# Dynamic behavior and control analysis in a new chaotic three-tier supply chain system with a sinusoidal modelling uncertainty for resilient manufacturing networks

## TL;DR

This paper introduces a new chaotic supply chain model with enhanced complexity and controllable dynamics for resilient manufacturing networks.

## Contribution

The model integrates sinusoidal nonlinearities and offers controllable chaotic behavior with higher Lyapunov exponents.

## Key findings

- The proposed model shows higher Lyapunov exponent values (l1 = 0.2121) indicating stronger chaotic dynamics.
- Amplitude and location of chaotic signals can be controlled without altering the system's chaotic nature.
- Numerical simulations confirm improved chaotic intensity and transitions between different dynamic states.

## Abstract

This paper introduces a novel chaotic three-tier supply chain system (CSCS) that integrates both absolute function and sinusoidal nonlinearities into the classical Hamidzadeh model to enhance its dynamic complexity. The key improvement in the proposed model is that it exhibits higher Lyapunov exponent values (l1 = 0.2121) compared to the existing models, conforming stringer chaotic dynamics. Further, amplitude and location of the chaotic signal can be controlled in the proposed model. The proposed model captures the interactions among manufacturers, distributors, and retailers while exhibiting rich chaotic behaviors characterized through Lyapunov exponents, Lyapunov dimensions, and bifurcation analysis. Numerical simulations reveal improved chaotic intensity compared to existing CSCS models, with clear transitions between fixed points, periodic orbits, and chaos under parameter variations. To improve practical applicability, two control strategies are implemented: amplitude control, enabling systematic scaling of state variables without altering the chaotic nature, and offset boosting control, which shifts attractors in phase space while preserving system dynamics. Comparative analysis demonstrates the superior dynamic range and flexibility of the proposed model, offering valuable insights for designing resilient and adaptive supply chain networks under uncertainty.