Supply chains with dynamical behavior (SCD) are significant in the current industrial management. They can help to reduce inventory, enable flow of materials, maximize profits, and minimize costs. Dynamics of SCD is usually represented by a nonlinear perturbed dynamical system with imprecise parameters and limited state vector. The potential application of SCDs in industrial scenarios requires an effective model representation that can be used in a posterior optimization approach. Differential neural networks (DNN) with continuous-time dynamics can be used to obtain a feasible approximate mathematical model of the SCD that can be further used as a part of the optimization approach. This study develops a DNN identifier to approximate the dynamics of SCD considering the limitations on the states. The differential learning laws for the aforementioned neural network, which take into account restrictions on the states, are presented using the concept of barrier Lyapunov functions. A formal analysis that justifies the existence of the barrier learning laws is presented. The explicit implementation of the identifier is explained in detail, high-lighting how particular SCD can be handled with the proposed continuous neural network. A numerically simulated example of a three level continuous-time model of the nonlinear supply chain is evidenced in this study to illustrate the applicability of the proposed identifier for a supply chain with imprecise mathematical description.