APPROXIMATE ANALYTIC SOLUTION TO THE LOTKA-VOLTERRA PREDATOR – PREY DIFFERENTIAL EQUATIONS MODEL
Keywords:
Lotka-Volterra, finite difference method, symbolic regression, Lambert W functionAbstract
The paper provides an approximate analytic solution to the Lotka Volterra predator-prey differential equations by symbolic regression. The approximate analytic solution can be made as close as desired to the actual analytic solution involving complicated Lambert W functions. As a side result, the symbolic regression approach also provides an approximation to the otherwise less tractable Lambert W integral equation.
References
Abate, H. and F. Hofelich(1968), Mode-Specic Coupling in Lasers, Z. Physik 209
Boyce, W. and R. DiPrima (1992), Elementary Dierential Equations and Boundary Value
Problems, 5th ed. (Wiley, New York, 1992)
Brearly, J. and , SoudackA. C. (1978) Linearization of the Lotka-Volterra Model. Int. J.
Control Vol. 27, page 933.
Brearly, J., Soudack A. C. (1978). Approximate solutions to the Lotka-Volterra competition
equations. International Journal of Control 27(6):933-941
Evan, C. M., Findley, G. L. (1998). Analytic solutions to the Lotka-Volterra model for
sustained chemical oscillations. Journal of Mathematical Chemistry. Vol. 25, Pages 1 32.
Evans, C. M.; Findley, G. L. (1999). \A new transformation for the Lotka-Volterra problem".
Journal of Mathematical Chemistry.Vol. 25: 105110.
Lotka, A. J. 1925. Elements of physical biology. Baltimore: Williams & Wilkins Co.
Nguyen Quang Uy et al. (2010). \Semantically-based crossover in genetic programming:
application to real-valued symbolic regression" Genetic Programming and Evolvable
Machines. June 2011, Volume 12, Issue 2, pp 91119
Noonburg V. W. (1989). A Neural Network Modeled by an Adaptive Lotka-Volterra System.
SIAM Journal on Applied Mathematics 49(6).
Padua, R., Libao, M., Azura, R., Cortez, M., Abato, T., Frias, M..(2018) \Approximate
Analytic Solutions to Dierential Equations from Numerical Methods" (Recoletos
Multidisciplinary Journal, Vol. 5, No. 1).
Sean Luke , Lee Spector L. (1998). A Revised Comparison of Crossover and Mutation
in Genetic Programming. Genetic Programming 1997: Proceedings of the Second Annual
Conference 1998, 240-248.
Takeuchi et al. (2006). Evolution of predatorprey systems described by a LotkaVolterra
equation under random environment. Volume 323, Issue 2, Pages 938-957.
Volterra V. (1926). Fluctuations in the Abundance of a Species considered Mathematically.
Nature volume 118, pages 558560.
Boyce, W. and R. DiPrima (1992), Elementary Dierential Equations and Boundary Value
Problems, 5th ed. (Wiley, New York, 1992)
Brearly, J. and , SoudackA. C. (1978) Linearization of the Lotka-Volterra Model. Int. J.
Control Vol. 27, page 933.
Brearly, J., Soudack A. C. (1978). Approximate solutions to the Lotka-Volterra competition
equations. International Journal of Control 27(6):933-941
Evan, C. M., Findley, G. L. (1998). Analytic solutions to the Lotka-Volterra model for
sustained chemical oscillations. Journal of Mathematical Chemistry. Vol. 25, Pages 1 32.
Evans, C. M.; Findley, G. L. (1999). \A new transformation for the Lotka-Volterra problem".
Journal of Mathematical Chemistry.Vol. 25: 105110.
Lotka, A. J. 1925. Elements of physical biology. Baltimore: Williams & Wilkins Co.
Nguyen Quang Uy et al. (2010). \Semantically-based crossover in genetic programming:
application to real-valued symbolic regression" Genetic Programming and Evolvable
Machines. June 2011, Volume 12, Issue 2, pp 91119
Noonburg V. W. (1989). A Neural Network Modeled by an Adaptive Lotka-Volterra System.
SIAM Journal on Applied Mathematics 49(6).
Padua, R., Libao, M., Azura, R., Cortez, M., Abato, T., Frias, M..(2018) \Approximate
Analytic Solutions to Dierential Equations from Numerical Methods" (Recoletos
Multidisciplinary Journal, Vol. 5, No. 1).
Sean Luke , Lee Spector L. (1998). A Revised Comparison of Crossover and Mutation
in Genetic Programming. Genetic Programming 1997: Proceedings of the Second Annual
Conference 1998, 240-248.
Takeuchi et al. (2006). Evolution of predatorprey systems described by a LotkaVolterra
equation under random environment. Volume 323, Issue 2, Pages 938-957.
Volterra V. (1926). Fluctuations in the Abundance of a Species considered Mathematically.
Nature volume 118, pages 558560.
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2019-06-28
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