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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, a rational difference equation with positive parameters and non-negative conditions is used to determine the presence and direction of the Neimark–Sacker bifurcation. The neimark–Sacker bifurcation of the system is first studied using the characteristic equation. In addition, we study bifurcation invariant curves from the perspective of normal form theory. A computer simulation is used to illustrate the analytical 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]

Across many fields, such as engineering, ecology, and social science, fuzzy differences are becoming more widely used; there is a wide variety of applications for difference equations in real-life problems. Our study shows that the fuzzy difference equation of sixth order has a nonnegative solution, an equilibrium point and asymptotic behavior. y i + 1 = D y i − 1 y i − 2 / E + F y i − 3 + G y i − 4 + H y i − 5 , i = 0,1,2 , ... , where y i is the sequence of fuzzy numbers and the parameter D , E , F , G , H and the initial condition y − 5 , y − 4 , y − 3 , y − 2 , y − 1 , y 0 are nonnegative fuzzy number. The characterization theorem is used to convert each single fuzzy difference equation into a set of two crisp difference equations in a fuzzy environment. So, a pair of crisp difference equations is formed by converting the difference equation. The stability of the equilibrium point of a fuzzy system has been evaluated. By using variational iteration techniques and inequality skills as well as a theory of comparison for fuzzy difference equations, we investigated the governing equation dynamics, such as its boundedness, existence, and local and global stability analysis. In addition, we provide some numerical solutions for the equation describing the system to verify our results. [ABSTRACT FROM AUTHOR]

In this paper, we study the boundedness character and persistence, local and global behavior, and rate of convergence of positive solutions of following system of rational difference equations x n + 1 = α 1 + β 1 e − y n a 1 + b 1 x n , y n + 1 = α 2 + β 2 e − z n a 2 + b 2 y n , z n + 1 = α 3 + β 3 e − x n a 3 + b 3 z n , wherein the parameters α i , β i , a i , b i for i ∈ { 1 , 2 , 3 } and the initial conditions x 0 , y 0 , z 0 are positive real numbers. Some numerical examples are given to verify our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we study the equilibrium points, local asymptotic stability of equilibrium points, global behavior of equilibrium points, boundedness and periodicity of the rational recursive sequence w n + 1 = w n − p α + β w n / γ w n + δ w n − r , where γ w n ≠ − δ w n − r for r ∈ 0 , ∞ , α , β , γ , δ ∈ 0 , ∞ , and r > p ≥ 0. With initial values w − p , w − p + 1 , ... , w − r , w − r + 1 , ... , w − 1 , and w 0 are positive real numbers. Some numerical examples are given to verify our theoretical results. [ABSTRACT FROM AUTHOR]

Our aim in this paper is to study the global stability character and the periodic nature of the solutions of the difference equation ... where the initial conditions x-r, x-r+1, x-r+2, ..., x0 are arbitrary positive real numbers, r = max{l, k, s, t} is nonnegative integer and a, b, c, d, e are positive constants. Finally, some numerical examples are presented and graphed by Matlab. [ABSTRACT FROM AUTHOR]

Our aim in this paper is to study the global stability character and the periodic nature of the solutions of the difference equation xn+1 = axn-l + b + cxn-k/dxn-s + exn-t, n = 0, 1, ..., where the initial conditions x-r, x-r+1, x-r+2, ..., x0 are arbitrary positive real numbers, r = max{l, k, s, t} is nonnegative integer and a, b, c, d, e are positive constants:Finally, some numerical examples are presented and graphed by Matlab. [ABSTRACT FROM AUTHOR]

Our aim in this paper is to study the global stability character and the periodic nature of the solutions of the difference equation xn+1 = axn-l + b + cxn-k/dxn-s + exn-t, n = 0, 1, ..., where the initial conditions x-r, x-r+1, x-r+2, ..., x0 are arbitrary positive real numbers, r = max{l, k, s, t} is nonnegative integer and a, b, c, d, e are positive constants:Finally, some numerical examples are presented and graphed by Matlab. [ABSTRACT FROM AUTHOR]

Our aim in this paper is to study the global stability character and the periodic nature of the solutions of the difference equation xn+1 = axn-1l + . . ., n = 0, 1, ..., where the initial conditions x-r, x-r+1, x-r+2, ..., x0 are arbitrary positive real numbers, r = max{l, k, s, t} is nonnegative integer and a, b, c, d, e are positive constants. [ABSTRACT FROM AUTHOR]

Our aim in this paper is to study the global stability character and the periodic nature of the solutions of the difference equation xn+1 = axn-1l + bxn-k + cxn-s/d + exn-t , n = 0, 1, ..., where the initial conditions x-r, x-r+1, x-r+2, ..., x0 are arbitrary positive real numbers, r = max{l, k, s, t} is nonnegative integer and a, b, c, d, e are positive constants. [ABSTRACT FROM AUTHOR]

We examine the unboundedness, persistence, boundedness, uniqueness, and existence of non-negative equilibrium of an exponential symmetric difference equations system: Ω n + 1 = α 1 + β 1 Ω n + γ 1 Ω n − 1 e − (Ω n + ϖ n) , ϖ n + 1 = α 2 + β 2 ϖ n + γ 2 ϖ n − 1 e − (Ω n + ϖ n) , n = 0 , 1 , ⋯ , whereby initial values Ω − 1 , ϖ − 1 , Ω 0 , ϖ 0 and parameters α 1 , α 2 are non-negative real numbers and β 1 , β 2 ∈ (0 , 1) and γ 1 , γ 2 ≤ 0 . We will discuss asymptotic global and local stability and the convergence rate of this system. Ultimately, to check our results, we set out some numerical explanations. [ABSTRACT FROM AUTHOR]