New Approach can Control Large, Nonlinear Complex Networks

Nonlinearity is a hallmark of complex systems, but has generally been regarded as an obstacle to controlling their behavior. Our new Nature Communications paper shows how nonlinear dynamics can be harnessed to control a network and drive it to desired states. Network Image The new approach can be used to identify control interventions in a range of large complex networks, from cells to power grids. In a related publication in Nature's Protocol Exchange we present in detail our core algorithm for the control of complex networks and other nonlinear, high-dimensional dynamical systems. The algorithm is highly scalable, with the computational cost scaling as the number of dynamical variables to the power 2.5. This protocol includes ready-to-use software that can be applied to identify eligible control interventions in a general system described by coupled ordinary differential equations, whose specific form can be specified by the user.

  • Movie: Animated step-by-step construction of control interventions in simple examples.

Energy, Cities, and the Control of Complex Systems

Erice photo, by Norbert Nagel / Wikimedia Commons

The Energy, Cities, and the Control of Complex Systems Workshop was held in the Ettore Majorana Foundation and Centre for Scientific Culture in Erice, from Monday May 12th to Wednesday May 14th, 2014.

The objective of this Workshop was to explore the applications of complex network theory to infrastructure and social systems, especially as applied to cities and energy, and to identify limitations and priorities for research. The Session was co-chaired by Prof. Adilson E. Motter of Northwestern University and Dr. Robert Schock, former Director of Studies at the World Energy Council and Senior Fellow in the Center for Global Security Research.

Synchronization and Observability in Power-Grid Networks

Power Grid Image

A key requirement for the functioning of a power-grid network is that its power generators remain synchronized. In our recent Nature Physics paper, we derive a condition under which the desired synchronous state of a power grid is stable, and use this condition to identify tunable parameters of the generators that can affect synchronization. A complementary problem concerns the comprehensive determination of the state of the system from limited measurements. In our most recent PRL paper, we show that this problem leads to a new type of percolation transition — a network observability transition. We also demonstrate a dual role of the network's community structure, which both facilitates optimal measurement placement and renders the networks substantially more sensitive to "observability attacks." These findings may be used to optimize stability and robustness and help devise new control schemes, contributing to the development of smart, self-healing power grids.

P&A Complex Systems Seminars

Seminars are held on the last Thursday of each month at 2:00 PM in Tech F160, unless otherwise noted.


Watch members of the Motter group explain complex systems research to general audiences.

Rosangela Follmann video

Rosangela Follmann
Unveiling Mysteries of Synchronization

Joo Sang Lee video

Joo Sang Lee
Sunja's Two Dreams

Yang Yang video

Yang Yang
Say No to Blackouts

Adilson Motter video

Adilson E. Motter
in What is Entropy?
by The Good Stuff


Mechanical Networks and Negative Compressibility Materials

Illustration of negative compressibility cube

When tensioned, ordinary materials expand along the direction of the applied force. In our recent Nature Materials paper, we explore network concepts to design metamaterials exhibiting negative compressibility transitions, during which a material undergoes contraction when tensioned (or expansion when pressured). Continuous contraction of a material in the same direction of an applied tension is inherently unstable. The conceptually similar effect we demonstrate can be achieved, however, through destabilizations of (meta)stable equilibria of the constituents. These destabilizations give rise to a stress-induced solid-solid phase transition associated with a twisted hysteresis curve for the stress-strain relationship. We suggest that the proposed materials could be useful for the design of actuators, force amplifiers, micromechanical controls, and protective devices.

  • Movie: Simulated response of the material to uniform, diagonal, pinched, and splayed stress profiles.

