Volume 42 Issue 12
Dec.  2021
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ZHENG Jingpan. The Wave Speed Signs for Bistable Traveling Wave Solutions in 3-Species Competition-Diffusion Systems[J]. Applied Mathematics and Mechanics, 2021, 42(12): 1296-1305. doi: 10.21656/1000-0887.420093
Citation: ZHENG Jingpan. The Wave Speed Signs for Bistable Traveling Wave Solutions in 3-Species Competition-Diffusion Systems[J]. Applied Mathematics and Mechanics, 2021, 42(12): 1296-1305. doi: 10.21656/1000-0887.420093

The Wave Speed Signs for Bistable Traveling Wave Solutions in 3-Species Competition-Diffusion Systems

doi: 10.21656/1000-0887.420093
  • Received Date: 2021-04-13
  • Rev Recd Date: 2021-06-02
  • Available Online: 2021-12-31
  • In the bistable competition-diffusion model, the wave speed signs for the traveling waves can predict which species are more dominant and will eventually occupy the whole habitat. Therefore, it is of great biological significance to study the speed signs for the traveling waves. Firstly, the Lotka-Volterra competition-diffusion system was transformed into a cooperative system. Under the comparison principle, the comparison theorem for the bistable wave speed and the specific upper-lower solution wave speeds of wave profile equations was obtained. Then, according to the comparison theorem and through construction of suitable upper-lower solutions, some sufficient conditions for determining the bistable traveling wave speed signs were obtained. The results help predict and control the competition results of biological populations.
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