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DU YANKE, XU RUI. TRAVELING WAVE SOLUTIONS IN A THREE-SPECIES FOOD-CHAIN MODEL WITH DIFFUSION AND DELAYS. INT J BIOMATH 2012. [DOI: 10.1142/s1793524511001350] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
This paper deals with the existence of traveling wave solutions in a three-species food-chain model with spatial diffusion and time delays due to gestation and negative feedback. By using a cross iteration scheme and Schauder's fixed point theorem, we reduce the existence of traveling wave solutions to the existence of a pair of upper-lower solutions. By constructing a pair of upper-lower solutions, we derive the existence of a traveling wave solution connecting the trivial steady state and the positive steady state. Numerical simulations are carried out to illustrate the main results. In particular, our results extend and improve some known results.
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Affiliation(s)
- YANKE DU
- Institute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang, 050003, P. R. China
| | - RUI XU
- Institute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang, 050003, P. R. China
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