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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

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, 2023. "On the Global Asymptotic Stability and 4‐Period Oscillation of the Third‐Order Difference Equation," Journal of Applied Mathematics, John Wiley & Sons, vol. 2023(1).
    • Handle: RePEc:wly:jnljam:v:2023:y:2023:i:1:n:5726617
    DOI: 10.1155/2023/5726617
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    References listed on IDEAS

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    1. Alaa E. Hamza & M. A. El-Sayed, 1998. "Stability problem of some nonlinear difference equations," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 21, pages 1-10, January.
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