Özet:
In this study, a phytoplankton–zooplankton system has been modelled
using a system of differential equations with piecewise constant arguments,
which represents a new approach to modelling phytoplankton–
zooplankton interaction. To analyse the dynamic behaviour of the
model, we consider the solution of the system in a certain subinterval,
which yields a system of difference equations. Some theoretical results
on the boundedness character and local stability properties for the
discrete dynamical system are obtained. In addition, we explain the
biological dynamics of the bloom in the plankton model through
Neimark–Sacker bifurcation and obtain the threshold values for different
parameters that govern the periodic nature of the bloom. We conclude
that, while other studies explained that the bloom depended on only
one parameter, this study explains that the bloom depended on three
different parameters, namely θ (rate of toxin production per phytoplankton),
β (zooplankton growth efficiency) and K (environmental carrying
capacity of phytoplankton).