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Many natural systems are organized as networks, in which the nodes (be they cells, individuals or populations) interact in a time-dependent fashion. The dynamic behavior of these networks depends on how these nodes are connected, which can be understood in terms of an adjacency matrix, and connection strengths. The object of our study is to relate connectivity to temporal behavior in networks of coupled nonlinear oscillators. We investigate the relationship between classes of system architectures and classes of their possible dynamics, when the nodes are coupled according to a connectivity scheme that obeys certain constrains, but also incorporates random aspects. We illustrate how the phase space dynamics and bifurcations of the system change when perturbing the underlying adjacency graph. We differentiate between the effects on dynamics of the following operations that directly modulate network connectivity: (1) increasing/decreasing edge weights, (2) increasing/decreasing edge density, (3) altering edge configuration by adding, deleting or moving edges. We discuss the significance of our results in the context of real life networks. Some interpretations lead us to draw conclusions that may apply to brain networks, synaptic restructuring and neural dynamics.
The understanding of neural activity patterns is fundamentally linked to an understanding of how the brains network architecture shapes dynamical processes. Established approaches rely mostly on deviations of a given network from certain classes of r
Functional brain network has been widely studied to understand the relationship between brain organization and behavior. In this paper, we aim to explore the functional connectivity of brain network under a emph{multi-step} cognitive task involving w
We apply the framework of optimal nonlinear control to steer the dynamics of a whole-brain network of FitzHugh-Nagumo oscillators. Its nodes correspond to the cortical areas of an atlas-based segmentation of the human cerebral cortex, and the inter-n
Working memory (WM) allows information to be stored and manipulated over short time scales. Performance on WM tasks is thought to be supported by the frontoparietal system (FPS), the default mode system (DMS), and interactions between them. Yet littl
The oxytocin effects on large-scale brain networks such as Default Mode Network (DMN) and Frontoparietal Network (FPN) have been largely studied using fMRI data. However, these studies are mainly based on the statistical correlation or Bayesian causa