Time-Delay Effects on the Collective Resonant Behavior in Two Coupled Fractional Oscillators with Frequency Fluctuations

IF 3.6 2区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Fractal and Fractional Pub Date : 2024-05-11 DOI:10.3390/fractalfract8050287

Minyue He, Huiqi Wang, Lifeng Lin

引用次数: 0

Abstract

In this study, we propose coupled time-delayed fractional oscillators with dichotomous fluctuating frequencies and investigate the collective resonant behavior. Firstly, we obtain the condition of complete synchronization between the average behavior of the two oscillators. Subsequently, we derive the precise analytical expression of the output amplitude gain. Based on the analytical results, we observe the collective resonant behavior of the coupled time-delayed system and further study its dependence on various system parameters. The observed results underscore that the coupling strength, fractional order, and time delay play significant roles in controlling the collective resonant behavior by facilitating the occurrence and optimizing the intensity. Finally, numerical simulations are also conducted and verify the accuracy of the analytical results.

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时间延迟对两个具有频率波动的耦合分数振荡器集体共振行为的影响

在本研究中，我们提出了具有二分波动频率的耦合延时分数振荡器，并研究了其集体共振行为。首先，我们得到了两个振荡器平均行为完全同步的条件。随后，我们推导出输出振幅增益的精确分析表达式。在分析结果的基础上，我们观察了耦合延时系统的集体共振行为，并进一步研究了其对各种系统参数的依赖性。观察结果表明，耦合强度、分数阶数和时间延迟在控制集体共振行为方面发挥着重要作用，它们促进了共振的发生并优化了共振的强度。最后，还进行了数值模拟，验证了分析结果的准确性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Fractal and Fractional MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-

CiteScore

4.60

自引率

18.50%

发文量

632

审稿时长

11 weeks

期刊介绍： Fractal and Fractional is an international, scientific, peer-reviewed, open access journal that focuses on the study of fractals and fractional calculus, as well as their applications across various fields of science and engineering. It is published monthly online by MDPI and offers a cutting-edge platform for research papers, reviews, and short notes in this specialized area. The journal, identified by ISSN 2504-3110, encourages scientists to submit their experimental and theoretical findings in great detail, with no limits on the length of manuscripts to ensure reproducibility. A key objective is to facilitate the publication of detailed research, including experimental procedures and calculations. "Fractal and Fractional" also stands out for its unique offerings: it warmly welcomes manuscripts related to research proposals and innovative ideas, and allows for the deposition of electronic files containing detailed calculations and experimental protocols as supplementary material.