Stability and Neimark–Sacker Bifurcation of a Delay Difference Equation

Abstract

In this paper, we revisit a delay differential equation. By using the semidiscretization method, we derive its discrete model. We mainly deeply dig out a Neimark–Sacker bifurcation of the discrete model. Namely, some results for the existence and stability of Neimark–Sacker bifurcation are derived by using the center manifold theorem and bifurcation theory. Some numerical simulations are also given to validate the existence of the Neimark–Sacker bifurcation derived.

Keywords

• delay difference equation
• semidiscretization method
• stability
• Neimark–Sacker bifurcation