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The boundedness nature and persistence, global and local behavior, and rate of convergence of positive solutions of a second-order system of exponential difference equations, is investigated in this work. Where the parameters A , B , C , α , β , γ , δ , η , and ξ are constants that are positive, and the initials U − 1 , U 0 , V − 1 , V 0 , W − 1 , and W 0 are non-negative real numbers. Some examples are provided to support our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the form and the periodicity of the solutions of the max-type system of difference equations u n + 1 = max A n / v n − 1 , u n − 1 , v n + 1 = max B n / w n − 1 , w n + 1 = max C n / u n − 1 , w n − 1 where the initial conditions u − 1 , u 0 ∈ 0 , ∞ , v − 1 , v 0 ∈ 0 , ∞ , w − 1 , w 0 ∈ 0 , ∞ and A n n ∈ N 0 , B n n ∈ N 0 , C n n ∈ N 0 are positive two-periodic sequences. [ABSTRACT FROM AUTHOR]

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 , .... [ABSTRACT FROM AUTHOR]