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Mathematics Colloquium

Malbor Asllani
University College Dublin

Title: Emergent dynamics in complex networked systems
Date: Monday, January 31, 2022
Place and Time: Zoom, 3:05-3:55 pm


Complex systems, naturally emerging in various domains, are well described by complex networks, resulting in numerous interesting features absent from their undirected counterparts. Among these properties is a strong non-normality inherited by a strong asymmetry that characterises such systems and guides their underlying hierarchy. Dynamical processes evolving on non-normal networks exhibit peculiar behaviour: initial small disturbances of stable systems may undergo a transient growth phase in the linear regime that can eventually transform to a permanent instability in the nonlinear one. Furthermore, modularity has been extensively investigated as a universal feature of many biological and social networks. Spectral methods have been paramount in graph partitioning and community detection. In this talk, we present recent findings related to emergent structural and dynamical properties of complex networks. In particular, we will focus on network-induced symmetry-breaking mechanisms responsible for the emergent phenomena in complex systems. We first show how network directedness gives birth to a topology-driven instability extending the paradigm of Turing patterns. Using information-theoretic tools and data analysis, we illustrate how hierarchical structural features shape real-world networks. We demonstrate that contrary to the common belief that strong directedness ensures the robustness of synchronisation, due to a transient growth induced by the structure?s non-normality, the system might lose synchronisation. For more, we show that network modularity is the basis of a systematic mechanism for generating the celebrated chimera states where clusters of coherent and incoherent oscillators simultaneously coexist.