Study On Three Classes Of Competition-cooperation-predation Hybrid Species Model

The classical Lotka-Volterra model study focuses only on simple interspecific competition or simple interspecific cooperation.However,due to the complexity of the real environment and the diversity of the relations between biological species,the interactions between populations are often not a single one but a mixture of multiple relations.In our paper,the following three kinds of inter-species hybrid models are established:a class of two-species Lotka-Volterra competition-cooperation hybrid model,a class of two-species Lotka-Volterra competition-predation hybrid model and a class of two-species Lotka-Volterra predation-cooperation hybrid model,the competition relationship,cooperation relationship,and predation relationship occur between the two species alternately,which are periodically alternating affected by environmental impact in different time intervals.By adding time delay to the model,three kinds of hybrid systems are established.The main contents of this paper can be summarized as the following four parts:In section 1,the biological background studied in this paper is firstly introduced.Secondly,the research contents of this paper are introduced: a two-species Lotka-Volterra competition-cooperation hybrid model,a two-species Lotka-Volterra competition-predation hybrid model and a two-species Lotka-Volterra predation-cooperation hybrid model.In section 2,under the condition of no time delay,by constructing appropriate Lyapunov functions and analyzing methods,sufficient criteria are obtained for the positive,boundedness and global asymptotic stability of the positive equilibrium point of the system,and numerical simulations are made using MATLAB and other mathematical software to verify the correctness of our theoretical results.In section 3,when the time delay is positive,Hopf bifurcation and stabilizes switch are obtained at the positive equilibrium point through analysis and other means.Numerical simulation is made using mathematical software such as MATLAB to verify the correctness of our theoretical results.In section 4,the full text is systematically summarized and discussed.