Academia.eduAcademia.edu

Outline

Title
Abstract
Key Takeaways
Figures
Methods
References

Spontaneous recovery in dynamical networks

Profile image of Eugene StanleyEugene Stanley
https://doi.org/10.1038/NPHYS2819
visibility

…

description

5 pages

link

1 file

Abstract

Much research has been carried out to explore the structural properties and vulnerability of complex networks. Of particular interest are abrupt dynamic events that cause networks to irreversibly fail. However, in many real-world phenomena, such as brain seizures in neuroscience or sudden market crashes in finance, after an inactive period of time a significant part of the damaged network is capable of spontaneously becoming active again. The process often occurs repeatedly. To model this marked network recovery, we examine the effect of local node recoveries and stochastic contiguous spreading, and find that they can lead to the spontaneous emergence of macroscopic ‘phase-flipping’ phenomena. As the network is of finite size and is stochastic, the fraction of active nodes z switches back and forth between the two network collective modes characterized by high network activity and low network activity. Furthermore, the system exhibits a strong hysteresis behaviour analogous to phase transitions near a critical point. We present real-world network data exhibiting phase switching behaviour in accord with the predictions of the model.

Key takeaways
sparkles

AI

  1. Spontaneous recovery in networks leads to phase-flipping phenomena characterized by high and low activity states.
  2. The model employs parameters p* and r to analyze internal and external failures in network dynamics.
  3. Numerical simulations reveal hysteresis behavior indicative of first-order phase transitions in network states.
  4. Real-world economic networks exhibit bimodal behavior in activity, supporting the model's predictions.
  5. Average lifetimes in network states exponentially increase with system size, confirming theoretical results.
Figures (3)
Figure 1 | Critical behaviour of the system with first-order phase transition and hysteresis. a, Equilibrium average fraction of active nodes, (z(p*)), simulation results (symbols) and the MFT prediction (solid lines), for three different values of r. Parameters for random regular networks, N=107, k=10 and m= 4 are used in this example. b, The phase diagram in model parameters (r, p*) exhibits two phases. Phase | (green region) represents a high-activity collective network mode; Phase II (orange) represents a low-activity mode. The hysteresis region (purple) is bounded with spinodals, denoted by red and blue lines. The lines merge at a critical point located at (r = 0.637, p* = 0.386). Colours in the diagram highlight regions of different phases. Analytical MFT results for spinodals are denoted by black lines. Point A shows the parameters used in Fig. 2. ¢, Comparison of analytical MFT result (dashed lines) with numerical results (dots), for the spinodals in the (r,p*) phase diagram, for regular networks. d, Comparison of analytical MFT result with simulation results, for an Erdés-Renyi (ER) network with (k) =10, m= 4, N=10’.
Figure 1 | Critical behaviour of the system with first-order phase transition and hysteresis. a, Equilibrium average fraction of active nodes, (z(p*)), simulation results (symbols) and the MFT prediction (solid lines), for three different values of r. Parameters for random regular networks, N=107, k=10 and m= 4 are used in this example. b, The phase diagram in model parameters (r, p*) exhibits two phases. Phase | (green region) represents a high-activity collective network mode; Phase II (orange) represents a low-activity mode. The hysteresis region (purple) is bounded with spinodals, denoted by red and blue lines. The lines merge at a critical point located at (r = 0.637, p* = 0.386). Colours in the diagram highlight regions of different phases. Analytical MFT results for spinodals are denoted by black lines. Point A shows the parameters used in Fig. 2. ¢, Comparison of analytical MFT result (dashed lines) with numerical results (dots), for the spinodals in the (r,p*) phase diagram, for regular networks. d, Comparison of analytical MFT result with simulation results, for an Erdés-Renyi (ER) network with (k) =10, m= 4, N=10’.
Figure 2 | Two network modes characterized by high and low network activity. a, Dynamical switching (flipping) of the fraction of active nodes z, between two collective modes in the subcritical region, an example for p* = 0.28, r= 0.80 (point A, in yellow, Fig. 1b), with k=10,m=4 and N=100. Green circles mark avoided transitions. b, The PDF of z shows a bimodal form. ¢, The white line represents the trajectory (r,(t), py*(t)) of the system in the phase diagram, from t= 0 to the moment of the first transition (point 1, Fig. 2a), in the same numerical simulation where z(t) in Fig. 2a was simulated. The system was in the low active phase until the trajectory crossed the left spinodal, resulting in a global recovery event. Analogously, when the system is in the high active state the right spinodal becomes relevant (points 2 and 4). Transitions between the macroscopic states are essentially first-passage processes on interchangeable spinodals. d, For the same parameters as in a-e¢, expected lifetime of the system in a certain state measured in simulations increases exponentially with the system size N, confirming our theoretical results. Black lines represent linear regressions in the (N, InT) diagram.
Figure 2 | Two network modes characterized by high and low network activity. a, Dynamical switching (flipping) of the fraction of active nodes z, between two collective modes in the subcritical region, an example for p* = 0.28, r= 0.80 (point A, in yellow, Fig. 1b), with k=10,m=4 and N=100. Green circles mark avoided transitions. b, The PDF of z shows a bimodal form. ¢, The white line represents the trajectory (r,(t), py*(t)) of the system in the phase diagram, from t= 0 to the moment of the first transition (point 1, Fig. 2a), in the same numerical simulation where z(t) in Fig. 2a was simulated. The system was in the low active phase until the trajectory crossed the left spinodal, resulting in a global recovery event. Analogously, when the system is in the high active state the right spinodal becomes relevant (points 2 and 4). Transitions between the macroscopic states are essentially first-passage processes on interchangeable spinodals. d, For the same parameters as in a-e¢, expected lifetime of the system in a certain state measured in simulations increases exponentially with the system size N, confirming our theoretical results. Black lines represent linear regressions in the (N, InT) diagram.
Figure 3 | Properties of phase-flipping phenomenon in financial data for developing and developed markets. a, For the constituents of the Indian index (BSE200), the fraction of stocks z with positive return as a function of time switches back and forth between the two network modes characterized by high and low network activity. b, Bimodal form in the PDF of financial data during the past decade. ¢, The same as in a but for the S&P500 financial index. d, Bimodal form in the PDF of the S&P500 financial data.
Figure 3 | Properties of phase-flipping phenomenon in financial data for developing and developed markets. a, For the constituents of the Indian index (BSE200), the fraction of stocks z with positive return as a function of time switches back and forth between the two network modes characterized by high and low network activity. b, Bimodal form in the PDF of financial data during the past decade. ¢, The same as in a but for the S&P500 financial index. d, Bimodal form in the PDF of the S&P500 financial data.

