The Dynamics of a General Model of the Nonlinear Difference Equation and Its Applications

Abstract

This article investigates the qualitative properties of solutions to a general difference equation. Studying the properties of solutions to general difference equations greatly contributes to the development of theoretical methods and provides many pieces of information that may help to understand the behavior of solutions of some special models. We present the sufficient and necessary conditions for the existence of prime period-two and -three solutions. We also obtain a complete perception of the local stability of the studied equation. Then, we investigate the boundedness and global stability of the solutions. Finally, we support the validity of the results by applying them to some special cases, as well as numerically simulating the solutions.

The Qualitative Analysis of Some Difference Equations Using Homogeneous Functions

“…Although it is known that the theory of difference equations emerged with the rabbit problem introduced by the famous Italian mathematician Fibonacci in 1202 has been a field of study that has been of interest to many scientists, especially in the last 30 years (see [1,2,3,4,5,6,7,8,9]). Difference equations are an important field of study in many applied sciences, including mathematics, physics, chemistry, statistics, sociology, psychology, and engineering.…”