Lie and conditional symmetries of the three-component diffusive Lotka - Volterra system

TL;DR

This paper classifies Lie and Q-conditional symmetries of a three-component diffusive Lotka-Volterra system, introducing new non-Lie symmetries and demonstrating their application to biological models.

Contribution

It provides a complete group-classification of symmetries for the system and constructs the first known non-Lie symmetry operators for such multi-component systems.

Findings

Complete classification of Lie symmetries.

First construction of non-Lie symmetries for multi-component systems.

Application of non-Lie symmetry reduction to a biological problem.

Abstract

Lie and Q-conditional symmetries of the classical three-component diffusive Lotka - Volterra system in the case of one space variable are studied. The group-classification problems for finding Lie symmetries and Q-conditional symmetries of the first type are completely solved. Notably, non-Lie symmetries (Q-conditional symmetry operators) for a multi-component non-linear reaction-diffusion system are constructed for the first time. An example of non-Lie symmetry reduction for solving a biologically motivated problem is presented.