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.

中文翻译：

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时滞具有Holling-II型开垦率的分数阶土地动力模型的复杂行为分析

本文研究了具有Holling-II型转化率和时滞的分数阶土地模型。首先，以Caputo类型定义变量阶数分数导数。其次，通过将时延作为分叉参数，提出了确定模型稳定性和Hopf分叉的一些准则。事实证明，即使模型处于稳定状态，时间延迟也可能导致模型振荡。最后，通过数值例子验证了理论分析的正确性。这些结果可能为开发控制土地利用变化的合理策略提供见解。