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Yıl 2016, Cilt: 6 Sayı: 2, 264 - 277, 01.12.2016

Öz

Kaynakça

  • Ahmed,E., El-Sayed,A.M.A. and El-Saka,H.A.A., (2006), On some Routh-Hurwitz conditions for frac- tional order differential equations and their applications in Lorenz, R¨ossler, Chua and Chen systems, Phys. Lett. A, pp. 358.
  • Allen,L.J.S., (2007), An Introduction to Mathematical Biology, Prentice Hall, New Jersey.
  • Arenas,A.J., Gonzalez-Parra,G. and Chen-Charpentier,B.M., (2010), A non-standard numerical scheme of predictor-corrector type for epidemic models, Comput. Math. Appl., 59(12), pp. 3740-3749.
  • Gonzalez-Parra,G., Arenas,A.J. and Chen-Charpentier,B.M., (2010), Combination of non-standard schemes and Richardsons extrapolation to improve the numerical solution of population models, Math. Comput. Modelling, 52(7-8), pp. 1030-1036.
  • Jordan,P.M., (2003), A non-standard finite difference scheme for nonlinear heat transfer in a thin finite rod, J. Difference Equ. Appl., 9(11), pp. 1015-1021.
  • Matignon,D., (1996), Stability result on fractional differential equations with applications to control processing, Computational Engineering in Systems Applications, pp. 963-968.
  • Mehmat,A.A., Secer,A. and Bayram,M., (2014), Stability, synchronization control and numerical so- lution of fractional Shimizu-Morioka dynamical system, Appl. Math. Inf. Sci., 8(14), pp. 1699-1705.
  • Mickens,R.E., (2007), Calculation of denominator functions for non-standard finite difference schemes for differential equations satisfying a positivity condition, Numer. Methods Partial Differential Equa- tions, 23(3), pp. 672-691.
  • Mickens,R.E., (2000), Applications of Nonstandard Finite Difference Schemes, Singapore.
  • Mickens,R.E., (1999), Discretizations of nonlinear differential equations using explicit non-standard methods, J. Comput. Appl. Math., 110, pp. 181-185.
  • Murray,J.D., (2003), Mathematical Biology I, II, Third edition, Springer.
  • Podlubny,I., (1999), Fractional Differential Equations, Academic Press, New York.
  • Roger,L.W., (2004), Local stability of Eulers and Kahans methods, J. Difference Equ. Appl., 10(6), pp. 601-614.
  • Zibaei,S. and Namjoo,M., (2014), A NSFD scheme for Lotka-Volterra food web model, Iran. J. Sci.Technol. Trans. A Sci., 38(4), pp. 399-414.

SOLVING FRACTIONAL-ORDER COMPETITIVE LOTKA-VOLTERRA MODEL BY NSFD SCHEMES

Yıl 2016, Cilt: 6 Sayı: 2, 264 - 277, 01.12.2016

Öz

In this paper, we introduce fractional-order into a model competitive Lotka- Volterra prey-predator system. We will discuss the stability analysis of this fractional system. The non-standard nite difference NSFD scheme is implemented to study the dynamic behaviors in the fractional-order Lotka-Volterra system. Proposed non-standard numerical scheme is compared with the forward Euler and fourth order Runge-Kutta methods. Numerical results show that the NSFD approach is easy and accurate for implementing when applied to fractional-order Lotka-Volterra model.

Kaynakça

  • Ahmed,E., El-Sayed,A.M.A. and El-Saka,H.A.A., (2006), On some Routh-Hurwitz conditions for frac- tional order differential equations and their applications in Lorenz, R¨ossler, Chua and Chen systems, Phys. Lett. A, pp. 358.
  • Allen,L.J.S., (2007), An Introduction to Mathematical Biology, Prentice Hall, New Jersey.
  • Arenas,A.J., Gonzalez-Parra,G. and Chen-Charpentier,B.M., (2010), A non-standard numerical scheme of predictor-corrector type for epidemic models, Comput. Math. Appl., 59(12), pp. 3740-3749.
  • Gonzalez-Parra,G., Arenas,A.J. and Chen-Charpentier,B.M., (2010), Combination of non-standard schemes and Richardsons extrapolation to improve the numerical solution of population models, Math. Comput. Modelling, 52(7-8), pp. 1030-1036.
  • Jordan,P.M., (2003), A non-standard finite difference scheme for nonlinear heat transfer in a thin finite rod, J. Difference Equ. Appl., 9(11), pp. 1015-1021.
  • Matignon,D., (1996), Stability result on fractional differential equations with applications to control processing, Computational Engineering in Systems Applications, pp. 963-968.
  • Mehmat,A.A., Secer,A. and Bayram,M., (2014), Stability, synchronization control and numerical so- lution of fractional Shimizu-Morioka dynamical system, Appl. Math. Inf. Sci., 8(14), pp. 1699-1705.
  • Mickens,R.E., (2007), Calculation of denominator functions for non-standard finite difference schemes for differential equations satisfying a positivity condition, Numer. Methods Partial Differential Equa- tions, 23(3), pp. 672-691.
  • Mickens,R.E., (2000), Applications of Nonstandard Finite Difference Schemes, Singapore.
  • Mickens,R.E., (1999), Discretizations of nonlinear differential equations using explicit non-standard methods, J. Comput. Appl. Math., 110, pp. 181-185.
  • Murray,J.D., (2003), Mathematical Biology I, II, Third edition, Springer.
  • Podlubny,I., (1999), Fractional Differential Equations, Academic Press, New York.
  • Roger,L.W., (2004), Local stability of Eulers and Kahans methods, J. Difference Equ. Appl., 10(6), pp. 601-614.
  • Zibaei,S. and Namjoo,M., (2014), A NSFD scheme for Lotka-Volterra food web model, Iran. J. Sci.Technol. Trans. A Sci., 38(4), pp. 399-414.
Toplam 14 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

S. Zibaei Bu kişi benim

M. Namjoo Bu kişi benim

Yayımlanma Tarihi 1 Aralık 2016
Yayımlandığı Sayı Yıl 2016 Cilt: 6 Sayı: 2

Kaynak Göster