Abstract
This paper studies a plankton–fish model with distributed delay in the context of marine plankton interaction together with predation by planktotrophic fish. The delay indicates that the growth of the zooplankton depends on the past density of phytoplankton. The positive equilibrium point and its local stability are investigated. Using the average time delay as bifurcation parameter, we obtain the conditions of the existence of Hopf bifurcation. Based on the normal form and center manifold theorem, stability, direction, and other properties of bifurcating periodic solutions are derived. Moreover, a state feedback control method, which can be implemented by adjusting the harvesting for zooplankton population, is proposed to drive the plankton–fish system to a steady state. Numerical simulations illustrate the effectiveness of results and the related biological implications are discussed.
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