Complex spatiotemporal oscillations emerge from transverse instabilities in large-scale brain networks

Spatiotemporal oscillations underlie all cognitive brain functions. Large-scale brain models, constrained by neuroimaging data, aim to trace the principles underlying such macroscopic neural activity from the intricate and multi-scale structure of the brain. Despite substantial progress in the field, many aspects about the mechanisms behind the onset of spatiotemporal neural dynamics are still unknown. In this work we establish a simple framework for the emergence of complex brain dynamics, including high-dimensional chaos and travelling waves. The model consists of a complex network of 90 brain regions, whose structural connectivity is obtained from tractography data. The activity of each brain area is governed by a Jansen neural mass model and we normalize the total input received by each node so it amounts the same across all brain areas. This assumption allows for the existence of an homogeneous invariant manifold, i.e., a set of different stationary and oscillatory states in which all nodes behave identically. Stability analysis of these homogeneous solutions unveils a transverse instability of the synchronized state, which gives rise to different types of spatiotemporal dynamics, such as chaotic alpha activity. Additionally, we illustrate the ubiquity of this route towards complex spatiotemporal activity in a network of next-generation neural mass models. Altogehter, our results unveil the bifurcation landscape that underlies the emergence of function from structure in the brain. Author summary Monitoring brain activity with techniques such as EEG and fMRI has revealed that normal brain function is characterized by complex spatiotemporal dynamics. This behavior is well captured by large-scale brain models that incorporate structural connectivity data obtained with MRI-based tractography methods. Nonetheless, it is not yet clear how these complex dynamics emerges from the interplay of the different brain regions. In this paper we show that complex spatiotemporal dynamics, including travelling waves and high-dimensional chaos can arise in simple large-scale brain models through the destabilization of a synchronized oscillatory state. Such transverse instabilities are akin to those observed in chemical reactions and turbulence, and allow for a semi-analytical treatment that uncovers the overall dynamical landscape of the system. Overall, our work establishes and characterizes a general route towards spatiotemporal oscillations in large-scale brain models.