Control strategies for a 4D chaotic supply chain model: dynamics, amplitude, and adaptive sliding mode control

Supply chains are complex, nonlinear systems that exhibit chaotic behaviour, leading to unpredictable demand fluctuations, inventory oscillations, and operational instability. These challenges necessitate advanced control mechanisms to improve resilience and efficiency. This paper presents a comprehensive analysis of the 4D Chaotic Supply Chain Model (4DCSCM) utilising chaos theory principles based on the model by Xu et al. (2022). Specifically, bifurcation and Lyapunov exponent analysis are employed to understand the behaviour of the system at specific parameter values in the chaos-based supply chain model. Furthermore, the effectiveness of control strategies such as amplitude control, offset boosting, and the Adaptive Sliding Mode Integral Proportional State (AS-MIPS) is examined to enhance the stability and performance of the 4DCSCM. The findings reveal complex dynamics in the system, including bifurcations, periodic patterns, and chaotic behaviour. This research enhances the understanding of 4DCSCM dynamics and provides practical approaches to address the challenges of complexity and uncertainty in contemporary 4DCSCM.