Analytic solutions and stability of sixth order difference equations (Q2004212)

Summary: In the present paper, the global attractor, local stability, and boundedness of the solution of sixth order difference equations are investigated analytically and numerically. The exact solutions of three equations are presented by utilizing Fibonacci sequence. We also analyse the periodicity of a sixth order difference equation. The considered difference equations are given by \(y_{n + 1}=A y_{n - 1}\pm\left( B y_{n - 1} y_{n - 3} / C y_{n - 3} \pm D y_{n - 5}\right)\), \(n=0,1,\ldots\), where the initial conditions \(y_{- 5}\), \(y_{- 4}\), \(y_{- 3}\), \(y_{- 2}\), \(y_{- 1}\), and \(y_0\) are arbitrary real numbers and the values \(A\), \(B\), \(C\), and \(D\) are defined as positive real numbers.