Diffusion And Time Delay Dynamics Mechanism Of Several Kinds Of Plankton Ecosystem

The ecological disaster problems such as the red tide,algal bloom caused by eutrophication have received extensive attention,and its mechanism is becoming a hot spot of research at home and abroad.Based on the theoretical knowledge of functional differential equations,partial differential equations and aquatic ecology,this paper studies the diffusion and timed delay dynamics mechanism of several kinds of plankton ecosystem.Firstly,a phytoplankton-zooplankton aquatic ecosystem is discussed,and the diffusion dynamics mechanism of aquatic ecosystem is researched.The theoretical works have been pursuing the investigation of the stability of the positive equilibrium,the existence of Hopf bifurcation and the conditions of Turing instability,which can deduce a standard parameter control relationship and in turn can provide a theoretical basis for the numerical simulation.Numerical analysis indicates that the theoretical results are feasible and correct,and the system can show complex diffusion dynamics mechanism.Secondly,we consider a phytoplankton and zooplankton ecosystem with a Holling-type II functional response and a Beddington-DeAngelis functional response.The theoretical works explore the local and global asymptotic stability of the positive equilibrium and the critical condition for the coexistence of the three species.In particular,we investigate the existence and nonexistence of non-constant positive steady state solutions.The results show that without considering the diffusion factor,the positive equilibrium of the ecosystem is locally asymptotically stable.However,in consideration of diffusion factor,the positive equilibrium becomes unstable,then the ecosystem produces non-constant steady-statesolutions.Finally,we analyze a nutrient–plankton ecosystem with a time delay.,and the time delay dynamics mechanism of the ecosystem is studied.Using the time delay as the parameter,we investigate the stability of a positive equilibrium and the existence of Hopf bifurcation.We then study the direction and stability of Hopf bifurcation.Our theoretical results indicate that a time delay can induce a positive equilibrium to switch from a stable to an unstable to a stable state,and so on.Numerical simulations show that the system exhibits rich complex dynamics.Important points to note are that a finite number of stability switches are possible and the time delay has an important influence on the dynamics of the ecosystem.