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

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.

Keywords

• Chaotic systems
• Dynamical systems
• Finance models
• Stability