t
and herbivorous
zooplankton
()yt
are persistent, while carnivorous
zooplankton
()zt
go to extinction with probability
one.
The proof is quite similar to Theorem 4.1 in (Liu
2019), so we omit it here.
3 CONCLUSIONS
In this work, we use the model of Hastings and
Powell as a starting point to construct a more
realistic tri-trophic plankton food chain model (4)
that includes environmental perturbation. The
persistence and extinction of the plankton in a long
time are discussed.
Theorem 2.1 implies that the plankton will be
persistent, that is to say, all the phytoplankton and
zooplankton will survive in a long time under certain
conditions. Theorem 2.2 shows that the plankton
will extinct in three cases.
We have explored dynamic behaviors of the food
chain model. We believe that this work can predict
the variation trend of the population of each species,
so as to better manage the population and provide
theoretical basis for the safety and protection of the
environment.
ACKNOWLEDGEMENTS
This work was funded by the National Nature
Science Foundation of China (No 11871473), the
Fundamental Research Funds for the Central
Universities (No. 15CX08011A).
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