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Global Period-Doubling Bifurcation of Quadratic Fractional Second Order Difference Equation

Author

Listed:
  • Senada Kalabušić
  • M. R. S. Kulenović
  • M. Mehuljić

Abstract

We investigate the local stability and the global asymptotic stability of the difference equation , with nonnegative parameters and initial conditions such that , for all . We obtain the local stability of the equilibrium for all values of parameters and give some global asymptotic stability results for some values of the parameters. We also obtain global dynamics in the special case, where , in which case we show that such equation exhibits a global period doubling bifurcation.

Suggested Citation

  • Senada Kalabušić & M. R. S. Kulenović & M. Mehuljić, 2014. "Global Period-Doubling Bifurcation of Quadratic Fractional Second Order Difference Equation," Discrete Dynamics in Nature and Society, Hindawi, vol. 2014, pages 1-13, April.
    • Handle: RePEc:hin:jnddns:920410
    DOI: 10.1155/2014/920410
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