Abstract
In this paper, we formulate a delayed phytoplankton-zooplankton model with impulsive diffusion on phytoplankton. Using the discrete dynamical system determining the stroboscopic map, we obtain the zooplankton-extinction periodic solution which is globally attractive. The conditions of the permanence are given by using the theory on the delay and impulsive differential equation. Finally, some numerical simulations are presented to illustrate the results.
Highlights
Plankton, including phytoplankton and zooplankton, are an important food source for organisms in an aquatic environment
Many mathematical models have been formulated to describe the dynamical interaction between zooplankton and phytoplankton [ – ]
In [ ], deterministic and stochastic models of nutrient-phytoplankton-zooplankton interaction are proposed to investigate the impact of toxin-producing phytoplankton upon persistence of the populations
Summary
Plankton, including phytoplankton and zooplankton, are an important food source for organisms in an aquatic environment. Many mathematical models have been formulated to describe the dynamical interaction between zooplankton and phytoplankton [ – ]. The author of [ ] formulated a toxin-producing phytoplankton-zooplankton model with stochastic perturbation and investigated the global stability of the positive equilibrium by means of constructing suitable Lyapunov functions. Wang et al [ ] proposed a single species model with impulsive diffusion between two patches and obtained a globally stable positive periodic solution by using the discrete dynamical system generated by a monotone, concave map for the population. K contributes to the death of zooplankton population, where is a halfsaturation constant, β denotes the rate of toxin liberation by toxin-producing phytoplankton.
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