Controlling the unpredictable: bifurcation and backstepping strategies in supply chain dynamics

Volume 35, Issue 2, pp 229--240 https://dx.doi.org/10.22436/jmcs.035.02.07

Publication Date: May 08, 2024 Submission Date: January 31, 2024 Revision Date: March 15, 2024 Accteptance Date: April 11, 2024

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Authors

M. D. Johansyah - Department of Mathematics, Universitas Padjadjaran, Jatinangor Sumedang 45363, Indonesia. A. Sambas - Faculty of Informatics and Computing, Universiti Sultan Zainal Abidin (UniSZA), Besut Campus, Besut 22200, Malaysia. - Department of Mechanical Engineering, Universitas Muhammadiyah Tasikmalaya, Tasikmalaya 46196, Indonesia. S. Vaidyanathan - Research and Development Center, Vel Tech University, Avadi, Chennai-600062, Tamil Nadu, India. C. Lazureanu - Department of Mathematics, Politehnica University Timişoara, P-ta Victoriei 2, 300006 Timişoara, Romania. Kh. Benkouider - Department of Electronics, Faculty of Technology, Badji-Mokhtar University, B.P. 12, Sidi Ammar, Annaba, Algeria. M. Mamat - Research Center, University College Bestari Putera Jaya, Setiu 22100 Permaisuri, Terengganu, Malaysia. M. Hidayanti - Department of Mathematics, Universitas Padjadjaran, Jatinangor Sumedang 45363, Indonesia. Ch. Aruna - Department of Computer Science and Engineering, KKR \(\&\) KSR Institute of Technology and Sciences Vinjanampadu, Vatticherukuru Mandal, Guntur-522017 Andhra Pradesh, India.

Abstract

Bifurcation points in a chaotic system represent critical thresholds where the system undergoes a qualitative change in behavior. In the context of supply chains, bifurcation points may signify shifts in demand patterns, disruptions in the flow of materials, or changes in market conditions. In this paper, we explore the intricacies of complexity within the Supply Chain Management Model (SCMM). The primary objective of this study involves an examination of the stability of the SCMM, revealing Hopf bifurcation, transcritical bifurcation, and double-zero bifurcation within the system. Additionally, we delve into the dynamical characteristics of the SCMM through the utilization of bifurcation diagrams and Lyapunov exponents. The findings indicate that the SCMM exhibits periodic, chaotic, and reverse period-doubling behaviors. To further comprehend the dynamics of the SCMM, we employ backstepping controllers to manage the chaotic SCMM and achieve synchronization between two SCMMs. Through numerical simulations, we demonstrate the effectiveness and applicability of the proposed methodologies.

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Keywords

• Chaos
• SCMM
• bifurcation
• Hopf bifurcation and backstepping controllers

MSC

•  34H10
•  34C23
•  93C10
•  91B74

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