A Generalised Difference Equation and Its Dynamics and Solutions

Ramazan Karatas, Ali Gelişken () and Murat Arı
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Ramazan Karatas: Education Faculty, Akdeniz University, Antalya 07058, Turkey
Ali Gelişken: Faculty of Engineering and Natural Sciences, Konya Technical University, Konya 42250, Turkey
Murat Arı: Faculty of Sciences, Karamanoğlu Mehmetbey University, Karaman 70200, Turkey

Mathematics, 2024, vol. 12, issue 22, 1-9

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.

Keywords: difference equation; stability; globally asymptotically; boundedness; periodicity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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