Existence Of Traveling Waves In Lotka-Volterra Competition Models With Stage Structure And Distributed Maturation Delay

This paper is concerned with a Lotka-Volterra competition model with stage structure and distributed maturation delays. The stability of uniform steady states are firstly studied by investigating the eigenvalues of the linearization in every equilibrium and then, the existence of traveling wave solutions connecting two boundary equilibriums is established by using monotone iteration together with upper and lower solutions method when the coexistence equilibrium is absence. The traveling wave solutions represent that some of the stronger competitor of two comptitors are introduced and then invade and dominate an environment, where only the weaker competitor initially inhabit, and drive the weaker to extinction so that the end result is that only the stronger species is present. Two cases are considered in this paper: One of cases is that the immatures do not move in spatial, which is studied in Chapter 2, and another case is that the immatures move in spatial while harvesting effect is introduced, which is studied in Chapter 3. The results presented in this paper expand a number of existing ones.