singularity, and finite-time death or extinction of species.