| Plankton model is a model that describes the dynamics of interaction between phyto-plankton and zooplankton,and studies the predation relationship between plankton,which is helpful to control and eliminate algal blooms,which is of great significance for the pro-tection of aquatic ecology.Among them,the growth of phytoplankton and zooplankton will inevitably be affected by environmental white noise,such as temperature,humidity,light changes,etc.;secondly,the delay caused by the gestation time of plankton and the digestion time after predation will affect the dynamic behavior of the system.Meanwhile,plankton will move around due to diffusion and water flow,so the spatial effect also has a great influ-ence on the model.In order to comprehensively analyze the complex dynamic relationship between phytoplankton and zooplankton,the influence of environmental noise,time delay and spatial effects on the model is considered.The main contents are as follows:1.Study the dynamics of a stochastic plankton model in foraging arena.It is proved that for any given positive initial value,the model has a unique global positive solution.By using the comparison theorem of stochastic differential equations,the sufficient conditions of model persistence and extinction and the existence of ergodic stationary distribution are obtained.The results show that environmental noise has a great influence on the model.Too large noise intensity will lead to the extinction of phytoplankton and zooplankton,but at low noise intensity,phytoplankton and zooplankton will persist.Finally,numerical simulation is used to verify the theoretical analysis results obtained.2.Study the dynamics of a plankton-fish model with time delay and toxin release.Firstly,it is proved that the solution of the model is non-negative and bounded.When the time delayτ=0,the stability condition of the equilibrium state of the model is obtained and the sufficient conditions for the existence of Hopf bifurcation and transcritical bifurcation are obtained by using toxin releaseρand zooplankton death rate d2as bifurcation parameters.The results show that the high toxin release will lead to fish extinction and when d2passes its multiple critical values,the model will switch stability several times.When the delayτ>0,takingτas the bifurcation parameter,using the canonical type theory and the central manifold theorem,the existence conditions of the Hopf bifurcation and the properties of the periodic solutions of the bifurcation,such as stability and direction are obtained.The conclusion shows that too large time delay will lead to the instability of the plankton model.Finally,the theoretical analysis results are verified by numerical simulation.3.Study the dynamics of a diffusive plankton model with time delay and different harvesting.When the time delayτ=0,sufficient conditions for the existence and stability of the model solution are obtained.The results show that the positive equilibrium point is locally stable when the phytoplankton capture rate c1is in a certain range.When the time delayτ>0,taking the time delayτas the bifurcation parameter,using the canonical type theory and the central manifold theorem,the existence conditions of the Hopf bifurcation and the properties of the periodic solutions of the bifurcation,such as stability and direction are obtained.The results show that too large time delay will lead to the instability of the plankton model.Finally,the theoretical results are verified by numerical simulation. |
