The Study On Control Of Plankton Systems With Impulsive Effects

In this paper, we mainly investigate the dynamics of plankton systems with biological andchemical control, and consider the complex cases with diferent fxed moments impulse and stateimpulse respectively. To study these systems has important signifcance in theory and practice.The article includes three chapters.The preface is in chapter1, we introduce the research background of this article, the maintask and some important preliminaries.In Chapter2, the dynamical behaviors of a phytoplankton, herbivorous zooplankton andfsh three-trophic food chain plankton system with diferent fxed moments pulse in one impulseperiod was studied. we introduced periodic spraying chemical agent at t=(n+k1)T andreleasing fsh at t=nT diferent fxed moments to control phytoplankton. By using the Floquetmultiplier theory of impulsive diferential equation and the comparison theorem, we obtainedsufcient conditions for global attractivity of periodic solution of the extinction of plankton, andthe sufcient condition for the permanence of the system. Numerical simulations were carriedout to illustrate the main theoretical results.In Chapter3, we mainly discusses the dynamical behaviors of control of a phytoplanktonzooplankton system with constant fsh population with state dependent impulsive efects. Whenthe amount of phytoplankton reaches the threshold value h, we can use the methods of periodicspraying chemical agent and releasing artifcial capture to control phytoplankton bloom. Byusing the Poincar′e map, we analysed the existence and stability of semi-trivial solution and pos-itive periodic solutions. Numerical simulations were carried out to illustrate the main theoreticalresults.