Abstract
In this paper we have considered a prey–predator type fishery model with stage-structure for predator and harvesting of both the prey and predator species. Our study shows that, using the harvesting effort as control, it is possible to break the cycle behaviour of the system and drive it to required steady state. It is also shown that the time delay can cause a stable equilibrium to become unstable and even a switching of stabilities. We also investigate the stability of the bifurcating limit cycles and direction of Hopf bifurcation by applying the normal form method and the center manifold theorem. Lastly some numerical simulations are carried out to validate our analytical results.
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