In this paper, we establish a cold chain dynamic game model including a milk manufacturer and two downstream oligopoly supermarkets under the wholesale price contract in the real world. The manufacturer is responsible for the production and cold transportation, and the two retailers sell the product. The Nash equilibrium points and the complexity of the system are discussed. The influence of the decision parameters and the stability of the system are studied by using complexity theory. We reveal the stable regions for the dynamic system. In addition, revenue sharing contract and profit sharing contract are two valuable contracts. In order to see how the two contracts would impact on the system's equilibrium solution and the profits, we establish and analyze two new dynamic models for the cold chain. By the comparison of the analyses under three contracts, we find that the manufacturer's effort of cold transportation will change under different contracts, and the profit distribution of the whole cold chain will be affected. Chaos control is also studied by the method of delay feedback control, in order to provide some management advice. [ABSTRACT FROM AUTHOR]