Approximate Analytic Solution to the Three Species Lotka – Volterra Differential Equation Model




approximation, analytic solution, Lotka-Volterra, differential equation model


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.


Cassol, M., Wortmann, S., & Rizza, U. (2009). Analytic
modeling of two-dimensional transient
atmospheric pollutant dispersion by double
GITT and Laplace Transform techniques.
Environmental Modelling & Software, 24(1), 144-151.

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.

Cotta, R.M., & Mikhailov, M.D. (1993). Integral transform method.
Applied Mathematical Modelling, 17(3), 156-161.

Devireddy, L. (2016). Extending the Lotka-Volterra equations.
University of Washington, Department of Mathematics.

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.

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.

Lotka, A. J. (1925). Elements of physical biology. Williams & Wilkins Company.

Pekalski, A., & Stauffer, D. (1998). Three species Lotka–Volterra Model.
International Journal of Modern Physics, 9(5), 777-783.

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.

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).

Volterra, V. (1926). Fluctuations in the abundance of a species
considered mathematically. Nature, 118(2972), 558-560.

Wei, F. (2007). Dynamics in 3-species predator-prey models with time delays.
Discrete and Continuous Dynamical Systems, (Supplement), 364-372.




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.