Resource allocation is one of the challenges in the time division multiple access (TDM) passive optical network (PON) area. Much research has been done to find an efficient resource allocation method. Using machine learning (ML) and finding proper ML algorithms in predictive dynamic bandwidth allocation remains an open research question. This paper aims to predict resource allocation accurately and efficiently based on historical requests. Artificial neural networks (ANN) with historically allocated bandwidth from different time series are used to build the prediction model. This model is constructed by the normal equation method. The proposed model needs a small dataset for its training phase, while its accuracy is higher than other models. The discrete dynamical system builds to find an equilibrium point, which is a stable point in the system. The proposed model can be implemented as a pre-training, or it can be dynamically refined when the model is running by using some of its output as feedback. The system evaluation verifies that the proposed DBA (EQ-ANN) elevates the quality of service (QoS) metrics, such as system throughput, packet drop probability, and packet means delay. The results show that the system throughput improves by up to 5%, and packet loss improves by up to 15%. Moreover, the prediction accuracy of the system reached 99.48%.