Related papers

Critical Cascading Failures in Interdependent Networks: Non Mean-Field Behavior." arXiv preprint
Amir Bashan

In a system of interdependent networks, an initial failure of nodes invokes a cascade of iterative failures that may lead to a total collapse of the whole system in a form of an abrupt first order transition. When the fraction of initial failed nodes 1 − p reaches criticality, p = p c , the abrupt collapse occurs by spontaneous cascading failures. At this stage, the giant component decreases slowly in a plateau form and the number of iterations in the cascade, τ, diverges. The origin of this plateau and its increasing with the size of the system remained unclear. Here we find that simultaneously with the abrupt first order transition a spontaneous second order percolation occurs during the cascade of iterative failures. This sheds light on the origin of the plateau and on how its length scales with the size of the system. Understanding the critical nature of the dynamical process of cascading failures may be useful for designing strategies for preventing and mitigating catastrophic collapses.

View PDFchevron_right
Multiple Tipping Points and Optimal Repairing in Interacting Networks
Lidia Braunstein

Systems that comprise many interacting dynamical networks, such as the human body with its biological networks or the global economic network consisting of regional clusters, often exhibit complicated collective dynamics. To understand the collective behavior of such systems, we investigate a model of interacting networks exhibiting the fundamental processes of failure, damage spread, and recovery. We find a very rich phase diagram that becomes exponentially more complex as the number of networks is increased. In the simplest example of n = 2 interacting networks we find two critical points, 4 triple points, 10 allowed transitions, and two "forbidden" transitions, as well as complex hysteresis loops. Remarkably, we find that triple points play the dominant role in constructing the optimal repairing strategy in damaged interacting systems. To support our model, we analyze an example of real interacting financial networks and find evidence of rapid dynamical transitions between well-defined states, in agreement with the predictions of our model.

