We study a general discrete planar system for modeling stage-structured populations. Our results include conditions for the global convergence of orbits to zero (extinction) when the parameters (vital rates) are time and density dependent. When the parameters are periodic we obtain weaker conditions for extinction. We also study a rational special case of the system for Beverton-Holt type interactions and show that the persistence equilibrium (in the positive quadrant) may be globally attracting even in the presence of interstage competition. However, we determine that with a sufficiently high level of competition, the persistence equilibrium becomes unstable (a saddle point) and the system exhibits period two oscillations.

We study the dynamics of a second-order difference equation that is derived from a planar Ricker model of two-stage biological populations. We obtain sufficient conditions for global convergence to zero in the non-autonomous case. This gives general conditions for extinction in the biological context. We also study the dynamics of an autonomous special case of the equation that generates multistable periodic and non-periodic orbits in the positive quadrant of the plane.

We study global and local dynamics of a simple search and matching model of the labor market. We show that the model can be locally indeterminate or have no equilibrium at all, but only for parameterizations that are empirically implausible. In contrast to the local results, we show that the model exhibits chaotic and periodic dynamics for reasonable parameter values both in backward and forward time. In contrast to earlier work, we establish these results analytically without placing numerical restrictions on the parameters.JEL Classification: C62, C65, E24, J64

We study global and local dynamics of a simple search and matching model of the labor market. We show that the model can be locally indeterminate or have no equilibrium at all, but only for parameterizations that are empirically implausible. In contrast to the local results, we show that the model exhibits chaotic and periodic dynamics for reasonable parameter values both in backward and forward time. In contrast to earlier work, we establish these results analytically without placing numerical restrictions on the parameters.

We study the evolution in discrete time of certain age-structured populations, such as adults and juveniles, with a Ricker fitness function. We determine conditions for the convergence of orbits to the origin (extinction) in the presence of the Allee effect and time-dependent vital rates. We show that when stages interact, they may survive in the absence of interior fixed points, a surprising situation that is impossible without inter-stage interactions. We also examine the shift in the interior Allee equilibrium caused by the occurrence of interactions between stages and find that the extinction or Allee threshold does not extend to the new boundaries set by the shift in equilibrium, i.e. no interior equilibria are on the extinction threshold.