Stability and Bifurcation Analysis of Fifth-Order Nonlinear Fractional Difference Equation

Abstract

In this paper, a rational difference equation with positive parameters and non-negative conditions is used to determine the presence and direction of the Neimark–Sacker bifurcation. The neimark–Sacker bifurcation of the system is first studied using the characteristic equation. In addition, we study bifurcation invariant curves from the perspective of normal form theory. A computer simulation is used to illustrate the analytical results.

Analytical Study of Nonlinear Systems of Higher-Order Difference Equations: Solutions, Stability, and Numerical Simulations

“…Following some initial computations, the characteristic polynomial of Θ q can be expressed as follows: 4 , By utilizing MATLAB R2021b, it is determined that all solutions to Q Θ q (λ) = 0, q ≥ 0 reside within the unit disc |λ| < 1. By Rouche's Theorem, it can be concluded that the positive equilibrium point Ξ is locally asymptotically stable.…”

“…Existing research has probed various facets of nonlinear dynamics, encompassing local dynamics, topological classifications, bifurcation analysis, and chaos control. For example, Khan et al [3] investigated these dynamics within the context of a discrete-time COVID-19 epidemic model, while other studies [4,5] have explored similar phenomena across different domains. However, while several methods exist for solving linear difference equations, the landscape of nonlinear systems remains largely uncharted.…”

The Dynamical Behavior of a Three-Dimensional System of Exponential Difference Equations

“…Analyzing the dynamics of solutions to systems of difference equations, and discussing the local and global asymptotic stability of their equilibriums, is interesting [10,12,13,[15][16][17][18]. The authors in [19], obtained the behavior of solutions to the difference equation:…”