skip to main content


Title: Fragility and Controllability Tradeoff in Complex Networks
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.  more » « less
Award ID(s):
1631112
NSF-PAR ID:
10105279
Author(s) / Creator(s):
; ; ;
Date Published:
Journal Name:
American Control Conference
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Synchronization is crucial for the correct functi- onality of many natural and man-made complex systems. In this work we characterize the formation of synchronization patterns in networks of Kuramoto oscillators. Specifically, we reveal conditions on the network weights, structure and on the oscillators’ natural frequencies that allow the phases of a group of oscillators to evolve cohesively, yet independently from the phases of oscillators in different clusters. Our conditions are applicable to general directed and weighted networks of heterogeneous oscillators. Surprisingly, although the oscillators exhibit nonlinear dynamics, our approach relies entirely on tools from linear algebra and graph theory. Further, we develop a control mechanism to determine the smallest (as measured by the Frobenius norm) network perturbation to ensure the formation of a desired synchronization pattern. Our procedure allows us to constrain the set of edges that can be modified, thus enforcing the sparsity structure of the network perturbation. The results are validated through a set of numerical examples. 
    more » « less
  2. Ellis, K ; Ferrell, W. ; Knapp, J. (Ed.)
    Failure identification and prediction in a power system are essential components that are prerequisites for optimizing the maintenance of the system. The incidences of power system failures have increased dramatically in recent times due to the uncertainties inherent in the advent of both man-made and natural disasters. This problem is further exacerbated due to the increasing demand for higher operational efficiency in power systems. Currently, there is a paucity of studies that predict and identify failure in a distribution power system. In this paper, we propose an integrated methodology for selecting the optimal maintenance plan based on predicting and identifying failure modes with the aid of Hidden Markov Models (HMM) and a probabilistic decision-making tool. While the model parameters of previous studies were determined utilizing observable prior knowledge, the use of HMM offers a different approach especially in the absence of such observable prior distributions. Thus, we determine the status of health of a power system by using an HMM to capture the relationship between unobservable degradation state and observed parameters. The preliminary outcome is instructive for the management of power systems especially in response to fortifying the system against aging and degradation. 
    more » « less
  3. Abstract The increased complexity of infrastructure systems has resulted in critical interdependencies between multiple networks—communication systems require electricity, while the normal functioning of the power grid relies on communication systems. These interdependencies have inspired an extensive literature on coupled multilayer networks, assuming a hard interdependence, where a component failure in one network causes failures in the other network, resulting in a cascade of failures across multiple systems. While empirical evidence of such hard failures is limited, the repair and recovery of a network requires resources typically supplied by other networks, resulting in documented interdependencies induced by the recovery process. In this work, we explore recovery coupling, capturing the dependence of the recovery of one system on the instantaneous functional state of another system. If the support networks are not functional, recovery will be slowed. Here we collected data on the recovery time of millions of power grid failures, finding evidence of universal nonlinear behavior in recovery following large perturbations. We develop a theoretical framework to address recovery coupling, predicting quantitative signatures different from the multilayer cascading failures. We then rely on controlled natural experiments to separate the role of recovery coupling from other effects like resource limitations, offering direct evidence of how recovery coupling affects a system’s functionality. 
    more » « less
  4. Abstract

    Although brain functionality is often remarkably robust to lesions and other insults, it may be fragile when these take place in specific locations. Previous attempts to quantify robustness and fragility sought to understand how the functional connectivity of brain networks is affected by structural changes, using either model-based predictions or empirical studies of the effects of lesions. We advance a geometric viewpoint relying on a notion of network curvature, the so-called Ollivier-Ricci curvature. This approach has been proposed to assess financial market robustness and to differentiate biological networks of cancer cells from healthy ones. Here, we apply curvature-based measures to brain structural networks to identify robust and fragile brain regions in healthy subjects. We show that curvature can also be used to track changes in brain connectivity related to age and autism spectrum disorder (ASD), and we obtain results that are in agreement with previous MRI studies.

     
    more » « less
  5. Rainey, Larry B. ; Holland, O. Thomas (Ed.)
    Biological neural networks offer some of the most striking and complex examples of emergence ever observed in natural or man-made systems. Individually, the behavior of a single neuron is rather simple, yet these basic building blocks are connected through synapses to form neural networks, which are capable of sophisticated capabilities such as pattern recognition and navigation. Lower-level functionality provided by a given network is combined with other networks to produce more sophisticated capabilities. These capabilities manifest emergently at two vastly different, yet interconnected time scales. At the time scale of neural dynamics, neural networks are responsible for turning noisy external stimuli and internal signals into signals capable of supporting complex computations. A key component in this process is the structure of the network, which itself forms emergently over much longer time scales based on the outputs of its constituent neurons, a process called learning. The analysis and interpretation of the behaviors of these interconnected dynamical systems of neurons should account for the network structure and the collective behavior of the network. The field of graph signal processing (GSP) combines signal processing with network science to study signals defined on irregular network structures. Here, we show that GSP can be a valuable tool in the analysis of emergence in biological neural networks. Beyond any purely scientific pursuits, understanding the emergence in biological neural networks directly impacts the design of more effective artificial neural networks for general machine learning and artificial intelligence tasks across domains, and motivates additional design motifs for novel emergent systems of systems. 
    more » « less