Integrability of the Basener-Ross model with time-dependent coefficients

TL;DR

This paper investigates the integrability of an extended Basener-Ross population model with time-dependent coefficients, identifying specific conditions on the coefficients that ensure the system can be solved analytically.

Contribution

It provides new relations among the coefficients of the model that guarantee its integrability, extending the classical Basener-Ross system to variable environmental conditions.

Findings

Derived conditions for integrability with time-dependent coefficients

Extended the classical model to include environmental variability

Identified specific relations among coefficients for solvability

Abstract

The Basener-Ross system is a known model in Population Dynamics for the interaction of consumers and resources in an isolated habitat. For an extended version with time-dependent coefficients as a model of possible variations of the environtmental conditions, some relations among the coefficients are provided leading to the integrability of the system.