Synchronization of a Supply Chain Model with Four Chaotic Attractors

Abstract

In this article, we construct a three-stage supply chain model using a system of differential equations to reveal the interplay among producers, distributors, and end customers. On the one hand, information about the products and production is exchanged between each stage in the supply chain system. Such information affects the behaviors of each stage. On the other hand, the transport of products between the stages of the supply chain affects the behavior of the system. Our findings are summarized as follows: First, we find that the supply chain model is a system with four chaotic attractors. Second, we explore the synchronization of such a chaotic system. Third, according to the characteristics of the chaotic system, we design a variety of simple control laws to realize the synchronization of two chaotic systems with the same structure. These control laws for the chaotic system are proved to realize local asymptotic synchronization or global exponential synchronization. Numerical simulations are conducted to confirm that the designed controls work well.