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

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.