Dynamics of Water Hyacinth in a Fishery System with Delay Effect

This paper analyses the dynamics of a fishery system in an aquatic environment that consists of two zones: water hyacinth zone and free zone. Fish harvesting is allowed in both the zones and fish migration is allowed from water hyacinth zone to free zone and not back. This paper presents dynamics of the stability when discrete time delay is incorporated in the fish death rate due to oxygen depletion and water pollution caused by water hyacinth. It is shown that the time delay can cause a switch from stable state to unstable state and there by Hopf-bifurcation occurs. Numerical simulations are carried out to validate the analytical findings.