Dynamics of planar systems that model stage-structured populations
Summary: 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.
scientific article; zbMATH DE number 7025225
scientific article