Open AccessTRAVELING WAVE SOLUTIONS IN A STAGE-STRUCTURED DELAYED REACTION-DIFFUSION MODEL WITH ADVECTION
Author(s) -
Liang Zhang,
Huiyan Zhao
Publication year - 2015
Publication title -
mathematical modelling and analysis/mathematical modeling and analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.491
H-Index - 25
eISSN - 1648-3510
pISSN - 1392-6292
DOI - 10.3846/13926292.2015.1020455
Subject(s) - traveling wave , advection , mathematics , stage (stratigraphy) , competition (biology) , diffusion , reaction–diffusion system , flow (mathematics) , competition model , stability (learning theory) , measure (data warehouse) , statistical physics , mathematical analysis , pure mathematics , physics , geometry , thermodynamics , computer science , economics , biology , ecology , database , machine learning , microeconomics , profit (economics) , paleontology
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.