Dynamical study of fractional order Leslie-Gower model of predator-prey with fear, Allee effect, and inter-species rivalry

G Ranjith Kumar , K Ramesh , Aziz Khan , K. Lakshminarayan , Thabet Abdeljawad
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Abstract

Employing an improved Leslie-Gower model, the Allee impact on the predator population and the fear influence on the prey population, a mathematical model of the interaction involving two populations, prey and predator, has been explored in the current work. The influence of the memory effect on the evolving behaviour of the model is integrated using a well-known fractional operator known as the Caputo fractional derivative of order (0, 1]. We were inspired to do this study because further research is desired to fully comprehend the dynamics of the Allee impact, fear, and Caputo fractional order. The innovative aspect of the current work is the consideration of the Caputo fractional derivative, which enhances the consistency domain of the system. To support the model's biological resilience and accuracy, the existence, uniqueness, positivity, and boundedness of the solution are provided. On the origin, axial, and interior, four distinct types of equilibrium points are distinguished along with the prerequisites for their existence. We additionally stated about the Hopf bifurcation of our proposed model at the interior equilibrium point in terms of fractional order and the fear influence as the bifurcation factors. To illustrate how various biological characteristics affect the dynamics of the solutions, numerical simulations are offered.

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带有恐惧、阿利效应和种间竞争的捕食者-猎物分数阶莱斯利-高尔模型的动力学研究
本研究采用改进的莱斯利-高尔模型、捕食者种群的阿利影响和猎物种群的恐惧影响,探索了一个涉及猎物和捕食者两个种群的相互作用数学模型。记忆效应对模型演化行为的影响是通过一个著名的分数算子(即阶次为(0,1)的卡普托分数导数)来整合的。我们之所以受启发进行这项研究,是因为我们需要进一步研究,以充分理解阿利影响、恐惧和卡普托分数阶的动态变化。当前工作的创新之处在于考虑了卡普托分数导数,从而增强了系统的一致性域。为了支持模型的生物适应性和准确性,提供了解的存在性、唯一性、正向性和有界性。在原点、轴向和内部,我们区分了四种不同类型的平衡点及其存在的前提条件。此外,我们还从分数阶数和分岔因素中的恐惧影响两个方面阐述了我们提出的模型在内部平衡点的霍普夫分岔。为了说明各种生物特征如何影响解的动态,我们进行了数值模拟。
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来源期刊
Results in Control and Optimization
Results in Control and Optimization Mathematics-Control and Optimization
CiteScore
3.00
自引率
0.00%
发文量
51
审稿时长
91 days
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