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Bifurcation and Chaos Control of a System of Rational Difference Equations

Yıl 2021, Cilt: 4 Sayı: 3, 169 - 178, 30.09.2021

Rizwan Ahmed Shehraz Akhtar Muzammil Mukhtar Faiza Anwar

https://doi.org/10.53006/rna.916750

Öz

We study a system of rational difference equations in this article. For equilibrium points, we present the stability conditions. In addition, we show that the system encounters period-doubling bifurcation at the trivial equilibrium point O and Neimark-Sacker bifurcation at the non-trivial equilibrium point E. To control the chaotic behavior of the system, we use the hybrid control approach. We also verify our theoretical outcomes at the end with some numerical applications

Anahtar Kelimeler

Stability Bifurcation Chaos control

Destekleyen Kurum

None

Proje Numarası

None

Kaynakça

  • I. Bajo, E. Liz, Global behaviour of a second-order nonlinear difference equation Journal of difference equations and applications, 17(10) (2011) 1471-1486.
  • N. Touafek, E. M. Elsayed, On the solutions of systems of rational difference equations, Math. Comput. Modelling 55 (2012) 1987-1997.
  • S. Stevic, On a system of difference equations, Appl. Math. Comput. 218 (2011) 3372-3378.
  • S. Stevic, On a third-order system of difference equations, Appl. Math. Comput. 218 (2012) 7649-7654.
  • Q. Din, On a system of rational difference equation, Demonstratio Math. 47 (2) (2014) 324-335.
  • R. Ahmed, Complex dynamics of a fractional-order predator-prey interaction with harvesting, Open journal of discrete applied mathematics, 3(3) (2020) 24-32.
  • S. L. J. Allen, An introduction to mathematical biology, Pearson prentice hall, 2007.
  • S. N. Elaydi, An introduction to difference equations, springer New York, 2005.
  • S. N. Elaydi, Discrete chaos with applications in science and engineering, CRC press, 2007.
  • J. Guckenheimer, P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer New York, 1983.
  • S. Wiggins., Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer New York, 2003.
  • Y. A. Kuznetsov, Elements of Applied Bifurcation Theory, Springer New York, 1997.
  • X. L. Liu, D. M. Xiao, Complex dynamic behaviors of discrete-time predator-prey system, Chaos Solitons Fract. 32 (2007) 80-94.

Yıl 2021, Cilt: 4 Sayı: 3, 169 - 178, 30.09.2021

Rizwan Ahmed Shehraz Akhtar Muzammil Mukhtar Faiza Anwar

https://doi.org/10.53006/rna.916750

Öz

Proje Numarası

None

Kaynakça

  • I. Bajo, E. Liz, Global behaviour of a second-order nonlinear difference equation Journal of difference equations and applications, 17(10) (2011) 1471-1486.
  • N. Touafek, E. M. Elsayed, On the solutions of systems of rational difference equations, Math. Comput. Modelling 55 (2012) 1987-1997.
  • S. Stevic, On a system of difference equations, Appl. Math. Comput. 218 (2011) 3372-3378.
  • S. Stevic, On a third-order system of difference equations, Appl. Math. Comput. 218 (2012) 7649-7654.
  • Q. Din, On a system of rational difference equation, Demonstratio Math. 47 (2) (2014) 324-335.
  • R. Ahmed, Complex dynamics of a fractional-order predator-prey interaction with harvesting, Open journal of discrete applied mathematics, 3(3) (2020) 24-32.
  • S. L. J. Allen, An introduction to mathematical biology, Pearson prentice hall, 2007.
  • S. N. Elaydi, An introduction to difference equations, springer New York, 2005.
  • S. N. Elaydi, Discrete chaos with applications in science and engineering, CRC press, 2007.
  • J. Guckenheimer, P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer New York, 1983.
  • S. Wiggins., Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer New York, 2003.
  • Y. A. Kuznetsov, Elements of Applied Bifurcation Theory, Springer New York, 1997.
  • X. L. Liu, D. M. Xiao, Complex dynamic behaviors of discrete-time predator-prey system, Chaos Solitons Fract. 32 (2007) 80-94.
Toplam 13 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

Rizwan Ahmed

Shehraz Akhtar

Muzammil Mukhtar Bu kişi benim

Faiza Anwar Bu kişi benim

Proje Numarası None
Yayımlanma Tarihi 30 Eylül 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 4 Sayı: 3

Kaynak Göster

APA Ahmed, R., Akhtar, S., Mukhtar, M., Anwar, F. (2021). Bifurcation and Chaos Control of a System of Rational Difference Equations. Results in Nonlinear Analysis, 4(3), 169-178. https://doi.org/10.53006/rna.916750
AMA Ahmed R, Akhtar S, Mukhtar M, Anwar F. Bifurcation and Chaos Control of a System of Rational Difference Equations. RNA. Eylül 2021;4(3):169-178. doi:10.53006/rna.916750
Chicago Ahmed, Rizwan, Shehraz Akhtar, Muzammil Mukhtar, ve Faiza Anwar. “Bifurcation and Chaos Control of a System of Rational Difference Equations”. Results in Nonlinear Analysis 4, sy. 3 (Eylül 2021): 169-78. https://doi.org/10.53006/rna.916750.
EndNote Ahmed R, Akhtar S, Mukhtar M, Anwar F (01 Eylül 2021) Bifurcation and Chaos Control of a System of Rational Difference Equations. Results in Nonlinear Analysis 4 3 169–178.
IEEE R. Ahmed, S. Akhtar, M. Mukhtar, ve F. Anwar, “Bifurcation and Chaos Control of a System of Rational Difference Equations”, RNA, c. 4, sy. 3, ss. 169–178, 2021, doi: 10.53006/rna.916750.
ISNAD Ahmed, Rizwan vd. “Bifurcation and Chaos Control of a System of Rational Difference Equations”. Results in Nonlinear Analysis 4/3 (Eylül 2021), 169-178. https://doi.org/10.53006/rna.916750.
JAMA Ahmed R, Akhtar S, Mukhtar M, Anwar F. Bifurcation and Chaos Control of a System of Rational Difference Equations. RNA. 2021;4:169–178.
MLA Ahmed, Rizwan vd. “Bifurcation and Chaos Control of a System of Rational Difference Equations”. Results in Nonlinear Analysis, c. 4, sy. 3, 2021, ss. 169-78, doi:10.53006/rna.916750.
Vancouver Ahmed R, Akhtar S, Mukhtar M, Anwar F. Bifurcation and Chaos Control of a System of Rational Difference Equations. RNA. 2021;4(3):169-78.