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A Generalised Difference Equation and Its Dynamics and Solutions

Author

Listed:
  • Ramazan Karatas

    (Education Faculty, Akdeniz University, Antalya 07058, Turkey
    These authors contributed equally to this work.)

  • Ali Gelişken

    (Faculty of Engineering and Natural Sciences, Konya Technical University, Konya 42250, Turkey
    These authors contributed equally to this work.)

  • Murat Arı

    (Faculty of Sciences, Karamanoğlu Mehmetbey University, Karaman 70200, Turkey
    These authors contributed equally to this work.)

Abstract

Rational difference equations have a wide range of applications in various fields of science. To illustrate, the equation x n + 1 = a + b x n c + d x n , n = 0 , 1 , . . . , known as the Riccati difference equation, has been applied in the field of optics. In this study, the global asymptotic stability of the difference equation x n + 1 = A x n − 2 k + j + 1 B + C x n − ( k + j ) x n − 2 k + j + 1 , n = 0 , 1 , . . . , is proved. The solutions of this difference equation are obtained by applying the standard iteration method, and the periodicity of these solutions is determined. Furthermore, this difference equation represents a generalisation of the results obtained in previous studies.

Suggested Citation

  • Ramazan Karatas & Ali Gelişken & Murat Arı, 2024. "A Generalised Difference Equation and Its Dynamics and Solutions," Mathematics, MDPI, vol. 12(22), pages 1-9, November.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:22:p:3531-:d:1519322
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    Citations

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    Cited by:

    1. Bashir Al-Hdaibat & Ramadan Sabra & Mahmoud H. DarAssi & Saleem Al-Ashhab, 2025. "On the Recursive Sequence x n + 1 = a x n − 1 b + c x n x n − 1," Mathematics, MDPI, vol. 13(5), pages 1-20, February.

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