Abstract
This paper concerns the propagation direction of the bistable traveling wave for a time-periodic Lotka–Volterra reaction–diffusion competition system. The speed is first shown to be bounded by the asymptotic spreading speeds of the monostable subsystems. General results toward the propagation direction are obtained by establishing two comparison principles on wave speed. These results rely on the establishment of the speed sign of an upper (or lower) solution to the system of wave profile equations. In particular, by subtly constructing upper or lower solutions, we derive a set of explicit formulas that determine whether the speed sign is positive or negative, which indicates whether the bistable traveling wave spatially propagates to the left or to the right. Finally, numerical simulations are given to demonstrate the effects of system parameters to the propagation direction of the bistable traveling wave.
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Acknowledgements
The work of the first two authors were supported by the National Natural Science Foundation of China (Nos. 12071434,12011530398). The work of the fourth author was partially supported by his NSERC discovery grant of Canada (Grant No. RGPIN2016-04709).
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Ma, M., Yue, J., Huang, Z. et al. Propagation Dynamics of Bistable Traveling Wave to a Time-Periodic Lotka-Volterra Competition Model: Effect of Seasonality. J Dyn Diff Equat 35, 1745–1767 (2023). https://doi.org/10.1007/s10884-022-10129-2
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DOI: https://doi.org/10.1007/s10884-022-10129-2