Border Collision Bifurcations in a Generalized Model of Population Dynamics

Figure 2

Regions in the parameter plane related to the different regimes involved in the definition of system for and . In (a) while in (b) . The black curves separate regions in which is defined by (1), and (1 + 2), and (1 + 4), and so on. (c) Given the parameters as in (b), the bifurcation curves and are depicted: they represent parameter values such that loses its stability or the two fixed points merge, respectively. (d) For case (b) the regions denote different asymptotic dynamics for a given initial condition: in red is the 2-period cycle, in blue is the convergence to , and in yellow is the convergence to .

(a)

(b)

(c)

(d)