View PDFchevron_right
Recovery patterns and physics of the network
Nazanin Tajik

PLOS ONE, 2021

In a progressively interconnected world, the loss of system resilience has consequences for human health, the economy, and the environment. Research has exploited the science of networks to explain the resilience of complex systems against random attacks, malicious attacks, and the localized attacks induced by natural disasters or mass attacks. Little is known about the elucidation of system recovery by the network topology. This study adds to the knowledge of network resilience by examining the nexus of recoverability and network topology. We establish a new paradigm for identifying the recovery behavior of networks and introduce the recoverability measure. Results indicate that the recovery response behavior and the recoverability measure are the function of both size and topology of networks. In small sized networks, the return to recovery exhibits homogeneous recovery behavior over topology, while the return shape is dispersed with an increase in the size of network. A network b...

View PDFchevron_right
System crash as dynamics of complex networks
Gaoxi Xiao

Proceedings of the National Academy of Sciences of the United States of America, 2016

Complex systems, from animal herds to human nations, sometimes crash drastically. Although the growth and evolution of systems have been extensively studied, our understanding of how systems crash is still limited. It remains rather puzzling why some systems, appearing to be doomed to fail, manage to survive for a long time whereas some other systems, which seem to be too big or too strong to fail, crash rapidly. In this contribution, we propose a network-based system dynamics model, where individual actions based on the local information accessible in their respective system structures may lead to the "peculiar" dynamics of system crash mentioned above. Extensive simulations are carried out on synthetic and real-life networks, which further reveal the interesting system evolution leading to the final crash. Applications and possible extensions of the proposed model are discussed.

View PDFchevron_right
Cascading failures in complex networks
Cristian La Rocca

Journal of Complex Networks, 2020

Cascading failure is a potentially devastating process that spreads on real-world complex networks and can impact the integrity of wide-ranging infrastructures, natural systems and societal cohesiveness. One of the essential features that create complex network vulnerability to failure propagation is the dependency among their components, exposing entire systems to significant risks from destabilizing hazards such as human attacks, natural disasters or internal breakdowns. Developing realistic models for cascading failures as well as strategies to halt and mitigate the failure propagation can point to new approaches to restoring and strengthening real-world networks. In this review, we summarize recent progress on models developed based on physics and complex network science to understand the mechanisms, dynamics and overall impact of cascading failures. We present models for cascading failures in single networks and interdependent networks and explain how different dynamic propagat...

View PDFchevron_right
Damage Spreading and Criticality in Finite Random Dynamical Networks
Natali Gulbahce

Physical Review Letters, 2007

View PDFchevron_right
Fragility and anomalous susceptibility of weakly interacting networks
Giulio Cimini

Percolation is a fundamental concept that brought new understanding on the robustness properties of complex systems. Here we consider percolation on weakly interacting networks, that is, network layers coupled together by much less interlinks than the connections within each layer. For these kinds of structures, both continuous and abrupt phase transition are observed in the size of the giant component. The continuous (second-order) transition corresponds to the formation of a giant cluster inside one layer, and has a well defined percolation threshold. The abrupt transition instead corresponds to the merger of coexisting giant clusters among different layers, and is characterised by a remarkable uncertainty in the percolation threshold, which in turns causes an anomalous trend in the observed susceptibility. We develop a simple mathematical model able to describe this phenomenon and to estimate the critical threshold for which the abrupt transition is more likely to occur. Remarkably, finite-size scaling analysis in the abrupt region supports the hypothesis of a genuine first-order phase transition.

View PDFchevron_right
Multiple phase transitions in networks of directed networks
Jianxi Gao

Physical Review E

The robustness in real-world complex systems with dependency connectivities differs from that in isolated networks. Although most complex network research has focused on interdependent undirected systems, many real-world networks-such as gene regulatory networks and traffic networksare directed. We thus develop an analytical framework for examining the robustness of networks made up of directed networks of differing topologies. We use it to predict the phase transitions that occur during node failures and to generate the phase diagrams of a number of different systems, including tree-like and random regular (RR) networks of directed Erdős-Rényi (ER) networks and scale-free (SF) networks. We find that the the phase transition and phase diagram of networks of directed networks differ from those of networks of undirected networks. For example, the RR networks of directed ER networks show a hybrid phase transition that does not occur in networks of undirected ER networks. In addition, system robustness is affected by network topology in networks of directed networks. As coupling strength q increases, tree-like networks of directed ER networks change from a second-order phase transition to a first-order phase transition, and RR networks of directed ER networks change from a second-order phase transition to a hybrid phase transition, then to a first-order phase transition, and finally to a region of collapse. We also find that heterogenous network systems are more robust than homogeneous network systems. We note that there are multiple phase transitions and triple points in the phase diagram of RR networks of directed networks, and this helps us understand how to increase network robustness when designing interdependent infrastructure systems.

