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 A i / z i , z i − 3 , i = 0,1,2 , … .

The Dynamical Behavior of a Three-Dimensional System of Exponential Difference Equations

“…I 1 , I 2 , and I 3 are defined in (9). Then, from (18), (19), (20), and (21), we see that for U ∈ I 1 , V ∈ I 2 , and…”

“…Let (U m , V m , W m ) be a solution of (1). As requirements (2) from Theorem (2) are implied by relations (18), (19), there exists n 0 such that relations U m ∈ I 1 , V m ∈ I 2 and W m ∈ I 3 hold.…”

“…Theorem 5. Consider system (1) that stores either (18) and (19) or (43). Assume that the following relationship holds true:…”

“…Analyzing the dynamics of solutions to systems of difference equations, and discussing the local and global asymptotic stability of their equilibriums, is interesting [10,12,13,[15][16][17][18]. The authors in [19], obtained the behavior of solutions to the difference equation:…”