Abstract: Emergencies result in random fluctuations to market demand and market prices, turning suppliers' risk attitude from neutral to aversion. Under this condition, the emergency buy-back contract model is build with the random market price and the risk-aversion supplier. The profit-CVaR risk assessment criterion of decentralized decision-making is revised to the Profit-CVaR risk evaluation criterion of centralized decision-making, the Buy-back contract is studied about whether it can realize the two-echelon supply chains' coordination under the new criterion. Numerical simulation is conducted to this model. The result shows that, when the market demand obeys normal distribution, the optimal order quantity of supply chain is related to the change of risk factors' step length and the variance of the normal distribution function. In certain range, when the risk factors change in a smaller step length, the optimal order quantity will occur bifurcation mutations, and the retailer and the suppliers' expected revenues and the wholesale price will also occur bifurcation mutations correspondingly. In addition, this kind of bifurcation mutations' intervals and the amplitude of above values will increase with the variance. And the supply chain can't be coordinated under the model in the bifurcation mutation area, while it can realize coordination in those areas without bifurcation mutations.

Key words: bifurcation phenomena, buy-back contract, risk aversion, stochastic price, supply chain coordination