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Traveling Wave Solutions in a Stage-Structured Delayed Reaction-Diffusion Model with Advection

    Liang Zhang Affiliation
    ; Huiyan Zhao Affiliation

Abstract

We investigate a stage-structured delayed reaction-diffusion model with advection that describes competition between two mature species in water flow. Time delays are incorporated to measure the time lengths from birth to maturity of the populations. We show there exists a finite positive number c that can be characterized as the slowest spreading speed of traveling wave solutions connecting two mono-culture equilibria or connecting a mono-culture with the coexistence equilibrium. The model and mathematical result in [J.F.M. Al-Omari, S.A. Gourley, Stability and travelling fronts in Lotka–Volterra competition models with stage structure, SIAM J. Appl. Math. 63 (2003) 2063–2086] are generalized.

Keyword : competition, stage structure, time delay, travelling wave solutions, advection

How to Cite
Zhang, L., & Zhao, H. (2015). Traveling Wave Solutions in a Stage-Structured Delayed Reaction-Diffusion Model with Advection. Mathematical Modelling and Analysis, 20(2), 168-187. https://doi.org/10.3846/13926292.2015.1020455
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Mar 30, 2015
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This work is licensed under a Creative Commons Attribution 4.0 International License.