The dynamics of the solutions of some difference equations
Summary: This paper is devoted to investigate the global behavior of the following rational difference equation: \(y_{n+1} = \alpha y_{n-t}/(\beta + \gamma \sum^k_{i=0} y^p_{n-(2i+1)} \prod^k_{i=0} y^q_{n-(2i+1)})\), \(n = 0, 1, 2, \dots\), where \(\alpha, \beta, \gamma, p, q \in (0, \infty)\) and \(k, t \in \{0, 1, 2, \dots\}\) with the initial conditions \(x_0, x_{-1}, \dots, x_{-2k}, x_{-2\max \{k, t\} - 1} \in (0, \infty)\). 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.
scientific article; zbMATH DE number 6096228
scientific article