A discrete-time Beverton-Holt competition model

Coexistence and extinction in a competitive exclusion Leslie/Gower model with harvesting and stocking

“…only the dominant species survives. Ackleh et al [1] also studied a special case of system (1.5) where the PCE was also well supported.…”

“…The monographs [24 -26] offer an excellent reference on results, open problems and conjectures about the global behaviour of rational difference equations. Systems of rational difference equations have also received some attention, see for instance [1,16,18,19,21].…”

“…1, the two lines are actually parallel. Ackleh et al [1] also considered the Beverton -Holt competition model described by the system of equations…”

“…then E 1 (conjectured to be GAS) is the only asymptotically stable fixed point [1]. Since system (3.1) does not allow coexistence between species, we introduce an outside intervention in an attempt to yield the survival of all species.…”

“…In fact, laboratory experiments on yeast and protoza [20], flour beetles [29 -32] and actual observations on the populations of tropical stream fishes [40] are all in total accord with the PCE. On the other hand, both continuous-time LoktaVolterra models [2] and discrete-time models [1,18], as well as chemostat models [36] have validated PCE under reasonable assumptions about model parameters.…”