In this paper, the dynamics of a collaborative supply chain have been analyzed using transform techniques. The general conditions for stability of the supply chains are derived and the effects of inter-player sampling intervals are analyzed. System dynamics simulation models of the different members of the supply chain are developed. Z-transform techniques are employed to derive the general stability conditions (settings of control parameters that produce stable response). The variation in the supply chain's stability in response to the information synchronization frequency is examined by relating the update frequency to the sampling interval of the underlying difference equations. Existence of instability due to improper parameter selection and improper sampling interval selection is thus confirmed, and guidance for the selection of appropriate parameters to guarantee system stability is presented. Simulations are used to confirm our analysis and help demonstrate the stable or unstable behavior of the supply chain.