On exploring \(\lambda \)-symmetries, Darboux polynomials and other integrable quantifiers of Easter Island Population Model

Abstract

Modelling biological processes is more important to analyse the real biological process in detail. Solving the modelled mathematical equations associated with the considered process/system gives us a better understanding of how complex interactions and processes work in that particular system. In this work, we consider Basener–Ross population model and study its integrability quantifiers for some restricted system parameters. We begin our analysis from finding \(\lambda \)-symmetries. Then, we relate \(\lambda \)-symmetries with Darboux polynomials via integrating factors. Also, we extract Lie point symmetries, null forms, Jacobi last multipliers and telescopic vector fields of the Basener–Ross population model from the obtained Darboux polynomials and \(\lambda \)-symmetries. The obtained results will help the biologist to analyse the Basener–Ross population model in a deeper way.