Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
758527 | Communications in Nonlinear Science and Numerical Simulation | 2011 | 12 Pages |
In this paper, we study the traveling wave fronts of a delayed reaction–diffusion system with a quiescent stage for a single species population with two separate mobile and stationary states. By transforming the corresponding wave system into a scalar delayed differential equation with an integral term, we establish the existence of the minimal wave speed cmin, and the asymptotic behavior, monotonicity and uniqueness (up to a translation) of the traveling wave fronts. In particular, the effects of the delay and transfer rates on the minimal wave speed are studied.
Research highlights► We study a delayed reaction–diffusion model with a quiescent stage. ► We investigate the phenomenon of biological invasion using traveling wave theory. ► The effects of the delay and transfer rates on the invasion speed are studied.