Abstract
Real world networks, from brain networks to social networks to critical infrastructure networks, are composed of nodes with nonlinear behaviors coupled together via highly non-trivial network structures. Approaches from statistical physics reveal the fundamental implications that complex network structure has on network function and resilience. In contrast, approaches from dynamical systems and control theory reveal the impact that nonlinear nodal dynamics have on emergent behaviors when connected together in simple networks. This talk will present recent work bridging the fields. Prof. D'Souza will show that the interaction between the nodal dynamics and network structure can give rise to novel emergent synchronization behaviors and extend the analysis of cluster synchronization to hypergraphs, capturing higher-order interactions in networks. With respect to cascading failures, Prof. D'Souza will show that adding in oscillatory nodal dynamics to classic models of self-organized-criticality leads to an emergent timescale and the occurrence of self-amplifying dragon king failures that wipe out the system. Finally, she will discuss the frontiers of control of complex networks with non-linear nodes, identifying the key challenges and opportunities for bridging control theory, dynamical systems and statistical physics.

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