Fragility and Controllability Tradeoff in Complex Networks

• Published in: 2018 Annual American Control Conference (ACC) pp. 216 - 221
• Main Authors: Pasqualetti, Fabio, Favaretto, Chiara, Shiyu Zhao, Zampieri, Sandro
• Format: Conference Proceeding
• Language: English
• Published: AACC 01.06.2018
• Subjects: Complex networks; Controllability; Eigenvalues and eigenfunctions; Perturbation methods; Robustness; Sociology; Statistics
• ISSN: 2378-5861
• DOI: 10.23919/ACC.2018.8431836

Mathematical theories and empirical evidence suggest that several complex natural and man-made systems are fragile: as their size increases, arbitrarily small and localized alterations of the system parameters may trigger system-wide failures. Examples are abundant, from perturbation of the population densities leading to extinction of species in ecological networks [1], to structural changes in metabolic networks preventing reactions [2], cascading failures in power networks [3], and the onset of epileptic seizures following alterations of structural connectivity among populations of neurons [4]. While fragility of these systems has long been recognized [5], convincing theories of why natural evolution or technological advance has failed, or avoided, to enhance robustness in complex systems are still lacking. In this paper we propose a mechanistic explanation of this phenomenon. We show that a fundamental tradeoff exists between fragility of a complex network and its controllability degree, that is, the control energy needed to drive the network state to a desirable state. We provide analytical and numerical evidence that easily controllable networks are fragile, suggesting that natural and man-made systems can either be resilient to parameters perturbation or efficient to adapt their state in response to external excitations and controls.