4D DYNAMIC SPATIAL BRAIN NETWORKS AT REST LINKED TO COGNITION SHOW ATYPICAL VARIABILITY AND COUPLING IN SCHIZOPHRENIA.

Despite increasing interest in the dynamics of functional brain networks, most studies focus on the changing relationships over time between spatially static networks or regions. Here we propose an approach to study dynamic spatial brain net-works in human resting state functional magnetic resonance imaging (rsfMRI) data and evaluate the temporal changes in the volumes of these 4D networks. Our results show significant volumetric coupling (i.e., synchronized shrinkage and growth) between networks during the scan. We find that several features of such dynamic spatial brain networks are associated with cognition, with higher dynamic variability in these networks and higher volumetric coupling between network pairs positively associated with cognitive performance. We show that these networks are modulated differently in individuals with schizophrenia versus typical controls, resulting in network growth or shrinkage, as well as altered focus of activity within a network. Schizophrenia also shows lower spatial dynamical variability in several networks, and lower volumetric coupling between pairs of networks, thus upholding the role of dynamic spatial brain networks in cognitive impairment seen in schizophrenia. Our data show evidence for the importance of studying the typically overlooked voxelwise changes within and between brain networks.

Ordered intricacy of Shilnikov saddle-focus homoclinics in symmetric systems.

Using the technique of Poincaré return maps, we disclose an intricate order of subsequent homoclinic bifurcations near the primary figure-8 connection of the Shilnikov saddle-focus in systems with reflection symmetry. We also reveal admissible shapes of the corresponding bifurcation curves in a parameter space. Their scalability ratio and organization are proven to be universal for such homoclinic bifurcations of higher orders. Two applications with similar dynamics due to the Shilnikov saddle-foci are used to illustrate the theory: a smooth adaptation of the Chua circuit and a 3D normal form.

Homoclinic chaos in the Rössler model.

We study the origin of homoclinic chaos in the classical 3D model proposed by Rössler in 1976. Of our particular interest are the convoluted bifurcations of the Shilnikov saddle-foci and how their synergy determines the global bifurcation unfolding of the model, along with transformations of its chaotic attractors. We apply two computational methods proposed, one based on interval maps and a symbolic approach specifically tailored to this model, to scrutinize homoclinic bifurcations, as well as to detect the regions of structurally stable and chaotic dynamics in the parameter space of the Rössler model.