ABSTRACT
In this paper, a delayed phytoplankton-zooplankton system with the coeffcient depending on delay is investigated. Firstly, it gives the nonnegative and boundedness of solutions of the delay differential equations. Secondly, it gives the asymptotical stability properties of equilibria in the absence of time delay. Then in the presence of time delay, the existence of local Hopf bifurcation is discussed when the delay changes. In addition to that, the stability of periodic solution and bifurcation direction are also obtained through the use of central manifold theory. Furthermore, he global continuity of the local Hopf bifurcation is discussed by using the global Hopf bifurcation result of FDE. At last, some numerical simulations are presented to show the rationality of theoretical analyses.
Subject(s)
Phytoplankton/physiology , Zooplankton/physiology , Algorithms , Animals , Computer Simulation , Eutrophication , Models, Biological , Population Dynamics , Reproducibility of Results , Time FactorsABSTRACT
A stochastic SIR model with vertical transmission and vaccination is proposed and investigated in this paper. The threshold dynamics are explored when the noise is small. The conditions for the extinction or persistence of infectious diseases are deduced. Our results show that large noise can lead to the extinction of infectious diseases which is conducive to epidemic diseases control.
