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Pattern transitions in a vegetation system with cross-diffusion

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  • Liu, Chen
  • Li, Li
  • Wang, Zhen
  • Wang, Ruiwu

Abstract

Regular pattern is a typical feature of vegetation distribution which can be recognized as early warnings of desertification. In this work, a vegetation system with cross diffusion is presented based on reaction-diffusion equations. By means of mathematical analysis, we obtain the appropriate parameter space which can ensure the emergence of stationary patterns. Moreover, it is unveiled that cross diffusion not only induces the pattern transitions, yet promotes the density of the vegetation. These obtained results suggest that cross diffusion is an important mechanism in vegetation dynamics.

Suggested Citation

  • Liu, Chen & Li, Li & Wang, Zhen & Wang, Ruiwu, 2019. "Pattern transitions in a vegetation system with cross-diffusion," Applied Mathematics and Computation, Elsevier, vol. 342(C), pages 255-262.
    • Handle: RePEc:eee:apmaco:v:342:y:2019:i:c:p:255-262
    DOI: 10.1016/j.amc.2018.09.039
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    References listed on IDEAS

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    1. Brolsma, R.J. & Karssenberg, D. & Bierkens, M.F.P., 2010. "Vegetation competition model for water and light limitation. I: Model description, one-dimensional competition and the influence of groundwater," Ecological Modelling, Elsevier, vol. 221(10), pages 1348-1363.
    2. Zhan, Xiu-Xiu & Liu, Chuang & Zhou, Ge & Zhang, Zi-Ke & Sun, Gui-Quan & Zhu, Jonathan J.H. & Jin, Zhen, 2018. "Coupling dynamics of epidemic spreading and information diffusion on complex networks," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 437-448.
    3. Corina E. Tarnita & Juan A. Bonachela & Efrat Sheffer & Jennifer A. Guyton & Tyler C. Coverdale & Ryan A. Long & Robert M. Pringle, 2017. "A theoretical foundation for multi-scale regular vegetation patterns," Nature, Nature, vol. 541(7637), pages 398-401, January.
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    Cited by:

    1. Mohan, Nishith & Kumari, Nitu, 2021. "Positive steady states of a SI epidemic model with cross diffusion," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    2. Huang, Yi Jie & Deng, Zheng Hong & Song, Qun & Wu, Tao & Deng, Zhi Long & Gao, Ming yu, 2019. "The evolution of cooperation in multi-games with aspiration-driven updating rule," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 313-317.
    3. Zhang, Hong-Tao & Wu, Yong-Ping & Sun, Gui-Quan & Liu, Chen & Feng, Guo-Lin, 2022. "Bifurcation analysis of a spatial vegetation model," Applied Mathematics and Computation, Elsevier, vol. 434(C).
    4. Currò, C. & Grifò, G. & Valenti, G., 2023. "Turing patterns in hyperbolic reaction-transport vegetation models with cross-diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    5. Chu, Chen & Zhai, Yao & Mu, Chunjiang & Hu, Die & Li, Tong & Shi, Lei, 2019. "Reputation-based popularity promotes cooperation in the spatial prisoner's dilemma game," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.

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