Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
837915 | Nonlinear Analysis: Real World Applications | 2011 | 14 Pages |
Abstract
In this paper, we study a reaction–diffusion model with a quiescent stage on a 2D spatial lattice for a single-species population with two separate mobile and stationary states. We investigate the phenomenon of biological invasion using traveling wave theory. Under the monostable assumptions, we show that, for any fixed θ∈Rθ∈R, there exists a minimal wave speed c∗(θ)>0c∗(θ)>0 such that a traveling wave front exists if and only if its speed is above this minimal wave speed. The asymptotic behavior, monotonicity and uniqueness of the wave profiles are then established. Of particular interest are the effects of the direction of propagation and transfer rates on the minimal wave speed, and we obtain some interesting results.
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Authors
Hai-Qin Zhao, Shi-Liang Wu,