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Stability of Traveling Wave Fronts for a Three Species Predator-Prey Model with Nonlocal Dispersals

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  • Dongmei Yuan
  • Yuzhen Bai

Abstract

In this paper, we consider a predator-prey model with nonlocal dispersals of two cooperative preys and one predator. We prove that the traveling wave fronts with the relatively large wave speed are exponentially stable as perturbation in some exponentially weighted spaces, when the difference between initial data and traveling wave fronts decay exponentially at negative infinity, but in other locations, the initial data can be very large. The adopted method is to use the weighted energy method and the squeezing technique with some new flavors to handle the nonlocal dispersals.

Suggested Citation

  • Dongmei Yuan & Yuzhen Bai, 2019. "Stability of Traveling Wave Fronts for a Three Species Predator-Prey Model with Nonlocal Dispersals," Complexity, Hindawi, vol. 2019, pages 1-15, December.
    • Handle: RePEc:hin:complx:8742958
    DOI: 10.1155/2019/8742958
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    References listed on IDEAS

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    1. Meng, Xinzhu & Li, Fei & Gao, Shujing, 2018. "Global analysis and numerical simulations of a novel stochastic eco-epidemiological model with time delay," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 701-726.
    2. Yu, Zhixian & Yuan, Rong, 2012. "Existence and asymptotics of traveling waves for nonlocal diffusion systems," Chaos, Solitons & Fractals, Elsevier, vol. 45(11), pages 1361-1367.
    3. Tingting Ma & Xinzhu Meng & Zhengbo Chang, 2019. "Dynamics and Optimal Harvesting Control for a Stochastic One-Predator-Two-Prey Time Delay System with Jumps," Complexity, Hindawi, vol. 2019, pages 1-19, March.
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