On a Class of Discrete Max-Type Difference Equation Model of Order Four

Abstract

Discrete models are versatile and effective tools for assessing and addressing a wide range of scientific and practical problems. As a type of discrete model, the difference equation model has been widely employed in domains such as algorithm analysis, signal processing, biology, economics, and computer science. The global dynamical behavior of a class of discrete models known as the max-type difference equation model is the subject of the research. The purpose of this work is to look into the behavior of the solution of the following four-order max-type difference equation: $z_{i+1}=\max \left\{A_i/z_i,z_{i-3}\right\},i=\mathrm{0,1,2},\dots .$