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In recent years, conventional Ricker maps have enjoyed widespread applications across crucial domains such as modeling and security. However, their limitation to a single changeable parameter poses constraints on their adaptability. This paper introduces a generalized form of the Ricker map, incorporating arbitrary powers, thus offering enhanced versatility compared to the traditional Ricker map. By introducing an additional parameter (arbitrary power), the map gains increased degrees of freedom, thereby accommodating a broader spectrum of applications. Consequently, the conventional Ricker map emerges as merely a special case within each proposed framework. This newfound parameter enhances system flexibility and elucidates the conventional system's performance across diverse contexts. Through numerous illustrations, we meticulously investigate the impact of the arbitrary power and equation parameters on equilibrium points, their positions, basin of attraction, stability conditions, and bifurcation diagrams, including the emergence of chaotic behavior. [ABSTRACT FROM AUTHOR]

In this paper, we study a stochastic SIS epidemic model with distributed delays. The positiveness of the solutions is established. We obtain sufficient conditions for the extinction of the disease through the study of stochastic stability of the disease-free equilibrium and stability of the same equilibrium in the mean. Compared to many works on the deterministic and stochastic SIS models and their stability, the distributed delays involved in the model offer new conditions with much more boundedness on the rate of losing immunity. The disease is extinct for small and large enough values of the intensity of noise and regardless of the initial history functions and the magnitude of the basic reproductive number R 0. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to study the global attractivity, and the boundedness for the solutions of the rational difference equation ... where the parameters &#945, &#945, &#945, A,B,p and q ∊ (0,∞) and the initial conditions x-l; x-l+1; :::; x-1; x0 where l = max{km} are positive real numbers. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to investigate the qualitative behavior of the solutions for the following rational difference equation: ... where α, β, ai,bi ∈ (0,∞),i =0, 1, ..., k; with the initial conditions x0,x-1, ..., x-2k,x-2k-1 ∈ (0,∞). We determine the equilibrium points of the considered equation and then study their local stability. Also we study the boundedness and the permanence of the solutions. Finally we investigate the global asymptotically stable of the equilibrium points. [ABSTRACT FROM AUTHOR]

This paper is devoted to investigate the global behavior of the following rational difference yn+1 = αyn-t/(β + γ Σi=0k yn-(2i+1)p ∏i=0k yn-(2i+1)q), n = 0, 1, 2, ... where α, β, γ, p, q ∈ (0, ∞) and k, t ∈ {0, 1, 2, ...} with the initial conditions x0, x-1, ..., x-2k, x-2 max {k, t}-1 ∈ (0, ∞). We will find and classify the equilibrium points of the equations under studying and then investigate their local and global stability. Also, we will study the oscillation and the permanence of the considered equations. [ABSTRACT FROM AUTHOR]

This paper deals with the investigation of the following more general rational difference equation: yn+1 = αyn/(βi=0k yn-(2i+1)p ∏i=0kyn-(2i+1)), n = 0, 1, 2,..., where α, β, γ, p ∈ (0, ∞) with the initial conditions x0, x-1,...,x-2k, x-2k-1 ∈ (0, ∞). We investigate the existence of the equilibrium points of the considered equation and then study their local and global stability. Also, some results related to the oscillation and the permanence of the considered equation have been presented. [ABSTRACT FROM AUTHOR]

We investigate some qualitative behavior of the solutions of the difference equation xn+1 = axn -bxn/(cxn -dxn-1), n = 0, 1, … , where the initial conditions x-1, x0 are arbitrary real numbers and a, b, c, d are positive constants. [ABSTRACT FROM AUTHOR]

We investigate some qualitative behavior of the solutions of the difference equation xn+1 = axn -bxn/(cxn -dxn-1), n = 0, 1, … , where the initial conditions x-1, x0 are arbitrary real numbers and a, b, c, d are positive constants. [ABSTRACT FROM AUTHOR]