| The population ecosystems are typical complex system.The dynamic model of the ecosystems can be established through big data analysis,and the nonlinear state equations of the ecosystems can be obtained.Because most of the system dimensions are too high or non-autonomous,it is difficult to find the analytical solution of the dynamics equations.In this paper,the dynamics equation have been analyzed and simulated by means of approximate dimensionality reduction and numerical simulation,and the dynamics stability of two tepys of population ecosystems have been studied.The ecosystem is home to thousands of species that interact in complex ecosystems of populations,including predation,mutual benefit and competition.In the current cognition,the predation behavior in the population ecosystem is a very common phenomenon.The classical Lotka-Volterra predator-prey model simulates this phenomenon,and the stability analysis of the singularity of the solution of the equation has been carried out.Stability analysis,however,predators and prey in the predation process are affected by many factors such as the natural environment,natural enemies,foraging,and reproduction.Because the classic Lotka-Volterra prey-predator model lacks practical considerations and can’t simulate the actual ecological environment,so a lot of modifications have been made to the model,such as functional response,noise,disease,refuge and Allee effect.The survey found that species migration is ubiquitous in complex ecosystems and often plays an important role in biodiversity.Therefore,we consider that in the two-system prey-predator model of two prey,there is a prey with migration that explores the dynamic behavior of such systems.In this work,by introducing a time-varying migration rate associated with the difference of subpopulation density into a prey,we study the Hopf bifurcation and the critical phenomenon of predator extinction of the three species prey-predator system,which consists of a predator,a prey and a mobile prey.It is found that the system with migration exhibits richer dynamic behaviors than that without migration,including two Hopf bifurcations and two limit cycles.Interestingly,the parameters of migration have a drastically influence on the critical point of predator extinction,determining the coexistence of species.Moreover,the population evolution dynamics of one-dimensional multiple prey-predator system are also discussed.Ecosystems have a wide range of biodiversity,which is related to network structure,environmental changes,and species fitness,leading to the equilibrium of the coexistence of different proportions of species.But a small disturbance can often cause dramatic changes in biodiversity and even lead to extinction of species.In our other work to study the population ecological dynamic stability,we introduced genetic diversity into a symbiotic network model and studied the impact of genetic diversity on the tipping point in the system.Through inquiry,we conclude that an appropriatelysized genetic diversity can induce critical points to move or even disappear,thereby improving the stability of the ecosystem.Numerical simulation results very good verification of the results of mathematical analysis.In addition,genetic diversity may also impair the bistable or lagging behavior of the system.The main chapters of the paper are as follows:The first chapter introduces the relevant research background of this topic and the progress of the research questions and the main conclusions of this paper,as well as an overview of the classic prey and predator model,Mutualistic Network model,and Holling functional response.The second chapter introduces the predator and prey model with time-varying migration of dual-system prey and the analysis of simulation results.The works of this part have been published in ’Commun.Theor.Phys.’.In chapter three,exploring the impact of genetic diversity on the tipping point in a symbiotic network.The works of this part have been submitted to ’Phys.Rev.E’. |
PDF Full Text Request