In this paper, the bifurcation control of a fractional-order mosaic virus infection model for Jatropha curcas with farming awareness and an execution delay is investigated. By analyzing the associated characteristic equation, Hopf bifurcation induced by the execution delay is studied for the uncontrolled system. Then, a time-delayed controller is introduced to control the occurrence of Hopf bifurcation. Our study implies that bifurcation dynamics is significantly affected by the change of the fractional order, the feedback gain and the extended feedback delay provided that the other parameters are fixed. A series of numerical simulations is performed, which not only verifies our theoretical results but also reveals some specific features. Numerically, we find that the Hopf bifurcation gradually occurs in advance with the increase of the fractional order, and there exist extreme points for the feedback gain and the extended feedback delay which can minimize the bifurcation value.

中文翻译：

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具有农耕意识的麻疯树延迟分形花叶病模型的分叉控制

本文针对麻疯树的分数阶花叶病毒感染模型进行分叉控制具有农业意识和执行延误的调查。通过分析相关的特征方程，研究了非受控系统由于执行延迟而引起的Hopf分支。然后，引入了延时控制器来控制Hopf分叉的发生。我们的研究表明，在其他参数固定的情况下，分数阶，反馈增益和扩展的反馈延迟的变化会显着影响分叉动力学。进行了一系列数值模拟，不仅验证了我们的理论结果，而且揭示了一些特定的功能。在数值上，我们发现Hopf分叉会随着分数阶的增加而提前逐渐发生，