Stability And Traveling Wave Solutions Of Reaction-Diffusion Systems

The thesis is concerned with the stability and the traveling wave solutions of reaction-diffusion systems and delayed reaction-diffusion systems.For diffusive Predator-Prey model with Holling-â…¢ functional response without time delay, shooting argument together with LaSalle's Invariance Principle and the Hopf bifurcation theorem are applied to prove the existence of traveling wave solutions and small amplitude traveling wave train solutions.For delayed reaction-diffusion systems, the existence of traveling wave fronts in diffusive and cooperative system with distributed delay is proved by the theory of Wang, Li and Ruan. Moreover, global stability results are established for each equilibrium of the model.For a class of delayed rection-diffusion systems with bistable nonliearities, the uniqueness and global asymptotic stability of traveling wave fronts are established by using the convergence result for monotone semiflow. As a application, we estabilish the uniqueness and global asymptotic stability of traveling wave fronts in a delayed diffusive epidemic model.