Nonlinear dynamics and control of a 3-echelon chaotic supply chain system having two stable equilibrium points

Abstract

Abstract This research work introduces a novel 3-echelon chaotic supply chain model incorporating a sinusoidal nonlinearity to represent modeling uncertainty, extending the Anne supply chain model. Through analytical calculations, we show that the new model exhibits chaotic behavior, verified by Lyapunov exponents and Kaplan–Yorke dimension. The largest Lyapunov value of the new model is 1.8336, which is higher than the existing Anne supply chain model. Interestingly, the proposed model has one unstable and two stable equilibrium points, which is rare in the literature. The dynamical analysis is carried out using classical nonlinear tools such as bifurcation plots and Lyapunov exponent spectra. Additionally, the multistability phenomenon is observed in the new model through bifurcation analysis and attractor plots. Finally, 1D and 2D offset boosting control schemes are applied to regulate the position of the attractor without affecting the chaotic dynamics of the system. In future research, these control strategies can be leveraged to optimize resource allocation and waste reduction, thereby enhancing the long-term sustainability of complex supply chain networks.