The characteristic approach in determining first integrals of a predator-prey system.
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Date
2016
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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.
Description
Master of Science in Mathematics, Statistics and Computer Science. University of KwaZulu-Natal, Durban 2016.
Keywords
Theses - Applied Mathematics.