View PDFchevron_right
ARTICLE Multiple tipping points and optimal repairing in interacting networks
Irena Vodenska

2020

Systems composed of many interacting dynamical networks-such as the human body with its biological networks or the global economic network consisting of regional clusters-often exhibit complicated collective dynamics. Three fundamental processes that are typically present are failure, damage spread and recovery. Here we develop a model for such systems and find a very rich phase diagram that becomes increasingly more complex as the number of interacting networks increases. In the simplest example of two interacting networks we find two critical points, four triple points, ten allowed transitions and two 'forbidden' transitions, as well as complex hysteresis loops. Remarkably, we find that triple points play the dominant role in constructing the optimal repairing strategy in damaged interacting systems. To test our model, we analyse an example of real interacting financial networks and find evidence of rapid dynamical transitions between well-defined states, in agreement wi...

View PDFchevron_right
Resilience of Complex Networks to Random Breakdown
Eugene Stanley

Using Monte Carlo simulations we calculate f c , the fraction of nodes that are randomly removed before global connectivity is lost, for networks with scale-free and bimodal degree distributions. Our results differ from the results predicted by an equation for f c proposed by Cohen et al. We discuss the reasons for this disagreement and clarify the domain for which the proposed equation is valid.

View PDFchevron_right

References (31)

  1. Watts, D. J. & Strogatz, S. H. Collective dynamics of 'small-world' networks. Nature 393, 440-442 (1998).
  2. Faloutsos, M., Faloutsos, P. & Faloutsos, C. On power-law relationships of the Internet topology. Comput. Commun. Rev. 29, 251-262 (1999).
  3. Barabási, A-L. & Albert, R. Emergence of scaling in random networks. Science 286, 509-512 (1999).
  4. Adamic, L. & Huberman, B. A. Internet: Growth dynamics of the world-wide web. Nature 401, 131-131 (1999).
  5. Krapivsky, P. L., Redner, S. & Leyraz, F. Connectivity of growing random networks. Phys. Rev. Lett. 85, 4629-4632 (2000).
  6. Milo, R. et al. Network motifs: Simple building blocks of complex networks. Science 298, 824-827 (2002).
  7. Newman, M. E. J. Networks: An Introduction (Oxford Univ. Press, 2010).
  8. Newman, M. E. J. The structure and function of complex networks. SIAM Rev. 45, 167-256 (2003).
  9. Garlaschelli, D., Caldarelli, G. & Pietronero, L. Universal scaling relations in food webs. Nature 423, 165-168 (2003).
  10. Albert, R. & Barabási, A-L. Statistical mechanics of complex networks. Rev. Mod. Phys. 74, 47-97 (2002).
  11. NATURE PHYSICS | VOL 10 | JANUARY 2014 | www.nature.com/naturephysics
  12. Albert, R., Jeong, H. & Barabási, A. L. Error and attack tolerance of complex networks. Nature 406, 378-382 (2000).
  13. Schneider, C. M., Moreira, A. A., Andrade, J. S. Jr, Havlin, S. & Herrmann, H. J. Mitigation of malicious attacks on networks. Proc. Natl Acad. Sci. USA 108, 3838-3841 (2011).
  14. Cohen, R., Erez, K., Ben-Avraham, D. & Havlin, S. Resilience of the Internet to random breakdowns. Phys. Rev. Lett. 85, 4626-4628 (2000).
  15. Buldyrev, S. V. et al. Catastrophic cascade of failures in interdependent networks. Nature 464, 1025-1028 (2010).
  16. Gao, J., Buldyrev, S. V., Havlin, S. & Stanley, H. E. Robustness of a network of networks. Phys. Rev. Lett. 107, 195701 (2011).
  17. Parshani, R., Buldyrev, S. V. & Havlin, S. Critical effect of dependency groups on the function of networks. Proc. Natl Acad. Sci. USA 108, 1007-1010 (2011).
  18. Gao, J., Buldyrev, S. V., Stanley, H. E. & Havlin, S. Networks formed from interdependent networks. Nature Phys. 8, 40-48 (2012).
  19. Vespignani, A. Modeling dynamical processes in complex socio-technical systems. Nature Phys. 8, 32-39 (2012).
  20. Schlapfer, M. & Shapiro, J. L. in Complex Sciences: Proc. First Int. Conf. (ed. Zhou, J.) 2127-2138 (Springer, 2009).
  21. Watts, D. J. A simple model of global cascades on random networks. Proc. Natl Acad. Sci. USA 99, 5766-5771 (2002).
  22. Gleeson, J. P. & Cahalane, D. J. Noise and Stochastics in Complex Systems and Finance 66010W (Proc. SPIE, Vol. 6601, 2007).
  23. Erdős, P. & Renyi, A. On random graphs. I. Publ. Math. 6, 290-297 (1959).
  24. Dorogovtsev, S. N. & Goltsev, A. V. Critical phenomena in complex networks. Rev. Mod. Phys. 80, 1275-1335 (2008).
  25. Bak, P., Chen, K. & Tang, C. A forest-fire model and some thoughts on turbulence. Phys. Lett. A 147, 297-300 (1990).
  26. Drossel, B. & Schwabl, F. Forest-fire model with immune trees. Physica A 199, 183-197 (1993).
  27. Ding, F. et al. Direct molecular dynamics observation of protein folding transition state ensemble. Biophys. J. 83, 3525-3532 (2002).
  28. Kesselring, T. A. et al. Finite-size scaling investigation of the liquid-liquid critical point in ST2 water and its stability with respect to crystallization. J. Chem. Phys. 138, 244506 (2013).
  29. Kenett, D. Y. et al. Index cohesive force analysis reveals that the US market became prone to systemic collapses since 2002. PLoS ONE 6, e19378 (2011).
  30. Barunik, J. & Vosvrda, M. Can a stochastic cusp catastrophe model explain stock market crashes? J. Econ. Dynam. Control 33, 1824-1836 (2009).
  31. Blanchard, O. J. & Summers, L. H. Hysteresis and the European unemployment problem. NBER Macroecon. Annu. 1, 15-90 (1986).

