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Global Asymptotic Stability and Naimark-Sacker Bifurcation of Certain Mix Monotone Difference Equation

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  • M. R. S. Kulenović
  • S. Moranjkić
  • M. Nurkanović
  • Z. Nurkanović

Abstract

We investigate the global asymptotic stability of the following second order rational difference equation of the form where the parameters , , , and and initial conditions and are positive real numbers. The map associated with this equation is always decreasing in the second variable and can be either increasing or decreasing in the first variable depending on the parametric space. In some cases, we prove that local asymptotic stability of the unique equilibrium point implies global asymptotic stability. Also, we show that considered equation exhibits the Naimark-Sacker bifurcation resulting in the existence of the locally stable periodic solution of unknown period.

Suggested Citation

  • M. R. S. Kulenović & S. Moranjkić & M. Nurkanović & Z. Nurkanović, 2018. "Global Asymptotic Stability and Naimark-Sacker Bifurcation of Certain Mix Monotone Difference Equation," Discrete Dynamics in Nature and Society, Hindawi, vol. 2018, pages 1-22, November.
    • Handle: RePEc:hin:jnddns:7052935
    DOI: 10.1155/2018/7052935
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