Dynamic Behavior Analysis Of Several Species With Cannibalism And Intraspecific Predation

Based on the cannibalism phenomena of natural biological populations and the intraspecific competition behaviors in a certain biological population,several types of population models with cannibalism are established in this thesis.One is a population model with cannibalism and intraspecific predation,and the other is a population infectious disease model with cannibalism and prions.Through the analysis of the dynamics of the two population models,it is shown that the effects of population cannibalism,intraspecific competition and time delay on the dynamics of the system.First of all,the biological background of cannibalism,predation among populations are introduced.As well as the current state of the research on population models with cannibalism,meanwhile the preliminary knowledge used in this thesis are introduced.Then a kind of population model with cannibalism,classifies and discusses cannibalism coefficients is constructed.The global stability of the model equilibrium point is obtained with or without cannibalism and the influence of the cannibalism behavior of the population on the dynamics of the model is analyzed and discussed.By consulting relevant literature and combining actual natural phenomena,the mutual predation phenomenon within the predator population is further considered.Through the analysis of the model,it is found that the intraspecific competition behaviors of adult individuals will lead to multiple locally asymptotically stable boundary equilibrium points,i.e.,prey extinction equilibrium points.And under certain conditions,the global stability can be discussed.But intraspecific competition between juvenile individuals will lead to multiple unstable boundary equilibrium points in the system.When the cannibalism coefficient meets certain conditions,there will be a locally asymptotically stable boundary equilibrium point.In addition,we also find that no matter what kind of competition behaviors are likely to produce periodic solutions with ? as the branching parameter.Finally,a population infectious disease model with stage structure and intraspecific competition is first discussed.It is shown that diseases transmitted only at the adult stage may cause backward branching phenomena.On this basis,a single-species prion transmission model with cannibalism and time-delay effects was studied.The model considers the spread of prions caused by cannibalism,and the double-delay effect of cannibalism that leads to an increase in the reproduction rate of adults and the spread of prions.The two-delay parameters in the model are classified,discussed and analyzed.Two single-delay systems are analyzed when one of them is setting to zero.In addition,two time-delay systems where one of them is fixed in a given interval and the other one is taken as a branching parameter.Through the qualitative analysis of the corresponding linear systems under different conditions,the local stability of the corresponding system equilibrium points,the possible switching phenomena under certain conditions,and the sufficient conditions for the generation of Hopf bifurcation are obtained.