No abstract

In this paper, solution of the following difference equation is examined x n+1 = x n−17 1 + x n−5 .x n−11 , where the initial conditions are positive reel numbers.

We explore the dynamics of adhering to rational difference formula $$ \psi_{m+1}=\frac{\psi_{m-20}}{\pm 1 \pm \psi_{m-2}\psi_{m-5}\psi_{m-8}\psi_{m-11}\psi_{m-14}\psi_{m-17}\psi_{m-20}}, \quad m \in \mathbb{N}_{0} $$ where the initials are arbitrary nonzero real numbers. Specifically, we examine global asymptotically stability. Additionally, we provide examples and solutions graphs of some special cases.

In the recent years, there has been a lot of interest in studying the global behavior of, the socalled, max-type difference equations; see, for example, [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]. The study of max type difference equations has also attracted some attention recently. We study the behaviour of the solutions of the following system of difference equation with the max operator: paper deals with the behaviour of the solutions of the max type system of difference equations, (1)\matrix{ {x_{n + 1} = max \left\{ {{A \over {x_{n - 1} }},{{y_n } \over {x_n }}} \right\};} & {y_{n + 1} = max \left\{ {{A \over {y_{n - 1} }},{{x_n } \over {y_n }}} \right\},}} where the parametr A and initial conditions x−1,x0, y−1,y0 are positive reel numbers.

In this paper, we are going to analyze the following difference equation