This presentation aims to highlight the utility of dynamical systems in bridging theoretical and practical aspects of neuroscience and machine learning, offering insights into the complex interplay of natural and artificial cognitive systems. The discussion begins with a critical review of existing models at the intersection of these fields. Then, a first study illustrates the application of dynamical systems theory to multi-brain neuroscience, showcasing its potential application to model inter-brain synchronization but also to predict autism diagnosis. Next, we show how integrating dynamical systems within deep learning models can significantly enhance the forecasting of brain activity at both microscopic and macroscopic scales. Lastly, we discuss the combination of dynamic systems and neuroscience methods to help in the mechanistic interpretability of machine learning, particularly examining the phenomenon of ‘grokking’.