Optimal stocking for semi-desert range: A catastrophe theory model

Abstract

An analytical model is developed for describing equilibrium states for simple grazing systems. Known general relationships are recast as a cusp catastrophe to enable analytic treatment within the powerful catastrophe theory formalism. The model allows explicit consideration of precipitation and intensity of livestock harvesting. The model may be used to determine management strategies that prevent degradation of grassland into desert, that minimize herd fluctuations, or that maximize harvest rates.