Modeling,analysis And Application Of Population Dynamics With Allee Effect And Crested Ibis Are Considered Respectively

With the progress of society,the overuse of resources has caused the loss of biodiversity,and biological protection has become the focus of our country at present.The rapid development of biomathematics has made many ecological problems solved through establishing dynamical models.Single-population models with stage structure have an important significance in the research of population dynamics,and Allee effect also plays an important role in population dynamics as an special regulatory mechanism.In this article,a class of single-species model with stage structure and Allee effect is established firstly,and its dynamics are analyzed theoretically.The theoretical results are verified by numerical simulation.Secondly,a stage-structured population model with seasonal breeding is established according to the biological traits of the endangered species Crested Ibis(Nipponia nippon).Based on this model,the effects of natural enemies and harsh climate on Crested Ibis are considered.the main research content is in the second and third chapters.In Chapter 2,a three-stage population dynamical model with Allee effect is established.It is proved that the extinct equilibrium is globally stable if the positive equilibrium does not exist.The conditions of the existence of one positive equilibrium and vi two positive equilibria are also obtained.If there is only one positive equilibrium in the system,the local stability of this positive equilibrium is verified,and then the condition of global stability of the positive equilibrium is studied.If two positive equilibria exist at the same time,we prove that the smaller positive equilibrium is unstable,and Hopf bifurcation can be generated from the larger positive equilibrium,which leads to the bistable phenomena of extinct equilibrium and positive periodic solution.In Chapter 3,from the perspective of dynamics,a two-stage structural population dynamical model with seasonal reproduction is established based on the main biological traits of wild Crested Ibis.Based on the previous research and statistics,the parameters of this model are estimated by ordinary least squares.The accuracy of the model and the estimated parameters is tested statistically.The growth trend of the wild Crested Ibis in the next 20 years in Ningshan,Shaanxi Province is predicted by this model,and the random hazards are taken into account.The results show that the population of Crested Ibis can grow steadily in the next 20 years.Predation by natural enemies occurring in non-breeding period makes a wider impact range.High-frequency predation by natural enemies also leads to extinction.Adverse weather in breeding and non-breeding periods has the same impact on population,and the adverse weather which causes extremely serious disasters might lead to Crested Ibis eliminating.However,the decrease of food caused by harsh climate has little effect on Crested Ibis.Finally,the extinct probability of Crested Ibis in the next 20 years is calculated to be zero under the two disasters.