Open AccessApproximate Analytic Solution to the Three Species Lotka – Volterra Differential Equation Model
Author(s) -
Dionisel Yamba Regalado,
AUTHOR_ID
Publication year - 2021
Publication title -
recoletos multidisciplinary research journal (online)/recoletos multidisciplinary research journal (usj-r. print).
Language(s) - English
Resource type - Journals
eISSN - 2423-1398
pISSN - 2408-3755
DOI - 10.32871/rmrj.2109.02.09
Subject(s) - jacobian matrix and determinant , eigenvalues and eigenvectors , mathematics , symbolic regression , convergence (economics) , differential equation , euler's formula , differential (mechanical device) , euler method , volterra equations , analytic function , regression , mathematical analysis , computer science , nonlinear system , statistics , physics , quantum mechanics , artificial intelligence , economics , genetic programming , economic growth , thermodynamics
This paper provides an approximate analytic solution to the three species Lotka – Volterra differential equations by symbolic regression. The approximate analytic solution through symbolic regression is made as close as desired to the actual analytic solution by using the Jacobian system. This is proposed as the equilibrium will be stabilized if and only if the real parts of each of the eigenvalues are negative. As a result, the symbolic regression approach is found to provide an approximation to the faster convergence that can be expected with a more refined Euler numerical approach.