GU Yumeng, HUANG Mingdi. Existence of Periodic Traveling Waves for Time-Periodic Lotka-Volterra Competition Systems With Delay[J]. Applied Mathematics and Mechanics, 2020, 41(6): 658-668. doi: 10.21656/1000-0887.400275
Citation: GU Yumeng, HUANG Mingdi. Existence of Periodic Traveling Waves for Time-Periodic Lotka-Volterra Competition Systems With Delay[J]. Applied Mathematics and Mechanics, 2020, 41(6): 658-668. doi: 10.21656/1000-0887.400275

Existence of Periodic Traveling Waves for Time-Periodic Lotka-Volterra Competition Systems With Delay

doi: 10.21656/1000-0887.400275
  • Received Date: 2019-09-16
  • Rev Recd Date: 2020-01-01
  • Publish Date: 2020-06-01
  • A time-periodic reaction-diffusion Lotka-Volterra competition model with delay was considered. Under certain conditions, with the method of super- and sub-solutions and monotone iterations, the existence of time-periodic traveling waves connecting 2 semi-trivial periodic solutions of the corresponding kinetic system was proved with wave speed c*.Furthermore, the traveling wave solutions for c* were proved to be monotone with the comparison principle, and the asymptotic behaviors of traveling wave solutions were obtained at minus/plus infinity. Finally, the existence of traveling wave solutions was proved at wave speed c=c*.
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