The brain is arguably one of the most complex natural dynamical systems that involves highly nonlinear interactions across billions of neurons. Accurate mathematical modeling of the full-brain dynamics remains a difficult open problem. Our current work presents an advancement in this direction, investigating (1) whether dynamical models, such as a set of coupled van der Pol oscillators, can accurately capture a low-dimensional representation of neural activity measured by different brain imaging modalities in various living organisms, and (2) whether a method could be developed to accurately estimate the parameters of such a model from imaging data. Furthermore, even if a model could accurately fit the observed data, (3) is it possible to predict the future brain activity based on its past using such analytical model? As we show in this work, all these questions can be answered positively.  Particularly, we show that the van der Pol model can not only provide a good fit (0.8-0.9 Pearson correlation) of brain imaging for two different modalities (calcium imaging and functional magnetic resonance imaging) and three different organisms (larval zebrafish, rat and human), but also be used to predict the future brain activity, especially when combined with machine-learning models such as deep recurrent neural networks. Finally, on the example of larval zebrafish, we show that the van der Pol's coupling matrix, representing interaction strength across multiple brain areas, can provide a meaningful anatomical interpretation and potentially add to our understanding of the whole brain functioning.