Recently, the potential theory has attracted attentions of researchers in the coding theory. It has been successfully used to simplify the proof of the threshold saturation phenomenon for spatially-coupled codes. Also, potential functions are used to characterize the performance of the system. In this work, we introduce a construction of the bivariate potential function for iterative vector systems. The univariate potential function can be obtained by a simple modification. The applications of the potential function in coding systems are explored as well.