生物害虫防治的Caputo和适形分数阶Guava模型:离散化、稳定性和分岔

IF 1.9 4区 工程技术 Q3 ENGINEERING, MECHANICAL
Senol Kartal
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引用次数: 0

摘要

摘要本文研究了描述番石榴蛀虫和天敌的两种捕食-食饵模型。研究了基于Caputo分数算子的第一类模型解的正性、存在性和唯一性,以及不动点的全局和局部稳定性分析。通过在第二个模型中加入分段常数函数,包括符合分数算子,我们可以通过离散化过程对离散动力系统进行转换。将Schur-Cohn准则应用于离散系统,得到了离散模型平衡点局部渐近稳定的一些区域。证明了离散模型在平衡点处存在超临界neimmark - sacker分岔。理论和数值结果表明,离散化后的系统比带Caputo算子的分数阶模型具有更丰富的动力学性质,如拟周期解、分岔和混沌动力学等。所有的理论结果都进行了生物学解释,并给出了番石榴果实的最佳采收时间间隔。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Caputo and Conformable Fractional Order Guava Model for Biological Pest Control: Discretization, Stability and Bifurcation
Abstract Two predator-prey model describing the guava borers and natural enemies are studied in this paper. Positivity, existence, and uniqueness of the solution, global and local stability analysis of the fixed points of the first model based on the Caputo fractional operator are studied. By adding piecewise constant functions to the second model including conformable fractional operator allows us to transition discrete dynamical system via discretization process. Applying Schur-Cohn criterion to the discrete system, we hold some regions where the equilibrium points in the discretized model are local asymptotically stable. We prove that discretized model displays supercritical Neimark–Sacker bifurcation at the equilibrium point. Theoretical and numerical results show that the discretized system demonstrates richer dynamic properties such as quasi-periodic solutions, bifurcation, and chaotic dynamics than the fractional order model with Caputo operator. All theoretical results are interpreted biologically and the optimum time interval for the harvesting of the guava fruit is given.
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来源期刊
CiteScore
4.00
自引率
10.00%
发文量
72
审稿时长
6-12 weeks
期刊介绍: The purpose of the Journal of Computational and Nonlinear Dynamics is to provide a medium for rapid dissemination of original research results in theoretical as well as applied computational and nonlinear dynamics. The journal serves as a forum for the exchange of new ideas and applications in computational, rigid and flexible multi-body system dynamics and all aspects (analytical, numerical, and experimental) of dynamics associated with nonlinear systems. The broad scope of the journal encompasses all computational and nonlinear problems occurring in aeronautical, biological, electrical, mechanical, physical, and structural systems.
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