Emergent stability dynamics in the human brain connectome through the inclusion of high order interactions between coupled oscillators

In complex systems such as the brain, interactions among their constituents units have been demonstrated to occur in groups of units and not limited only to pairwise interactions, like for example, neural coupling among different brain regions. This investigation delves into the inclusion of higher order interactions to simulate the dynamics of brain oscillations. Specifically, we employed a coupled oscillators approach to model large scale neural networks using an extended Kuramoto model to simulate high order synchronization dynamics in the brain using the human connectome. We found that the human connectome used in this study has a high order architecture, with simplicial complexes up to the 11th order. Furthermore, stability dynamics emerge through the addition of simplex of higher order to the simulations: hysteresis when considering from 3-simplex to 6-simplex and metastability when considering 7-simplex onward. This investigation is relevant in the modelling of neural oscillatory signals representing phenomenon of abrupt changes in synchrony, where non-linear regimes emerge.