Abstract
This article is concerned with the existence of traveling wave solutions for a discrete diffusive ratio-dependent predator-prey model. By applying Schauder’s fixed point theorem with the help of suitable upper and lower solutions, we prove that there exists a positive constant c* such that when c > c*, the discrete diffusive predator-prey system admits an invasion traveling wave. The existence of an invasion traveling wave with c = c* is also established by a limiting argument and a delicate analysis of the boundary conditions. Finally, by the asymptotic spreading theory and the comparison principle, the non-existence of invasion traveling waves with speed c < c* is also proved.
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This work was supported by NSF of China (11861056), Gansu Provincial Natural Science Foundation (18JR3RA093).
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Su, T., Zhang, G. Invasion Traveling Waves for a Discrete Diffusive Ratio-Dependent Predator-Prey Model. Acta Math Sci 40, 1459–1476 (2020). https://doi.org/10.1007/s10473-020-0517-7
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DOI: https://doi.org/10.1007/s10473-020-0517-7