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On the Global Asymptotic Stability and 4-Period Oscillation of the Third-Order Difference Equation

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  • M. E. Erdogan
  • Sheng Zhang

Abstract

The main objective of this paper is to study the global behavior and oscillation of the following third-order rational difference equation xn+1=αxnxn−1xn−2/βxn−12+γxn−22, where the initial conditions x−2,x−1,x0 are nonzero real numbers and α,β,γ are positive constants such that α≤β+γ. Visual examples supporting solutions are given at the end of the study. The figures are found with the help of MATLAB.

Suggested Citation

  • M. E. Erdogan & Sheng Zhang, 2023. "On the Global Asymptotic Stability and 4-Period Oscillation of the Third-Order Difference Equation," Journal of Applied Mathematics, Hindawi, vol. 2023, pages 1-7, November.
    • Handle: RePEc:hin:jnljam:5726617
    DOI: 10.1155/2023/5726617
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