Abstract:
Abstract: We study the equilibrium point (n
∗
, E∗
) of the fishery model with Allee effect in its population growth dynamics.
The Allee effect is considered to be induced by the harvesting of the fish stock. The aggregated model is a set of two
differential equations with the fish population and harvesting effort as the dependent variables, with the market price having
been taken to evolve faster hence the aggregation from a three dimensional system to a two dimensional system. The analysis
of the equilibrium point is performed by looking at three cases in which the threshold population is set at three different values;
4
n
T = ,
2
n
T = and 3
4
n
T = . Three different equilibrium solutions are obtained: A stable equilibrium, coexistence of three
equilibria points with two being saddles and the other stable and the co-existence of three equilibria points with two being
stable and a saddle between them. The equilibrium solutions depicts three kinds of fishery: A fishery with fish population
maintained at high levels far from extinction but with little economic activity, a fishery with co-existence of an over-exploited
and an under-exploited state, which is a dilemma since neither of the state supports sustainable fish resource exploitation, and a
fishery that is well managed with fish population being harvested in a sustainable manner thus a balance between commercial
harvesting and species existence.
Keywords: Allee Effect, Fishing Mortality, Equilibrium Solution
