Soluciones numéricas para diferentes casos del modelo biológico no lineal de presa- depredador

• Gilder Cieza Altamirano Universidad Nacional Autónoma de Chota http://orcid.org/0000-0002-7936-1495
• Manuel Jesús Sánchez-Chero Universidad Señor de Sipán S.A.C. http://orcid.org/0000-0003-1646-3037
• Rafaél Artidoro Sandoval-Núñez Universidad Nacional Autónoma de Chota http://orcid.org/0000-0003-3930-2332
• José Antonio Sánchez-Chero Universidad César Vallejo http://orcid.org/0000-0002-3157-8935
• María Verónica Seminario Morales Universidad Nacional de Frontera http://orcid.org/0000-0002-6787-7371

Palabras clave: Modelo biológico, presa – depredador, no lineal, Runge – Kutta, método de Adams.

Resumen

La presente investigación se elaboró con el objetivo realizar una comparación de la solución numérica del modelo biológico no lineal de presa depredador, utilizando el método numérico Adams predicción-corrección junto con los métodos explícitos de Runge-Kutta. Los resultados numéricos para los métodos en mención comparan todos los casos de modelo de presa- depredador, encontrándose que los resultados se superponen entre si hasta un nivel de precisión de 7 a 8, cuando el intervalo se toma de [1,30] con el tamaño de paso de 1.

Citas

Ash, J. H. (1965). An Adams Runge-Kutta subroutine for systems of ordinary differential equations. Toronto. University of Toronto.

Batiha, B. (2014). The solution of the prey and predator problem by differential transformation method. International Journal of Basic and Applied Sciences, 4(1), pp.36-43.

Bashkirtseva, I. and Ryashko, L. (2014). Analysis of the noise-induced regimes in Ricker population model with Allee effect via confidence domains technique. BioMed research international, 2014.

Biazar, J. and Montazeri, R. (2005). A computational method for solution of the prey and predator problem. Applied Mathematics and Computation, 163(2), pp.841-847.

Bildik, N. and Deniz, S. (2016). The Use of Sumudu Decomposition Method for Solving Predator-Prey Systems. Mathematical Sciences Letters, 5(3), pp.285-289.

Danca, M., Codreanu, S., Bako, B. (1997). Detailed analysis of a nonlinear prey-predator model, J. Biol. Phys. 23 (1997) 11–20.

Effati, S., Mansoori, A. and Eshaghnezhad, M. (2015). An efficient projection neural network for solving bilinear programming problems. Neurocomputing, 168, pp.1188-1197

Elsadany, A. E. A., El-Metwally, H. A., Elabbasy, E. M. and Agiza, H. N. (2012). Chaos and bifurcation of a nonlinear discrete prey-predator system. Computational Ecology and Software, 2(3), p.169.

Garvie, M.R., Burkardt, J. and Morgan, J. (2015). Simple Finite Element Methods for Approximating Predator–Prey Dynamics in Two Dimensions Using Matlab. Bulletin of mathematical biology, 77(3), pp.548-578.

Holling, C. S. (1966). The functional response of invertebrate predators to prey density. Memoirs of the Entomological Society of Canada, 98(S48), pp.5-86.

Jing, Z. and Yang, J. (2006). Bifurcation and chaos in discrete-time predator–prey system. Chaos, Solitons & Fractals, 27(1), pp.259-277.

Liu, X. and Xiao, D. (2007). Complex dynamic behaviors of a discrete-time predator–prey system. Chaos, Solitons & Fractals, 32(1), pp.80-94.

Moulton, Forest R. (1926). New methods in exterior ballistics, University of Chicago Press.

Paul, S., Mondal, S.P. and Bhattacharya, P. (2016). Numerical solution of Lotka Volterra prey predator model by using Runge–Kutta–Fehlberg method and Laplace Adomian decomposition method. Alexandria Engineering Journal, 55(1), pp.613-617.

Ray, S.S. (2015). A New Coupled Fractional Reduced Differential Transform Method for the Numerical Solution of Fractional Predator-Prey System. CMES: Computer Modeling in Engineering & Sciences, 105(3), pp.231-249.

Solis, F. J. (2008). Self-limitation in a discrete predator–prey model. Mathematical and Computer Modelling, 48(1), pp.191-196

Summers, D., Cranford, J. G. and Healey, B.P. (2000). Chaos in periodically forced discrete-time ecosystem models. Chaos, Solitons & Fractals, 11(14), pp.2331-2342.

Yu, J. and Yu, J. (2014). Homotopy Analysis Method for a Prey-Predator System with Holling IV Functional Response. Applied Mechanics & Materials.