Stability loss delay in harvesting competing populations

When populations are in competition, it often happens that one of them disa ppears. Harvesting may be used for the control and management of competing species to stabilize the populations at a persistent equilibrium. A three-d imensional model, where the harvesting effort is a dynamic variable, is stu died in the case where the growth rate of the harvesting effort is very slo w. The analysis shows that the system can have relaxation oscillations. Dyn amic bifurcation theory is used to determine the maximal and minimal values of harvesting effort along this cycle of oscillations. (C) 1999 Academic P ress.