Topological resilience in non-normal networked systems

Abstract

The network of interactions in complex systems, strongly influences their resilience, the system capability to resist to external perturbations or structural damages and to promptly recover thereafter. The phenomenon manifests itself in different domains, e.g. cascade failures in computer networks or parasitic species invasion in ecosystems. Understanding the networks topological features that affect the resilience phenomenon remains a challenging goal of the design of robust complex systems. We prove that the non-normality character of the network of interactions amplifies the response of the system to exogenous disturbances and can drastically change the global dynamics. We provide an illustrative application to ecology by proposing a mechanism to mute the Allee effect and eventually a new theory of patterns formation involving a single diffusing species.

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• The Efficiency of Synchronization Dynamics and the Role of Network Syncreactivity
• Broken detailed balance and entropy production in directed networks
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• Self-segregation in heterogeneous metapopulation landscapes
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• Emergence of power-law distributions in self-segregation reaction-diffusion processes
• Pattern reconstruction through generalized eigenvectors on defective networks
• Hierarchical route to the emergence of leader nodes in real-world networks
• Network Hierarchy and Pattern Recovery in Directed Sparse Hopfield Networks
• Geometric Approaches to Matrix Normalization and Graph Balancing
• Nonmodal amplitude equations
• Organisational Social Influence on Directed Hierarchical Graphs, from Tyranny to Anarchy