In this paper, we propose to analyze artificial neural networks using a signed-rank objective function as the error function. We prove that the variance of the gradient of the learning process is bounded as a function of the number of patterns and/or outputs, therefore preventing the gradient explosion phenomenon. Simulations show that the method is particularly efficient at reproducing chaotic behaviors from biological models such as the Logistic and Ricker models. In particular, the accuracy of the learning process is improved relatively to the least squares objective function in these cases. Applications in regression settings on two real datasets, one small and the other relatively large are also considered.