A Generalised Difference Equation and Its Dynamics and Solutions
Ramazan Karatas, Ali Gelişken, Murat Arı
Source abstract
Rational difference equations have a wide range of applications in various fields of science. To illustrate, the equation xn+1=a+bxnc+dxn,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 xn+1=Axn−2k+j+1B+Cxn−(k+j)xn−2k+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.
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