Study On The Propagation Problem Of Competitive Cooperative Systems Of Three Species

In recent years,many biological problems are studied and solved by establishing mathematical models,and many models can be reduced to reaction-diffusion equations or systems.At present,the dynamics of the interaction between multiple species has attracted the attention of many scholars.Among them,the competition and cooperation are two common interspecific relationships among biological populations,which are the basis of the study of multi-population biodynamics.Therefore,it is of great biological significance to study the propagation of multipopulation reaction-diffusion competitive cooperative systems.At the same time,the interaction between species brings nonlinear terms to the model,which makes it difficult to use mathematical methods to study related problems.Based on this,this paper mainly studies the propagation problems of a three species reaction-diffusion competitive cooperative system and a lattice three species diffusion competitive cooperative system.In Chapter 1,we mainly introduce the research background of the three population reaction-diffusion competitive cooperative system.Firstly,the existence and the asymptotic behavior of wavefront solutions of connecting the boundary equilibria(0,0,1)and(b1,b2,0),the selection mechanism of minimum wave speed are covered in detail.Secondly,the existence of connecting(0,0,1)and(b1,b2,0)wavefront solutions,the selection mechanism of minimum wave speed and the asymptotic behavior of the three species of lattice diffusion competitive cooperative systems are also introduced.Finally,we introduce the main work of this paper and the methods.In Chapter 2,we mainly study the propagation problem of connecting wavefront solutions of the boundary equilibria(0,0,1)and(b1,b2,0)of the following three species reactiondiffusion competitive cooperative system (?)Firstly,we give the linearized eigenvalues at different equilibrium points of the corresponding diffusion-free system.Secondly,by constructing the upper and lower solutions and combining with the strict analysis process,some sufficient conditions are given to guarantee the existence of wavefront solutions of the system,which improves the existing research results.Finally,on the basis of the existence results,further presentation of the minimal speed can provide some sufficient conditions on linearly determinacy.These conclusions enrich the content of the research on such system.In Chapter 3,we study the propagation of wavefront solutions connecting the boundary equilibria(0,0,1)and(b1,b2,0)of the following lattice three species diffusion competitive cooperative system (?)including the existence of wavefront solutions and some sufficient conditions on the minimal speed,which is linearly determined,have been proved.Then,we use Ikehara’s theorem to study the asymptotic behavior of wavefront solutions of the lattice reactive-diffusion competitive cooperative system with three species,which complete the conclusions on the asymptotic behavior.