Controlling extreme events on complex networks

Extreme events, a type of collective behavior in complex networked dynamical systems, often can have catastrophic consequences. To develop effective strategies to control extreme events is of fundamental importance and practical interest. Utilizing transportation dynamics on complex networks as a prototypical setting, we find that making the network “mobile” can effectively suppress extreme events. A striking, resonance-like phenomenon is uncovered, where an optimal degree of mobility exists for which the probability of extreme events is minimized. We derive an analytic theory to understand the mechanism of control at a detailed and quantitative level, and validate the theory numerically. Implications of our finding to current areas such as cybersecurity are discussed.

[1]  Satya N Majumdar,et al.  Density of near-extreme events. , 2007, Physical review letters.

[2]  Bo Hu,et al.  General dynamics of topology and traffic on weighted technological networks. , 2005, Physical review letters.

[3]  Beom Jun Kim,et al.  Vertex overload breakdown in evolving networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  Ying-Cheng Lai,et al.  Emergence and scaling of synchronization in moving-agent networks with restrictive interactions. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  Yamir Moreno,et al.  Dynamics of jamming transitions in complex networks , 2005 .

[6]  Donal O'Mahony,et al.  Secure routing for mobile ad hoc networks , 2005, IEEE Communications Surveys & Tutorials.

[7]  Heiko Rieger,et al.  Random walks on complex networks. , 2004, Physical review letters.

[8]  M. A. de Menezes,et al.  Fluctuations in network dynamics. , 2004, Physical review letters.

[9]  Zhiyong Wu,et al.  Enhancing Transport Efficiency by Hybrid Routing Strategy , 2012, 1204.3277.

[10]  K. Górska,et al.  Exact and explicit probability densities for one-sided Lévy stable distributions. , 2010, Physical review letters.

[11]  G. J. Rodgers,et al.  Preferential behaviour and scaling in diffusive dynamics on networks , 2007, cond-mat/0701785.

[12]  Yih-Chun Hu,et al.  Packet leashes: a defense against wormhole attacks in wireless networks , 2003, IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428).

[13]  Wen-Xu Wang,et al.  Transportation dynamics on networks of mobile agents , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  R. E. Amritkar,et al.  Extreme events on complex networks , 2011, Physical review letters.

[15]  Panagiotis Papadimitratos,et al.  Secure message transmission in mobile ad hoc networks , 2003, Ad Hoc Networks.

[16]  G. Zaslavsky,et al.  Lévy Flights and Related Topics in Physics , 2013 .

[17]  K. Goh,et al.  Universal behavior of load distribution in scale-free networks. , 2001, Physical review letters.

[18]  Ying-Cheng Lai,et al.  Universality of flux-fluctuation law in complex dynamical systems. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  Yamir Moreno,et al.  Improved routing strategies for Internet traffic delivery. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  R. E. Amritkar,et al.  Extreme events and event size fluctuations in biased random walks on networks. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  J. Gómez-Gardeñes,et al.  Scaling breakdown in flow fluctuations on complex networks. , 2008, Physical review letters.

[22]  J. Kertész,et al.  Random walks on complex networks with inhomogeneous impact. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  Alan M. Frieze,et al.  Random graphs , 2006, SODA '06.

[24]  Joseph D Skufca,et al.  Communication and synchronization in, disconnected networks with dynamic topology: moving neighborhood networks. , 2004, Mathematical biosciences and engineering : MBE.

[25]  Alexandre Arenas,et al.  Optimal network topologies for local search with congestion , 2002, Physical review letters.

[26]  Petter Holme.  Edge overload breakdown in evolving networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  O. Bénichou,et al.  Global mean first-passage times of random walks on complex networks. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[28]  Ruben Juanes,et al.  Anomalous physical transport in complex networks. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[29]  M S Santhanam,et al.  Manipulation of extreme events on scale-free networks. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[30]  Sheng Li,et al.  Integrating fluctuations into distribution of resources in transportation networks , 2009, 0906.0844.

[31]  Alex Arenas,et al.  Scaling of fluctuations in traffic on complex networks. , 2006, Physical review letters.

[32]  Jie Gao,et al.  Detecting Wormhole Attacks in Wireless Networks Using Connectivity Information , 2007, IEEE INFOCOM 2007 - 26th IEEE International Conference on Computer Communications.

[33]  Nong Ye,et al.  Onset of traffic congestion in complex networks. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[34]  Sheng-Jun Wang,et al.  Effect of degree correlations on networked traffic dynamics , 2009 .

[35]  Soon-Hyung Yook,et al.  Scaling property of flux fluctuations from random walks. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[36]  Erik M. Bollt,et al.  Sufficient Conditions for Fast Switching Synchronization in Time-Varying Network Topologies , 2006, SIAM J. Appl. Dyn. Syst..