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.

Keywords

• difference equation
• stability
• fixed points
• Neimark–Sacker bifurcation
• phase portraits