Chaos in chains: Exploring a novel supply chain model through bifurcation analysis, multi-stability and complete synchronization via backstepping control

Q1 Mathematics Partial Differential Equations in Applied Mathematics Pub Date : 2024-09-01 Epub Date: 2024-08-13 DOI:10.1016/j.padiff.2024.100866

Muhamad Deni Johansyah , Sundarapandian Vaidyanathan , Fareh Hannachi , Aceng Sambas , Bob Foster , Chittineni Aruna , Repudi Ramesh , Endang Rusyaman

{"title":"Chaos in chains: Exploring a novel supply chain model through bifurcation analysis, multi-stability and complete synchronization via backstepping control","authors":"Muhamad Deni Johansyah , Sundarapandian Vaidyanathan , Fareh Hannachi , Aceng Sambas , Bob Foster , Chittineni Aruna , Repudi Ramesh , Endang Rusyaman","doi":"10.1016/j.padiff.2024.100866","DOIUrl":null,"url":null,"abstract":"<div><p>Chaotic systems are highly sensitive to initial conditions, meaning small changes can lead to significant outcomes. This sensitivity can be leveraged to enhance the flexibility and adaptability of supply chains, allowing them to respond quickly to changing market demands and conditions. In this research work, we obtain a New Chaotic Supply Chain Model (NCSCM) by introducing a sinusoidal model uncertainty in the third differential equation of the Hamidzadeh chaotic supply chain model (2023). The sinusoidal uncertainty in the model accounts for the volatility and fluctuations of the supply chain model. We investigate the dynamic behaviors of NCSCM by performing a detailed Bifurcation Diagram (BD) analysis and Lyapunov Exponents (LEs). Next, we carry out a <span><math><mrow><mn>0</mn><mo>−</mo><mn>1</mn></mrow></math></span> test for the NCSCM to confirm the chaotic attractor of the system. We also study the multi-stability properties of the NCSCM. Finally, with the help of backstepping control, we derive new results for the complete synchronization of the novel chaotic supply chain models.</p></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"11 ","pages":"Article 100866"},"PeriodicalIF":0.0000,"publicationDate":"2024-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2666818124002523/pdfft?md5=39ff10f9bcc10750525c515bb18d5a1e&pid=1-s2.0-S2666818124002523-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Partial Differential Equations in Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2666818124002523","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2024/8/13 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}

引用次数: 0

Abstract

Chaotic systems are highly sensitive to initial conditions, meaning small changes can lead to significant outcomes. This sensitivity can be leveraged to enhance the flexibility and adaptability of supply chains, allowing them to respond quickly to changing market demands and conditions. In this research work, we obtain a New Chaotic Supply Chain Model (NCSCM) by introducing a sinusoidal model uncertainty in the third differential equation of the Hamidzadeh chaotic supply chain model (2023). The sinusoidal uncertainty in the model accounts for the volatility and fluctuations of the supply chain model. We investigate the dynamic behaviors of NCSCM by performing a detailed Bifurcation Diagram (BD) analysis and Lyapunov Exponents (LEs). Next, we carry out a $0 - 1$ test for the NCSCM to confirm the chaotic attractor of the system. We also study the multi-stability properties of the NCSCM. Finally, with the help of backstepping control, we derive new results for the complete synchronization of the novel chaotic supply chain models.

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

链中的混沌：通过分岔分析、多稳定性和反步态控制实现完全同步，探索新型供应链模型

混沌系统对初始条件高度敏感，这意味着微小的变化就可能导致重大的结果。可以利用这种敏感性来提高供应链的灵活性和适应性，使其能够快速响应不断变化的市场需求和条件。在这项研究工作中，我们在 Hamidzadeh 混沌供应链模型（2023 年）的第三个微分方程中引入了正弦模型不确定性，从而获得了新的混沌供应链模型（NCSCM）。模型中的正弦不确定性反映了供应链模型的波动性和不稳定性。我们通过详细的分岔图（BD）分析和 Lyapunov 指数（LE）研究了 NCSCM 的动态行为。接下来，我们对 NCSCM 进行了 0-1 检验，以确认系统的混沌吸引子。我们还研究了 NCSCM 的多重稳定性。最后，在反步态控制的帮助下，我们得出了新型混沌供应链模型完全同步的新结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文去求助

来源期刊