Neimark‐Sacker bifurcation of a fourth order difference equation

Abstract

In this article, we study stability and bifurcation of a fourth order rational difference equation. We give condition for local stability, and we show that the equation undergoes a Neimark‐Sacker bifurcation. Moreover, we consider the direction of the Neimark‐Sacker bifurcation. Finally, we numerically validate our analytical results.

Existence of infinitely many solutions of nonlinear fourth-order discrete boundary value problems

“…In recent years, due to the wide applications of difference equations [7][8][9], the discrete elastic beam problems have attracted extensive attention of scholars. The methods include the fixed point theorem [10], invariant sets of descending flow [11], bifurcation techniques [12], etc. In 2003, the critical point theory was first used to prove the existence of periodic and subharmonic solutions of second-order difference equations [13].…”