Related papers

Transient disorder in dynamically growing networks
Rui Yang

2009

The occurrence of a temporally disordered state before a more ordered state is reached is a common phenomenon in nonlinear dynamical systems. In the case of transient chaos, for example, starting from a random initial condition a trajectory typically exhibits chaotic behavior for a finite amount of time before settling into a regular asymptotic state such as a periodic attractor 1. Such behaviors occur in many physical, chemical, and biological systems 2.

View PDFchevron_right
Abrupt transition in the structural formation of interconnected networks
alex arenas

Nature Physics, 2013

Our world is linked by a complex mesh of networks through which information, people and goods flow. These networks are interdependent on each other, and present structural and dynamical features 1-6 different from those observed in isolated networks . Although examples of such dissimilar properties are becoming more abundant-such as in diffusion, robustness and competition-it is not yet clear where these differences are rooted. Here we show that the process of building independent networks into an interconnected network of networks undergoes a structurally sharp transition as the interconnections are formed. Depending on the relative importance of inter-and intra-layer connections, we find that the entire interdependent system can be tuned between two regimes: in one regime, the various layers are structurally decoupled and they act as independent entities; in the other regime, network layers are indistinguishable and the whole system behaves as a singlelevel network. We analytically show that the transition between the two regimes is discontinuous even for finite-size networks. Thus, any real-world interconnected system is potentially at risk of abrupt changes in its structure, which may manifest new dynamical properties. Interacting, interdependent or multiplex networks are different ways of naming the same class of complex systems where networks are not considered as isolated entities but interacting with each other. In multiplex, the nodes at each network are instances of the same entity; thus, the networks are representing simply different categorical relationships between entities, and usually categories are represented by layers. Interdependent networks is a more general framework where nodes can be different at each network. Many, if not all, real networks are coupled with other real networks. Examples can be found in several domains: social networks (for example, Facebook, Twitter and so on) are coupled because they share the same actors 10 ; multimodal transportation networks are composed of different layers (for example, bus, subway and so on) that share the same locations 11 ; the functioning of communication and power grid systems depends one on the other 1 . So far, all phenomena that have been studied on interdependent networks, including percolation 1,3 , epidemics 4 and linear dynamical systems 5 , have provided results that differ much from those valid in the case of isolated complex networks. Sometimes the difference is radical: for example, whereas isolated scale-free networks are robust against failures of their nodes or edges 12 , scale-free interdependent networks are instead very fragile 1,3 . Given such observations, two fundamentally important theoretical questions are in order: Why do dynamical and critical phenomena running on interdependent network models differ

