Session V3: Complex Network Dynamics

Cascading Failures and Recovery in Networks of Networks

Network science have been focused on the properties of a single isolated network that does not interact or depends on other networks. In reality, many real-networks, such as power grids, transportation and communication infrastructures interact and depend on other networks. I will present a framework for studying the vulnerability and the recovery of networks of interdependent networks. In interdependent networks, when nodes in one network fail, they cause dependent nodes in other networks to also fail. This is also the case when some nodes like certain locations play a role in two networks --multiplex. This may happen recursively and can lead to a cascade of failures and to a sudden fragmentation of the system. I will present analytical solutions for the critical threshold and the giant component of a network of n interdependent networks. I will show, that the general theory has many novel features that are not present in the classical network theory. When recovery of components is possible global spontaneous recovery of the networks and hysteresis phenomena occur and the theory suggests an optimal repairing strategy of system of systems. I will also show that interdependent networks embedded in space are significantly more vulnerable compared to non embedded networks. In particular, small localized attacks may lead to cascading failures and catastrophic consequences.Thus, analyzing data of real network of networks is highly required to understand the system vulnerability. References: [1] S. Buldyrev, R. Parshani, G. Paul, H.E. Stanley, S. Havlin, Nature, 465, 0893 (2010) [2] R. Parshani, S. Buldyrev, S. Havlin, PRL, 105, 048701 (2010) [3] R. Parshani, S.V. Buldyrev, S. Havlin, PNAS 108, 1007 (2011) [4] J. Gao, S. Buldyrev, H. E. Stanley, S. Havlin, Nature Physics, 8, 40 (2012). [5] A. Bashan et al, Nature Communications 3, 702 (2012) [6] A. Bashan et al, Nature Physics, 9, 667 (2013) [7] A Majdandzic et al, Nature Physics 10 (1), 34 (2014)   

The Life-Changing Magic of Nonlinearity in Network Control

The proper functioning and reliability of many man-made and natural systems is fundamentally tied to our ability to control them. Indeed, applications as diverse as ecosystem management, emergency response and cell reprogramming all, at their heart, require us to drive a system to---or keep it in---a desired state. This process is complicated by the nonlinear dynamics inherent to most real systems, which has traditionally been viewed as the principle obstacle to their control. In this talk, I will discuss two ways in which nonlinearity turns this view on its head, in fact representing an asset to the control of complex systems. First, I will show how nonlinearity in the form of multistability allows one to systematically design control interventions that can deliberately induce ``reverse cascading failures'', in which a network spontaneously evolves to a desirable (rather than a failed) state. Second, I will show that nonlinearity in the form of time-varying dynamics unexpectedly makes temporal networks easier to control than their static counterparts, with the former enjoying dramatic and simultaneous reductions in all costs of control. This is true despite the fact that temporality tends to fragment a network's structure, disrupting the paths that allow the directly-controlled or ``driver'' nodes to communicate with the rest of the network. Taken together, these studies shed new light on the crucial role of nonlinearity in network control, and provide support to the idea we can control nonlinearity, rather than letting nonlinearity control us.   

Novel percolation transitions and coupled catastrophes

Collections of interdependent networks are at the core of modern society, spanning physical, biological and social systems. Simple mathematical models of the structure and function of networks can provide important insights into real-world systems, enhancing our ability to steer and control them. Here our focus is on abrupt changes in networks, due both to phase transitions and to jumping between bi-stable equilibria. We begin with an overview of novel classes of percolation phase transitions that result from repeated, small interventions intended to delay the transition. These new phenomena allow us to extend percolation approaches to modular networks, Brownian motion, and cluster growth dynamics. We then focus on abrupt transitions due to a system jumping between bi-stable equilibria, modeled as a cusp catastrophe in nonlinear dynamics. We show that when systems that each undergo a cusp catastrophe interact, we can observe a new phenomena of catastrophe-hopping leading to non-local cascading failures. Here an intermediate system facilitates the propagation of a sudden change or collapse, and we show that catastrophe hopping is consistent with the outbreak of protests observed during the Arab Spring of 2011.   

Interdisciplinary applications of network dynamics: From microscopic to Macroscopic

“Everything touches everything.” We are living in a connected world, which has been modeled successfully by complex networks. Ever since, network science becomes new paradigm for understanding our connected yet complex world. After investigating network structure itself, our focus naturally moved to dynamics of/on the network because our connected world is not static but dynamic. In this presentation, we will briefly review the historical development of network science and show some applications of network dynamics ranging from microscopic (metabolic engineering, PNAS, 104 13638) to macroscopic scale (price of anarchy in transportation network, Phys.Rev.Lett. 101 128701).   

Rank Dynamics

Studies of rank distributions have been popular for decades, especially since the work of Zipf. For example, if we rank words of a given language by use frequency (most used word in English is ’the’, rank 1; second most common word is ‘of’, rank 2), the distribution can be approximated roughly with a power law. The same applies for cities (most populated city in a country ranks first), earthquakes, metabolism, the Internet, and dozens of other phenomena. We recently proposed “rank diversity” to measure how ranks change in time [1], using the Google Books Ngram dataset. Studying six languages between 1800 and 2009, we found that the rank diversity curves of languages are universal, adjusted with a sigmoid on log-normal scale. We are studying several other datasets (sports, economies, social systems, urban systems, earthquakes, artificial life). Rank diversity seems to be universal, independently of the shape of the rank distribution. I will present our work in progress towards a general description of the features of rank change in time, along with simple models which reproduce it. [1] Cocho G, Flores J, Gershenson C, Pineda C, Sanchez S (2015) Rank Diversity of Languages: Generic Behavior in Computational Linguistics. PLoS ONE 10(4): e0121898. http://dx.doi.org/10.1371/journal.pone.0121898