Global Dynamics of Delayed Sigmoid Beverton–Holt Equation

Abstract EN

In this paper, certain dynamic scenarios for general competitive maps in the plane are presented and applied to some cases of second-order difference equation xn+1=fxn,xn−1, n=0,1,…, where f is decreasing in the variable xn and increasing in the variable xn−1.

As a case study, we use the difference equation xn+1=xn−12/cxn−12+dxn+f, n=0,1,…, where the initial conditions x−1,x0≥0 and the parameters satisfy c,d,f>0.

In this special case, we characterize completely the global dynamics of this equation by finding the basins of attraction of its equilibria and periodic solutions.

We describe the global dynamics as a sequence of global transcritical or period-doubling bifurcations.