Dynamical Behavior of the Rational Difference Equation Xn+1 = Xn-13/±1 ± Xn-1Xn-3Xn-5Xn-7Xn-9Xn-11Xn-13

Abstract

Discrete-time systems are sometimes used to explain natural phenomena encountered in nonlinear sciences. We study the periodicity, boundedness, oscillation, stability, and some exact solutions of nonlinear difference equations. Exact solutions are obtained by using the standard iterative method. Some well-known theorems are used to test the stability of equilibrium points. Some numerical examples are also provided to confirm the validity of the theoretical results. The numerical component is implemented with the Wolfram Mathematica. The presented method may be simply applied to some other rational recursive issues. We explore the dynamics of adhering to the rational difference formula x(n+1) = x(n-13)/+/- 1 +/- x(n-1)x(n-3)x(n-5)x(n-7)x(n-9)x(n-11)x(n-13), where the initials are arbitrary nonzero real numbers.