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Mathematical modeling and mechanisms of pattern formation in ecological systems: a review

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Abstract

How populations distribute in both space and time is one of the key issues in ecological systems, which can characterize the relationship between populations, space–time structure and evolution law. Consequently, pattern dynamics in ecosystems has been widely investigated including their causes and ecological functions. In order to systematically understand the interactions in ecosystems, we summarize the related results in pattern formation of ecological systems. Based on mathematical modeling and analysis, we show the mechanisms of different patterns including feedback, scale-dependent, phase separation, nonlocal effects, time delay and spatial heterogeneity. This work offers assistance for better understanding the complexity of ecosystems and provides new insights for self-organizations evolution and ecosystem protection. We hope that our results may be applied in other related fields such as epidemiology, medical science, atmospheric science and so on.

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Acknowledgements

This work is supported by the National Key Research and Development Program of China (Grant No. 2018YFE0109600), National Natural Science Foundation of China under Grant Nos. 42075029, 11671241 and 11801532, Program for the Outstanding Innovative Teams (OIT) of Higher Learning Institutions of Shanxi, Natural Science Foundation of Shanxi Province Grant No. 201801D221003, Outstanding Young Talents Support Plan of Shanxi province, and Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan) under Grant No. CUGGC05.

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Authors and Affiliations

  1. Department of Mathematics, North University of China, Shanxi, 030051, Taiyuan, China

    Gui-Quan Sun

  2. Complex Systems Research Center, Shanxi University, Shanxi, 030006, Taiyuan, China

    Gui-Quan Sun, Hong-Tao Zhang, Jin-Shan Wang, Jing Li & Zhen Jin

  3. School of Applied Mathematics, Shanxi University of Finance and Economics, Shanxi, 030006, Taiyuan, China

    Jing Li

  4. School of Mathematics and Physics, China University of Geosciences, Wuhan, 430074, Hubei, China

    Yi Wang

  5. School of Computer and Information Technology, Shanxi University, Taiyuan, 030006, Shanxi, China

    Li Li

  6. College of Physics Science and Technology, Yangzhou University, Yangzhou, 225002, Jiangsu Province, China

    Yong-Ping Wu & Guo-Lin Feng

  7. Laboratory for Climate Studies, National Climate Center, China Meteorological Administration, Beijing, 100081, China

    Guo-Lin Feng

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Correspondence to Gui-Quan Sun.

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Sun, GQ., Zhang, HT., Wang, JS. et al. Mathematical modeling and mechanisms of pattern formation in ecological systems: a review . Nonlinear Dyn 104, 1677–1696 (2021). https://doi.org/10.1007/s11071-021-06314-5

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