In this article, we investigate a fractional-order singular Leslie-Gower prey-predator bioeconomic model, which describes the interaction between populations of prey and predator, and takes into account the economic interest. We firstly obtain the solvability condition and the stability of the model system, and discuss the singularity induced bifurcation phenomenon. Next, we introduce a state feedback controller to eliminate the singularity induced bifurcation phenomenon, and discuss the optimal control problems. Finally, numerical solutions and their simulations are considered in order to illustrate the theoretical results and reveal the more complex dynamical behavior.

中文翻译：

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分数阶奇异 Leslie-Gower Prey-Predator 模型的动态分析和优化控制

在本文中，我们研究了一个分数阶奇异 Leslie-Gower 猎物-捕食者生物经济模型，该模型描述了猎物和捕食者种群之间的相互作用，并考虑了经济利益。我们首先得到了模型系统的可解性条件和稳定性，并讨论了奇点引起的分岔现象。接下来，我们引入状态反馈控制器来消除奇异引起的分岔现象，并讨论最优控制问题。最后，考虑数值解及其模拟，以说明理论结果并揭示更复杂的动力学行为。