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Instabilities and spatiotemporal patterns behind predator invasions with nonlocal prey competition

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  • Merchant, Sandra M.
  • Nagata, Wayne

Abstract

We study the influence of nonlocal intraspecies prey competition on the spatiotemporal patterns arising behind predator invasions in two oscillatory reaction–diffusion integro-differential models. We use three common types of integral kernels as well as develop a caricature system, to describe the influence of the standard deviation and kurtosis of the kernel function on the patterns observed. We find that nonlocal competition can destabilize the spatially homogeneous state behind the invasion and lead to the formation of complex spatiotemporal patterns, including stationary spatially periodic patterns, wave trains and irregular spatiotemporal oscillations. In addition, the caricature system illustrates how large standard deviation and low kurtosis facilitate the formation of these spatiotemporal patterns. This suggests that nonlocal competition may be an important mechanism underlying spatial pattern formation, particularly in systems where the competition between individuals varies over space in a platykurtic manner.

Suggested Citation

  • Merchant, Sandra M. & Nagata, Wayne, 2011. "Instabilities and spatiotemporal patterns behind predator invasions with nonlocal prey competition," Theoretical Population Biology, Elsevier, vol. 80(4), pages 289-297.
    • Handle: RePEc:eee:thpobi:v:80:y:2011:i:4:p:289-297
    DOI: 10.1016/j.tpb.2011.10.001
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    References listed on IDEAS

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    1. Saralees Nadarajah, 2005. "A generalized normal distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(7), pages 685-694.
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    1. Kalyan Manna & Vitaly Volpert & Malay Banerjee, 2020. "Dynamics of a Diffusive Two-Prey-One-Predator Model with Nonlocal Intra-Specific Competition for Both the Prey Species," Mathematics, MDPI, vol. 8(1), pages 1-28, January.
    2. Yang, Feng & Song, Yongli, 2022. "Stability and spatiotemporal dynamics of a diffusive predator–prey system with generalist predator and nonlocal intraspecific competition," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 159-168.
    3. Yang, Youwei & Wu, Daiyong & Shen, Chuansheng & Lu, Fengping, 2023. "Allee effect in a diffusive predator–prey system with nonlocal prey competition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 615(C).
    4. Peng, Yahong & Zhang, Guoying, 2020. "Dynamics analysis of a predator–prey model with herd behavior and nonlocal prey competition," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 170(C), pages 366-378.

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