Recent Publications

A.E. Motter, M. Gruiz, G. Károlyi, and T. Tél,
Doubly transient chaos: Generic form of chaos in autonomous dissipative systems,
Phys. Rev. Lett. 111, 194101 (2013).
arXiv:1310.4209 - doi:10.1103/PhysRevLett.111.194101 - Synopsis

S.P. Cornelius, W.L. Kath, and A.E. Motter,
Realistic control of network dynamics,
Nature Communications 4, 1942 (2013).
arXiv:1307.0015v1 - doi:10.1038/ncomms2939 - PDF - Supplementary Information - Movie
Nontechnical Overview Article

S.P. Cornelius and A.E. Motter,
NECO - A scalable algorithm for NEtwork COntrol,
Protocol Exchange (2013), doi:10.1038/protex.2013.063.
arXiv:1307.2582 - doi:10.1038/protex.2013.063 - Source Codes

J. Sun and A.E. Motter,
Controllability transition and nonlocality in network control,
Phys. Rev. Lett. 110, 208701 (2013).
arXiv:1305.5848 - doi:10.1103/PhysRevLett.110.208701

A.E. Motter, S.A. Myers, M. Anghel, and T. Nishikawa,
Spontaneous synchrony in power-grid networks,
Nature Physics 9, 191 (2013).
arXiv:1302.1914 - doi:10.1038/nphys2535 - Supplementary Information

Y. Yang, J. Wang, and A. E. Motter,
Network observability transitions,
Phys. Rev. Lett. 109, 258701 (2012).
arXiv:1301.5916 - doi:10.1103/PhysRevLett.109.258701 - Supplementary Information

Z.G. Nicolaou and A.E. Motter,
Mechanical metamaterials with negative compressibility transitions,
Nature Materials 11, 608 (2012).
arXiv:1207.2185 - doi:10.1038/nmat3331 - Supplementary Information - Movie
Nontechnical Overview Article

S.P. Cornelius, J.S. Lee, and A.E. Motter,
Dispensability of Escherichia coli's latent pathways,
Proc. Natl. Acad. Sci. USA 108, 3124 (2011).
arXiv:1103.5176v1 - doi:10.1073/pnas.1009772108 - Supplementary Information

B. Ravoori, A.B. Cohen, J. Sun, A.E. Motter, T.E. Murphy, and R. Roy,
Robustness of optimal synchronization in real networks,
Phys. Rev. Lett. 107, 034102 (2011).
arXiv:1106.3994v1 - doi:10.1103/PhysRevLett.107.034102 - Supplementary Information

S. Sahasrabudhe and A.E. Motter,
Rescuing ecosystems from extinction cascades through compensatory perturbations,
Nature Communications 2, 170 (2011).
arXiv:1103.1653v1 - doi:10.1038/ncomms1163 - PDF - Supplementary Information

Positions Available

New Image

Prof. Motter has an opening for a Postdoctoral Researcher in a project focused on the use of network dynamics concepts to design novel materials with unprecedented properties. Candidates seeking positions in other areas of complex networks may also be considered. The application deadline is October 15, 2014.

Network Control

New Image

Featured projects on the control of complex systems and networks.

Group News

May 2014: Sean Cornelius is awarded the 2014 SIAM Student Paper Prize for the paper Realistic Control of Network Dynamics.

Que Pasa cover

May 2014: Adilson E. Motter is featured among the 30 promising scientists under the age of 40 born in Latin America.

November 2013: Motter and Campbell's article Chaos at Fifty is translated into French by Pour la Science.

September 2013: Adilson E. Motter is elected APS Fellow.

August 2013: Joo Sang Lee receives Baxter Young Investigator Award.

June 2013: Adilson E. Motter is awarded the Erdös-Rényi Prize in Network Science.

March 2013: Sascha Herrmann is awarded NSF Graduate Research Fellowship.

Selected Press

New Scientist cover

When not to Tackle Problems Head-on
New Scientist (January 18, 2014) - cover story
http://..Preview http://..Full Article

Chaos Reigns in Unexpected Places
Physics World (November 20, 2013)

Upgrading the US Grid - Building a Smart Self-Healing Grid
Power Technology (September 23, 2013)

Tiny Trouble Spots can Fix Complex Networks
Futurity (July 9, 2013)

How Network Monitoring Could be Like Fishing
Slashdot (June 28, 2013)

Keeping Networks Under Control
NU Press Release (June 27, 2013)

Stabilizing the Electric Grid by
Keeping Generators in Sync
Ars Technica (March 13, 2013)

Mystifying Materials
NU Press Release (May 23, 2012)

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