A New 5D Chaotic Supply Chain System with Transport Lag: Modeling, Bifurcation Analysis, Offset Boosting Control and Synchronization

Muhamad Deni Johansyah (), Khaled Benkouider, Sundarapandian Vaidyanathan, Aceng Sambas and Chittineni Aruna
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Muhamad Deni Johansyah: Department of Mathematic, Universitas Padjadjaran, Jatinangor 45363, Indonesia
Khaled Benkouider: Department of Electronics, Faculty of Technology, Badji-Mokhtar University, B.P. 12, Sidi Ammar 23000, Annaba, Algeria
Sundarapandian Vaidyanathan: Centre for Control Systems, Vel Tech University, Avadi Chennai 600062, Tamil Nadu, India
Aceng Sambas: Faculty of Informatics and Computing, Universiti Sultan Zainal Abidin, Besut Campus, Kuala Terengganu 22200, Terengganu, Malaysia
Chittineni Aruna: Department of Computer Science and Engineering, KKR & KSR Institute of Technology and Sciences, Guntur 522017, Andhra Pradesh, India

Mathematics, 2025, vol. 13, issue 21, 1-20

Abstract: This paper introduces an enhanced five-dimensional Chaotic Supply Chain Model (5DCSCM) by incorporating a transport lag variable into a previously established four-dimensional model. The newly added differential equation in the transit dynamics of the supply chain model captures the inherent lag between customer demand and the physical response in transportation, modeled as a first-order transport lag system. Through comprehensive numerical simulations, the influence of various system parameters—including customer demand rate, delivery efficiency, information distortion, contingency reserve, safety stock, and transportation lag—are examined. The study utilizes bifurcation diagrams and a Lyapunov Exponent (LE) to investigate tran-sitions between periodic and chaotic behavior. Additionally, the model is extended with offset boosting control, allowing for controlled amplitude adjustment without altering the underlying chaotic dynamics. Offset boosting control (OBC) is useful in chaotic supply chain systems because it stabilizes inventory and order fluctuations by counter-acting the amplification of small disturbances, reducing the bullwhip effect, and im-proving overall system reliability and responsiveness. As an application, integral sliding mode control (ISMC) technique has been applied to achieve complete synchronization between a pair of the 5DCSCM. Synchronization based on ISMC is useful in chaotic supply chain systems because it ensures robust coordination between different tiers, suppresses chaos-induced fluctuations, and maintains stable inventory and order patterns even under disturbances and uncertainties.

Keywords: chaotic supply chain; transport lag; nonlinear dynamics; synchronization; integral sliding mode control (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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