| Dynamical systems generated by predator-prey models have long been an important subject of research interest of many many theoretical and empirical ecologists and mathe-matical scientists for several decades years, and there has been vast literatures to investigate the dynamics of predator-prey models. As it was said in [29], space and spatial features are now solidly established as essential considerations in ecology both in terms of theory and practice, and the mathematical challenges in advancing understanding of the role of space in ecology are substantial and mathematically seductive.In the dissertation, traveling wave solution for a class of diffusive predator-prey system with linear density dependence is considered, where the birth function of prey and functional response function are both very general. Using methods of topological shooting, we show that the existence of non-negative traveling wave solution connecting a boundary equilibrium to the co-existence steady state with the help of a Wazewski-like set constructed elaborately, and give the formula of the minimum wave speed. This means that the traveling wave solution established by Huang [1] can be preserved in the presence of the linear density dependence for the predator.The thesis is organized as follows. In Chapter 1, we recall the history of the development of the predator-prey models concisely and current research situation on the topic of the traveling wave solutions of the models with diffusion, we also put forward the main research contents. Chapter 2 contains the hypothesis upon the considered models and the main results of the dissertation. Chapter 3 gives some basic properties of the corresponding traveling-wave system for the considered system. The chapter 4 is the central of dissertation, which is devoted to the construction of set ∑ and the establishment of desired connecting orbit. The chapter 5 just completes the proof of main results which stated in Chapter 2. |
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