Approximate Analytic Solution to the Three Species Lotka – Volterra Differential Equation Model
DOI:
https://doi.org/10.32871/rmrj.2109.02.09Keywords:
approximation, analytic solution, Lotka-Volterra, differential equation modelAbstract
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.
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Approximate analytic solution to the Lotka –
Volterra Predator – Prey Differential Equations
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http://www.nmsc.edu.ph/ojs/index.php/jherd/article/view/150
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species_predator-prey_models_with_time_delays
modeling of two-dimensional transient
atmospheric pollutant dispersion by double
GITT and Laplace Transform techniques.
Environmental Modelling & Software, 24(1), 144-151.
https://doi.org/10.1016/j.envsoft.2008.06.001
Chauvet, E., Paullet, J. E., Previte, J. P., & Walls, Z. (2002, October).
A Lotka-Volterra three species food chain.
Mathematics Magazine, 75(4), 243-55.
https://doi.org/10.2307/3219158
Cotta, R.M., & Mikhailov, M.D. (1993). Integral transform method.
Applied Mathematical Modelling, 17(3), 156-161.
https://doi.org/10.1016/0307-904X(93)90041-E
Devireddy, L. (2016). Extending the Lotka-Volterra equations.
University of Washington, Department of Mathematics.
https://sites.math.washington.edu/~morrow/336_16/2016papers/lalith.pdf
Guerrero, J. S. P., Skaggs, T. H., & van Genuchten, M. (2009).
Analytical solution for multi-species contaminant transport
subject to sequential first-order decay reactions in finite media.
Transport in Porous Media, 80, 373-387.
https://doi.org/10.1007/s11242-009-9368-3
Hsu, S. B., Ruan, S., & Yang, T. H. (2015). Analysis of
three species Lotka–Volterra food web models with omnivory.
Journal of Mathematical Analysis and Applications, 426(2), 659-687.
https://doi.org/10.1016/j.jmaa.2015.01.035
Lotka, A. J. (1925). Elements of physical biology. Williams & Wilkins Company. https://archive.org/details/elementsofphysic017171mbp
Pekalski, A., & Stauffer, D. (1998). Three species Lotka–Volterra Model.
International Journal of Modern Physics, 9(5), 777-783.
https://doi.org/10.1142/S0129183198000674
Pontedeiro, E.M., Heilbron, P.F.L., & Cotta, R.M. (2007).
Assessment of the mineral industry NORM/TENORM
disposal in hazardous landfills.
Journal of Hazardous Materials, 139(3), 563-568.
https://doi.org/10.1016/j.jhazmat.2006.02.063
Regalado, D. Y., & Castillano, E. C. (2019).
Approximate analytic solution to the Lotka –
Volterra Predator – Prey Differential Equations
Model. Journal of Higher Education Research Disciplines, 4(1).
http://www.nmsc.edu.ph/ojs/index.php/jherd/article/view/150
Volterra, V. (1926). Fluctuations in the abundance of a species
considered mathematically. Nature, 118(2972), 558-560.
https://doi.org/10.1038/118558a0
Wei, F. (2007). Dynamics in 3-species predator-prey models with time delays.
Discrete and Continuous Dynamical Systems, (Supplement), 364-372.
https://www.researchgate.net/publication/234108762_Dynamics_in_3-
species_predator-prey_models_with_time_delays
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Published
2021-12-30
How to Cite
Regalado, D. Y. (2021). Approximate Analytic Solution to the Three Species Lotka – Volterra Differential Equation Model. Recoletos Multidisciplinary Research Journal, 9(2), 123–128. https://doi.org/10.32871/rmrj.2109.02.09
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