Dynamics of Fractional-Order Digital Manufacturing Supply Chain System and Its Control and Synchronization

Abstract

Digital manufacturing is widely used in the production of automobiles and aircrafts, and plays a profound role in the whole supply chain. Due to the long memory property of demand, production, and stocks, a fractional-order digital manufacturing supply chain system can describe their dynamics more precisely. In addition, their control and synchronization may have potential applications in the management of real-word supply chain systems to control uncertainties that occur within it. In this paper, a fractional-order digital manufacturing supply chain system is proposed and solved by the Adomian decomposition method (ADM). Dynamical characteristics of this system are studied by using a phase portrait, bifurcation diagram, and a maximum Lyapunov exponent diagram. The complexity of the system is also investigated by means of SE complexity and C0 complexity. It is shown that the complexity results are consistent with the bifurcation diagrams, indicating that the complexity can reflect the dynamical properties of the system. Meanwhile, the importance of the fractional-order derivative in the modeling of the system is shown. Moreover, to further investigate the dynamics of the fractional-order supply chain system, we design the feedback controllers to control the chaotic supply chain system and synchronize two supply chain systems, respectively. Numerical simulations illustrate the effectiveness and applicability of the proposed methods.