CODIMENSION TWO PHENOMENA OF A DELAY DIFFERENCE EQUATION

In this paper, the bifurcations of a difference equation are explored in their entirety. Codimension one and two bifurcations are then studied both analytically and numerically. We reveal the complex dynamics that can emerge from the interplay of time delays and non-linearities using numerical continuation. Our findings determine the complex bifurcation structures inherent in the DDE model, provide new insights into critical transition phenomena, and advance our understanding of the mechanisms that drive complex dynamical systems.