  This study investigates the dynamic game behaviors of dual-channel supply
chains involving an oligopoly manufacturer selling low-carbon products to
online and offline retailers. The price game models under government subsidy
are discussed under three scenarios: (1) simultaneous decision, (2)
manufacturer dominates the market, and (3) retailer dominates the market. The
equilibrium strategies are compared under the government subsidy policy. Using
numerical simulation,complex characteristics of the dual-channel supply chain
under the carbon subsidy policy are investigated. The complexity of wholesale
price and sales commission of each channel are analyzed by bifurcation, largest
Lyapunov exponent and basin of attraction diagrams. Furthermore,parameter
adjustment and delayed feedback control methods are proven to be effective
approaches to chaos control.
