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Complex Behavior Analysis of a Fractional-Order Land Dynamical Model with Holling-II Type Land Reclamation Rate on Time Delay

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  • Li Wu
  • Zhouhong Li
  • Yuan Zhang
  • Binggeng Xie

Abstract

In this paper, a fractional-order land model with Holling-II type transformation rate and time delay is investigated. First of all, the variable-order fractional derivative is defined in the Caputo type. Second, by applying time delay as the bifurcation parameter, some criteria to determine the stability and Hopf bifurcation of the model are presented. It turns out that the time delay can drive the model to be oscillatory, even when its steady state is stable. Finally, one numerical example is proposed to justify the validity of theoretical analysis. These results may provide insights to the development of a reasonable strategy to control land-use change.

Suggested Citation

  • Li Wu & Zhouhong Li & Yuan Zhang & Binggeng Xie, 2020. "Complex Behavior Analysis of a Fractional-Order Land Dynamical Model with Holling-II Type Land Reclamation Rate on Time Delay," Discrete Dynamics in Nature and Society, Hindawi, vol. 2020, pages 1-10, July.
    • Handle: RePEc:hin:jnddns:1053283
    DOI: 10.1155/2020/1053283
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    Cited by:

    1. Li Wu & Yanjun Yang & Hailan Yang & Binggeng Xie & Weiqun Luo, 2023. "A Comparative Study on Land Use/Land Cover Change and Topographic Gradient Effect between Mountains and Flatlands of Southwest China," Land, MDPI, vol. 12(6), pages 1-20, June.
    2. Li Wu & Yanjun Yang & Binggeng Xie, 2022. "Modeling Analysis on Coupling Mechanisms of Mountain–Basin Human–Land Systems: Take Yuxi City as an Example," Land, MDPI, vol. 11(7), pages 1-16, July.

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