The global dynamics of a discrete juvenile–adult model with continuous and seasonal reproduction

Abstract

A general discrete juvenile–adult population model with time-dependent birth rate and nonlinear survivorship rates is studied. When breeding is continuous, it is shown that the model has a unique globally asymptotically stable positive equilibrium provided the net reproductive number is larger than one. If it is smaller than one, then the extinction equilibrium is globally asymptotically stable. When breeding is seasonal, it is shown that there exists a unique globally asymptotically stable periodic solution provided the net reproductive number is larger than one. When this value is less than one, the population goes to extinction. Conditions on the birth rate where the population with seasonal breeding survives while the population with continuous breeding becomes extinct are provided. © 2009 Taylor & Francis Group, LLC.