Solution of the prey-predator problem by He's parameterized perturbation methods

International Journal of Nonlinear Sciences and Numerical Simulation

Volumn 10, Issue 9, 2009, Pages 1223-1226

  Zhang, Lei ^a   Ding, Xiao Hua ^a  

^a HARBIN INSTITUTE OF TECHNOLOGY   (China)

Author keywords

Parameter expansion method; Parameterized perturbation method; Predator prey system; System of nonlinear differential equations

Indexed keywords

EID: 72449157499     PISSN: 15651339     EISSN: None     Source Type: Journal    
DOI: 10.1515/IJNSNS.2009.10.9.1223     Document Type: Article

References (13)

1. M. Kallay, Y. Cohen, The simplest predator-prey model, Ecol. Model, 2 (2008), 398-399.
2. J. Biazar, R. Montazeri, A computational method for solution of the prey and predator problem, Appl. Math. Comput., 163(2005), 841-847. (Pubitemid 40219924)
3. J. Biazar, M.Ilie, A. Khoshkenar, A new approach to the solution of the prey and predator problem and comparison of the results with the Adomian method, Appl. Math. Comput., 171(2005), 486-491.
4. M. Rafei, H. Daniali, D. D. Ganji, H. Pashaei, solution of the prey and predator problem by homotopy perturbation method, Appl. Math. Comput., 188(2007), 1419-1425. (Pubitemid 46710032)
5. M.S.H. Chowdhury, I. Hashim, R. Roslan, Simulation of the predator-prey problem by the homotopy-perturbation method revised, Topol. Method Nonl. An., 31(2)(2008) 263-270.
6. K. Batiha, Numerical solutions of the multispecies predator-prey model by variational iteration method, J. Comput. Sci., 3(2007), 523-527.
7. J.H. He, Some new approaches to Duffing equation with strongly and high order nonlinearity (II) parametrized perturbation technique, Communications in Nonlinear Science and Numerical Simulation, 4(1)(1999) 81-83. (Pubitemid 40491983)
8. J. H. He, some asymptotic methods for strongly nonlinear equations, International Journal of Modern Physics B. 20(10) (2006) 1141-1199.
9. D. H. Shou, J.H. He, Application of parameter-expanding method to strongly nonlinear oscillators, Int. J Nonlin. Sci. Num., 8(2007) 121-124.
10. L. Xu, Determination of limit cycle by He's parameter-expanding method for strongly nonlinear oscillators, J. Sound Vib., 302(2007) 178-184.
11. S.Q. Wang, J.H. He, Nonlinear oscillator with discontinuity by parameter-expansion method, Chaos Soliton. Fract., 35(2008) 688-691
12. Zengin FO, Kaya MO, Demirbag SA. Application of parameter-expansion method to nonlinear oscillators with discontinuities, Int. J. Nonlin. Sci. Num., 9(2008) 267-270.
13. He JH. Recent development of the homotopy perturbation method, Topol. Method Nonl. An., 31(2008) 205-209.