This work is devoted to explore the dynamics of the proposed discrete fractional-order prey–predator model. The model is the generalization of the conventional discrete prey–predator model to its corresponding fractional-order counterpart. The fixed points of the proposed model are first found and their stability analyses are carried out. Then, the nonlinear dynamical behaviors of the model, including quasi-periodicity and chaotic behaviors, are investigated. The influences of fractional order and different parameters in the model are examined using several techniques such as Lyapunov exponents, bifurcation diagrams, phase portraits and $C_0$ complexity. The feedback control method is suggested to suppress the chaotic dynamics of the model and stabilize any selected unstable fixed point of the system.

这项工作致力于探索所提出的离散分数阶猎物 - 捕食者模型的动力学。该模型是传统离散猎物-捕食者模型对其相应分数阶对应模型的推广。首先找到所提出模型的不动点并对其进行稳定性分析。然后，研究了模型的非线性动力学行为，包括准周期性和混沌行为。模型中分数阶和不同参数的影响使用多种技术进行检查，如李雅普诺夫指数、分岔图、相图和$C_0$复杂。建议采用反馈控制方法来抑制模型的混沌动力学并稳定系统的任何选定的不稳定不动点。