View PDFchevron_right
Inherently unstable networks collapse to a critical point
Gijsje Koenderink

Physical Review E, 2015

Nonequilibrium systems that are driven or drive themselves towards a critical point have been studied for almost three decades. Here we present a minimalist example of such a system, motivated by experiments on collapsing active elastic networks. Our model of an unstable elastic network exhibits a collapse towards a critical point from any macroscopically connected initial configuration. Taking into account steric interactions within the network, the model qualitatively and quantitatively reproduces results of the experiments on collapsing active gels.

View PDFchevron_right
Self-Organized-Critical network dynamics
Ginestra Bianconi

AIP Conference Proceedings, 2005

We propose a simple model that aims at describing, in a stylized manner, how local breakdowns due to imbalances or congestion propagate in real dynamical networks. The model converges to a self-organized critical stationary state in which the network shapes itself as a consequence of avalanches of rewiring processes. Depending on the model's specification, we obtain either single-scale or scale-free networks. We characterize in detail the relation between the statistical properties of the network and the nature of the critical state, by computing the critical exponents. The model also displays a nontrivial, sudden collapse to a complete network.

View PDFchevron_right
Oscillations of complex networks
Choy Heng Lai

Physical Review E, 2006

A complex network processing information or physical flows is usually characterized by a number of macroscopic quantities such as the diameter and the betweenness centrality. An issue of significant theoretical and practical interest is how such a network responds to sudden changes caused by attacks or disturbances. By introducing a model to address this issue, we find that, for a finite-capacity network, perturbations can cause the network to oscillate persistently in the sense that the characterizing quantities vary periodically or randomly with time. We provide a theoretical estimate of the critical capacity-parameter value for the onset of the network oscillation. The finding is expected to have broad implications as it suggests that complex networks may be structurally highly dynamic.

View PDFchevron_right

Cited by

Validation of Network Communicability Metrics for the Analysis of Brain Structural Networks
Eugenio Abela

PLoS ONE, 2014

Computational network analysis provides new methods to analyze the brain's structural organization based on diffusion imaging tractography data. Networks are characterized by global and local metrics that have recently given promising insights into diagnosis and the further understanding of psychiatric and neurologic disorders. Most of these metrics are based on the idea that information in a network flows along the shortest paths. In contrast to this notion, communicability is a broader measure of connectivity which assumes that information could flow along all possible paths between two nodes. In our work, the features of network metrics related to communicability were explored for the first time in the healthy structural brain network. In addition, the sensitivity of such metrics was analysed using simulated lesions to specific nodes and network connections. Results showed advantages of communicability over conventional metrics in detecting densely connected nodes as well as subsets of nodes vulnerable to lesions. In addition, communicability centrality was shown to be widely affected by the lesions and the changes were negatively correlated with the distance from lesion site. In summary, our analysis suggests that communicability metrics that may provide an insight into the integrative properties of the structural brain network and that these metrics may be useful for the analysis of brain networks in the presence of lesions. Nevertheless, the interpretation of communicability is not straightforward; hence these metrics should be used as a supplement to the more standard connectivity network metrics.

View PDFchevron_right
Temporal condensation and dynamic λ-transition within the complex network: an application to real-life market evolution
Zbigniew Struzik

The European Physical Journal B, 2015

We fill a void in merging empirical and phenomenological characterisation of the dynamical phase transitions in complex networks by identifying and thoroughly characterising a triple sequence of such transitions on a real-life financial market. We extract and interpret the empirical, numerical, and analytical evidences for the existence of these dynamical phase transitions, by considering the medium size Frankfurt stock exchange (FSE), as a typical example of a financial market. By using the canonical object for the graph theory, i.e. the minimal spanning tree (MST) network, we observe: (i) the (initial) dynamical phase transition from equilibrium to non-equilibrium nucleation phase of the MST network, occurring at some critical time. Coalescence of edges on the FSE's transient leader (defined by its largest degree) is observed within the nucleation phase; (ii) subsequent acceleration of the process of nucleation and the emergence of the condensation phase (the second dynamical phase transition), forming a logarithmically diverging temporal λ-peak of the leader's degree at the second critical time; (iii) the third dynamical fragmentation phase transition (after passing the second critical time), where the λ-peak logarithmically relaxes over three quarters of the year, resulting in a few loosely connected sub-graphs. This λ-peak (comparable to that of the specific heat vs. temperature forming during the equilibrium continuous phase transition from the normal fluid I 4 He to the superfluid II 4 He) is considered as a prominent result of a non-equilibrium superstar-like superhub or a dragon-king's abrupt evolution over about two and a half year of market evolution. We capture and meticulously characterise a remarkable phenomenon in which a peripheral company becomes progressively promoted to become the dragon-king strongly dominating the complex network over an exceptionally long period of time containing the crash. Detailed analysis of the complete trio of the dynamical phase transitions constituting the λ-peak allows us to derive a generic nonlinear constitutive equation of the dragon-king dynamics describing the complexity of the MST network by the corresponding inherent nonlinearity of the underlying dynamical processes.

