Spatial Dynamics Of Reaction-Diffusion System With Quiescent Stage In A Periodic Habitat

For most organisms,the quiescent stage or dormant state plays an important role in their growth.The study of reaction-diffusion system with quiescent stage is helpful to understand the survival and development of such organisms.In addition,the environment in which species live is usually unbalanced and individuals have different habits in the different environments.Therefore,it is necessary to take spatial heterogeneity into account when constructing the models.The thesis is concerned with two kinds of reaction-diffusion systems with quiescent stage in the periodic habitat.The main results of the thesis are as follows:For a delayed lattice dynamical system with quiescent stage in the periodic habitat,the propagation dynamics of the system is studied.Firstly,we obtain the dynamics of the system with spatially periodic initial conditions by using the theory of dynamic system and the sign of principal eigenvalue.Then,we prove the existence of the spreading speeds and its specific expression by applying the monotone semiflow theory to the system with the general initial data.Next,we prove the existence of the non-critical pulsating traveling waves by monotone iteration technique combined with the method of upper and lower solutions.Finally,we investigate respectively the influence of the delay and the species transfer rates on the spreading speeds of the system in the periodic environment based on the variational expression of the spreading speeds.For a class of non-local diffusion models with quiescent stage in the periodic habitat,we study the uniqueness and stability of the pulsating traveling waves.Firstly,we prove the uniqueness of the non-critical traveling wave front by the sliding plane technique.Then,the exponential stability and a specific convergence rate of all non-critical traveling wave fronts are proved by constructing an appropriate weight function and comparison theorem.