Fractal viewpoint in supply chain price competition

Abstract

This paper investigates the dynamical behaviors of the classical dual-channel supply chain from the perspective of fractal theory. First, the definition of filled Julia set in supply chain price competition model is introduced. Second, according to the periodicities of the attractors, the filled Julia set is divided into several sub basins. On this basis, the importance of mixed coexisting attraction basins’ connectivity is further illustrated. Then, the inner characteristics of filled Julia sets under different online preferences are analyzed, which indicates that online preference increase has negative influence on filled Julia sets’ structures. Finally, for the unstable cases caused by high online preference, we adopt three control strategies and analyze their control effects by quantifying the connectivity restorations. The results suggest that the fractal viewpoint is beneficial for a global observation of the prices evolutions in different initial states, and could also evaluate the market status more comprehensively.