Dynamic analysis, and offset boosting control of a new multi-echelon chaotic supply chain model with a sinusoidal nonlinearity for SDG-oriented resilient logistics

Abstract This paper proposes a new multi-echelon 4-D chaotic supply chain model (NME-4D-CSCM) incorporating a sinusoidal nonlinearity to better represent uncertainties in supply chain dynamics. The model extends the existing framework by introducing periodic fluctuations in the supply-side variables, which significantly enhances the system’s complexity. The dynamical behavior of the proposed NME-4D-CSCM is investigated using phase portraits, bifurcation diagrams, and Lyapunov exponent (LE) spectra. Numerical results confirm the presence of chaotic attractors with higher sensitivity to initial conditions compared to the existing model, as indicated by larger maximum LE values. Stability analysis of equilibrium points is performed using the Jacobian matrix and eigenvalue analysis, revealing the instability of all equilibrium states. Furthermore, amplitude control is achieved through a rescaling method, allowing regulation of oscillation magnitude without altering the system’s chaotic nature. In addition, an offset boosting control strategy is implemented to shift the attractor position without affecting the underlying dynamics. The proposed NME-4D-CSCM provides a more comprehensive framework for analyzing complex behaviors in supply chain systems and offers practical control approaches for managing chaotic fluctuations.