Abstract
A consumer-resource reaction-diffusion model with a single consumer species was proposed and experimentally studied by Zhang et al.(Ecol Lett 20:1118-1128, 2017). Analytical study on its dynamics was further performed by He et al.(J Math Biol 78:1605-1636, 2019). In this work, we completely settle the conjecture proposed by He et al.(J Math Biol 78:1605-1636, 2019) about the global dynamics of the consumer-resource model for small yield rate. We then study a multi-species consumer-resource model where all the consumer species compete with each other through depression of the limited resources by consumption and there is no direct competition between them. We show that in this case, all consumer species persist uniformly, which implies that “competition exclusion” phenomenon will never happen. We also clarify its dynamics in both homogeneous and heterogeneous environments under various circumstances.
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Acknowledgements
The research of X. He is supported in part by National Key R &D Program of China 2022YFA1004401, NSFC grant No. 12071141 and Science and Technology Commission of Shanghai Municipality (No. 22DZ2229014). The research of W.-M. Ni is partially supported by NSFC grants No. 11431005 and No. 12071141, the Presidential Fund PF1-000923 at CUHK(SZ) and the Shenzhen Municipal Grant No. GXWD20201231105722002. The authors are grateful to the two anonymous referees for their careful and thorough reviews with numerous suggestions, which greatly improve the presentation of this paper.
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He, X., Ni, WM. & Wang, H. Dynamics of consumer-resource reaction-diffusion models: single and multiple consumer species. J. Math. Biol. 87, 39 (2023). https://doi.org/10.1007/s00285-023-01970-0
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DOI: https://doi.org/10.1007/s00285-023-01970-0
Keywords
- Global asymptotic stability
- Reaction-diffusion system
- Consumer-resource model
- Spatial heterogeneity
- Lyapunov function