On the basis of the previous publications, a new fractional-order prey-predator model is set up. Firstly, we discuss the existence, uniqueness, and nonnegativity for the involved fractional-order prey-predator model. Secondly, by analyzing the characteristic equation of the considered fractional-order Lotka–Volterra model and regarding the delay as bifurcation variable, we set up a new sufficient criterion to guarantee the stability behavior and the appearance of Hopf bifurcation for the addressed fractional-order Lotka–Volterra system. Thirdly, we perform the computer simulations with Matlab software to substantiate the rationalisation of the analysis conclusions. The obtained results play an important role in maintaining the balance of population in natural world.

中文翻译：

---

分数阶竞争者-竞争者-多元论者Lotka-Volterra系统动力学的进一步研究

在以前的出版物的基础上，建立了一个新的分数阶猎物-捕食者模型。首先，我们讨论了所涉及的分数阶猎物-捕食者模型的存在性，唯一性和非负性。其次，通过分析考虑的分数阶Lotka-Volterra模型的特征方程，并将时延视为分叉变量，我们建立了一个新的充分准则，以保证所处理分数阶Lotka的稳定性和Hopf分叉的出现。 –Volterra系统。第三，我们使用Matlab软件进行计算机仿真，以证实分析结论的合理性。获得的结果在维持自然世界人口平衡方面起着重要作用。