Date on Master's Thesis/Doctoral Dissertation


Document Type

Doctoral Dissertation

Degree Name

Ph. D.



Committee Chair

Li, Bingtuan

Author's Keywords

Delayed reaction-diffusion system; Integral system; Stage-structure; Traveling wave solutions; Global stability; Lotka-Volterra competition


Reaction-diffusion equations; Biomathematics; Biology--Mathematical models


We formulate a delayed reaction-diffusion model that describes competition between two species in a stream. We divide each species into two compartments, individuals inhabiting on the benthos and individuals drifting in the stream. Time delays are incorporated to measure the time lengths from birth to maturity of the benthic populations. We assume that the growth of population takes place on the benthos and that dispersal occurs in the stream. Our system consists of two linear reaction-diffusion equations and two delayed ordinary differential equations. We study the dynamics of the non-spatial model, determine the existence and global stability of the equilibria, and provide conditions under which solutions converge to the equilibria. We show that the existence of traveling wave solutions can be established through compact integral operators. We define two real numbers and prove that they serve as the lower bounds of the speeds of traveling wave solutions in the system.