On constant effort harvesting and stocking in a class of predator-prey systems

Abstract

We analyze the global behaviour of predator-prey systems under constant effort harvesting and stocking of either or both species. Mathematically this is equivalent to the behaviour of an unharvested system with different parameters; in particular every solution tends either to an equilibrium or to a limit cycle, and there is no possibility of finite-time extinction of either species if both populations are positive initially. The dependence of the behaviour on the harvesting efforts is discussed.