View PDFchevron_right
Operational resilience: concepts, design and analysis
Rami Mangoubi

Scientific Reports, 2016

Building resilience into today's complex infrastructures is critical to the daily functioning of society and its ability to withstand and recover from natural disasters, epidemics, and cyber-threats. This study proposes quantitative measures that implement the definition of engineering resilience advanced by the National Academy of Sciences. The approach is applicable across physical, information, and social domains. It evaluates the critical functionality, defined as a performance function of time set by the stakeholders. Critical functionality is a source of valuable information, such as the integrated system resilience over a time interval, and its robustness. The paper demonstrates the formulation on two classes of models: 1) multi-level directed acyclic graphs, and 2) interdependent coupled networks. For both models synthetic case studies are used to explore trends. For the first class, the approach is also applied to the Linux operating system. Results indicate that desired resilience and robustness levels are achievable by trading off different design parameters, such as redundancy, node recovery time, and backup supply available. The nonlinear relationship between network parameters and resilience levels confirms the utility of the proposed approach, which is of benefit to analysts and designers of complex systems and networks.

View PDFchevron_right
Explosive synchronization coexists with classical synchronization in the Kuramoto model
Olga Moskalenko

Chaos: An Interdisciplinary Journal of Nonlinear Science, 2016

Explosive synchronization has recently been reported in a system of adaptively coupled Kuramoto oscillators, without any conditions on the frequency or degree of the nodes. Here, we find that, in fact, the explosive phase coexists with the standard phase of the Kuramoto oscillators. We determine this by extending the mean-field theory of adaptively coupled oscillators with full coupling to the case with partial coupling of a fraction f. This analysis shows that a metastable region exists for all finite values of f > 0, and therefore explosive synchronization is expected for any perturbation of adaptively coupling added to the standard Kuramoto model. We verify this theory with GPU-accelerated simulations on very large networks (N $ 10 6 ) and find that, in fact, an explosive transition with hysteresis is observed for all finite couplings. By demonstrating that explosive transitions coexist with standard transitions in the limit of f ! 0, we show that this behavior is far more likely to occur naturally than was previously believed. Published by AIP Publishing.

View PDFchevron_right
Behavioral incentives in a vaccination-dilemma setting with optional treatment
K M Ariful Kabir

Physical Review E

Social dilemmas are situations wherein individuals choose between selfish interest and common good. One example of this is the vaccination dilemma, in which an individual who vaccinates at a cost protects not only himself but also others by helping maintain a common good called herd immunity. There is, however, a strong incentive to forgo vaccination, thus avoiding the associated cost, all the while enjoying the protection of herd immunity. To analyze behavioral incentives in a vaccination-dilemma setting in which an optional treatment is available to infected individuals, we combined epidemiological and game-theoretic methodologies by coupling a disease-spreading model with treatment and an evolutionary decision-making model. Extensive numerical simulations show that vaccine characteristics are more important in controlling the treatment adoption than the cost of treatment itself. The main effect of the latter is that expensive treatment incentivizes vaccination, which somewhat surprisingly comes at a little cost to society. More surprising is that the margin for a true synergy between vaccine and treatment in reducing the final epidemic size is very small. We furthermore find that society-centered decision making helps protect herd immunity relative to individual-centered decision making, but the latter may be better in establishing a novel vaccine. These results point to useful policy recommendations as well as to intriguing future research directions.

View PDFchevron_right
580 California St., Suite 400
San Francisco, CA, 94104
© 2025 Academia. All rights reserved