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Bifurcation and Chaos Control of a System of Rational Difference Equations

Year 2021, Volume: 4 Issue: 3, 169 - 178, 30.09.2021

Rizwan Ahmed , Shehraz Akhtar , Muzammil Mukhtar Faiza Anwar

https://doi.org/10.53006/rna.916750
Cited By: 1

Abstract

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

Keywords

Stability Bifurcation Chaos control

Supporting Institution

None

Project Number

None

References

  • 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.

Year 2021, Volume: 4 Issue: 3, 169 - 178, 30.09.2021

Rizwan Ahmed , Shehraz Akhtar , Muzammil Mukhtar Faiza Anwar

https://doi.org/10.53006/rna.916750
Cited By: 1

Abstract

Project Number

None

References

  • 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.
There are 13 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Rizwan Ahmed

Shehraz Akhtar

Muzammil Mukhtar This is me

Faiza Anwar This is me

Project Number None
Publication Date September 30, 2021
Published in Issue Year 2021 Volume: 4 Issue: 3

Cite

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. September 2021;4(3):169-178. doi:10.53006/rna.916750
Chicago Ahmed, Rizwan, Shehraz Akhtar, Muzammil Mukhtar, and Faiza Anwar. “Bifurcation and Chaos Control of a System of Rational Difference Equations”. Results in Nonlinear Analysis 4, no. 3 (September 2021): 169-78. https://doi.org/10.53006/rna.916750.
EndNote Ahmed R, Akhtar S, Mukhtar M, Anwar F (September 1, 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, and F. Anwar, “Bifurcation and Chaos Control of a System of Rational Difference Equations”, RNA, vol. 4, no. 3, pp. 169–178, 2021, doi: 10.53006/rna.916750.
ISNAD Ahmed, Rizwan et al. “Bifurcation and Chaos Control of a System of Rational Difference Equations”. Results in Nonlinear Analysis 4/3 (September 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 et al. “Bifurcation and Chaos Control of a System of Rational Difference Equations”. Results in Nonlinear Analysis, vol. 4, no. 3, 2021, pp. 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.

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