The characteristic approach in determining first integrals of a predator-prey system.

Abstract

Predator-Prey systems are an intriguing symbiosis of living species that interplay during the fluctuations of birth, growth and death during any period. In the light of understanding the behavioural patterns of the species, models are constructed via differential equations. These differential equations can be solved through a variety of techniques. We focus on applying the characteristic method via the multiplier approach. The multiplier is applied to the differential equation. This leads to a first integral which can be used to obtain a solution for the system under certain initial conditions. We then look at the comparison of first integrals by using two different approaches for various biological models. The method of the Jacobi Last Multiplier is used to obtain a Lagrangian. The Lagrangian can be used via Noether’s Theorem to obtain a first integral for the system.