Dynamics of Planar Systems That Model Stage-Structured Populations

Abstract EN

We study a general discrete planar system for modeling stage-structuredpopulations.

Our results include conditions for the global convergence oforbits to zero (extinction) when the parameters (vital rates) are time and density dependent.

When the parameters areperiodic we obtain weaker conditions for extinction.

We also study a rationalspecial case of the system for Beverton-Holt type interactions and show thatthe persistence equilibrium (in the positive quadrant) may be globallyattracting even in the presence of interstage competition.

However, wedetermine that with a sufficiently high level of competition, the persistence equilibrium becomes unstable (a saddle point) and the system exhibits period twooscillations.