Bifurcation and Chaos Control of a System of Rational Difference Equations

Bifurcation and Chaos Control of a System of Rational Difference Equations

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

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  • 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.