Global Dynamics of Delayed Sigmoid Beverton-Holt Equation
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.