Solving Predator-Prey Model Using Maple 18 Coded Variational Iteration Method (VIM)

Falade, K. I., Salisu, U., Ayodele, V.I


In this paper, MAPLE 18 codes are used to utilize Variational Iteration method for the numerical solution of two species LotkaVolterra prey-predator interaction species which are governed by a system of nonlinear differential equations. Two examples are provided to show the ability and reliability of the method. The obtained approximate solution shows that Variational Iteration Method (VIM) is powerful numerical technique for solving a system of nonlinear differential equation, which can be easily applied to other nonlinear problems in biomathematics. This technique has shown to be very effective and yields accurate results. Read full PDF

Keywords: Lotka-Volterra prey-predator, system of nonlinear differential equations, MAPLE 18 codes, variational iteration method, approximate solution


[1] H. F. Karwan. Jwamer and Aram M. Rashid (2012) New Technique For Solving System of First Order Linear Differential Equations Applied Mathematical Sciences, Vol. 6, no. 64, 3177 – 3183.

[2] V. Marinca and Nicolae H, (2012) Optimal Parametric Iteration Method for Solving Multispecies LotkaVolterra Equations Hindawi Publishing Corporation Discrete Dynamics in Nature and Society Volume 2012, Article ID 842121,pp 10-21.

[3] J.H He, (2000)A coupling method of a Homotopy technique and a perturbation technique for non-linear problems, International Journal of Non-Linear Mechanics, vol. 35, no. 1, pp. 37–43.

[4] F. Stephenie (2014) Predator-Prey Model Lecture note

[5] M.S .Giovanni, R. Daniele (2003) A New Method for the Explicit Integration of Lotka-Volterra Equations Divulgaciones Matem´aticas Vol. 11 No. 1, pp. 1–17.

[6] F. Hosseini, M. Shekarab, M. Khodabin (2016) Numerical solutions of stochastic Lotka-Volterra equations via operational matrices Journal of Interpolation and Approximation in Scientific Computing SI.1 (2016) 37-42.

[7] C.G .Zhu, Yin. (2009).On competitive Lotka-Volterra model in random environments, Journal of Mathematical Analysis and Applications, 357(1), 154-170 Falade, K. I et al./ NIPES Journal of Science and Technology Research 2(2) 2020 pp. 166 – 177 177

[8] H.Vahidin, Midhat. M,Jasmin Bektešević (2017) Lotka-Volterra Model with Two Predators and Their Prey TEM Journal. Volume 6, Issue 1, Pages 132-136.

[9] S Alebraheem,. Hussaın, F. Ahmad, K. Nımer (2020) Application of differential transformation method for solving prey predator model with holling type 1 Italian Journal of Pure and Applied Mathematics ISSN2239- 0227 pp 115–127.

[10]D. Venu, R. Gopala (2011)A Study on Series Solutions of Two Species Lotka Volterra Equations by Adomian Decomposition and Homotopy Perturbation Methods Gen. Math. Notes, Vol. 3, No. 2 pp. 13-26 ISSN 2219- 7184; Copyright © ICSRS Publication,

[11]A.Veronıca, B. Mostafa and S.Maurıcıo (2010) Mathematical and numerical analysis for Predator-prey system in a polluted Networks and heterogeneous medıa doi:10.3934/nhm.2010.5.813 American ınstitute of mathematical sciences volume 5, number 4.

[12]J.H He. (2000) Variational iteration method for autonomous ordinary differential systems. Applied Mathematics and Computation, 118 (2-3), 115-123.

[13]J.H He. (1999). A new approach to nonlinear partial differential equation. Communication in Nonlinear Science and Numerical Simulation, 2(4), 230-235.

[14] J.H He. (1998) A variational approach to nonlinear problems and its application. Mech. Applc., 20(1), 30-31.

[15]M. Inokuti, Sekine, H., T. Mura. (1978). General use of the Lagrange multiplier in nonlinear mathematical physics, In: S.Nemat-Nassed (ed.),Variational Method in the Mechanics of solids. Pergemon Press, 156-162

[16]J.H He (2006). Some asymptotic methods for strongly nonlinear equation. International Journal of Modern Physics A, B20 (10), 1141-1199.

[17]N. Bildik, A.Konuralp (2006) The use of variational iteration method, differential transform and Adomian decomposition method for solving different types of nonlinear partial differential equation. International Journal of Nonlinear Sciences and Numerical Simulation, 7(1), 65-70.

[18]Abdulwaf, E.M., Abdou, M.A., Mahmoud, A.A. (2006) The solution of nonlinear coagulation problem with mass loss. Chaos Solutions and Fractals, 26, 313-330.

[19]J.H He (1999) Variational iteration method a kind of nonlinear analytical technique: Some examples. International Journal of Non-Linear Mechanics, 34, 669-708.

[20]J.H He, J.H (2007) The variational iteration method for eight-order initial boundary value problems. Physical Scripta, 76, 680-682.

[21]Inokuti, M., Sekine, H., Mura, T.(1978) General use of the Lagrange multiplier in nonlinear mathematical physics, S.Nemat-Nassed (ed.),Variational Method in the Mechanics of solids. Pergemon Press, 156-162.

[22]Abbasbandy, S., Shivanian, E. (2009) Application of the variational iteration method for system of nonlinear Volterra’s integro -differential equations. Mathematical and Computational Applications, 14 (2), 147-158.

[23]Stephanie Forrest (2000) Predator-Prey Models Dept. of Computer Science Univ. of New Mexico Albuquerque, NM pp13-15.

[24]P. Susmita, P.M Sankar, B. Paritosh B. (2016) Numerical solution of Lotka Volterra prey predator model by using Runge–Kutta–Fehlberg method and Laplace Adomian decomposition method, Alexandria Eng. J. University