## 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. 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.

## 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.

## Synchronization and Observability in Power-Grid Networks

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.

## Videos

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

## Mechanical Networks and Negative Compressibility Materials

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

T. Nishikawa and A.E. Motter,

Comparative analysis of existing models for power-grid synchronization,

New J. Phys. **17**, 015012 (2015).

arXiv:1501.06926 -
doi:10.1088/1367-2630/17/1/015012

J.-R. Angilella, R.D. Vilela, and A.E. Motter,

Inertial particle trapping in an open vortical flow,

J. Fluid Mech. **744**, 183 (2014).

arXiv:1403.7563 -
doi:10.1017/jfm.2014.38

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

Although we do not have a specific position open at the moment, we are always interested in excellent postdoctoral candidates. Areas of interest in our group include network control, network dynamics, metamaterials, and modeling of biological networks. E-mail Luciana Zanella to send your CV or to request more information.

## Group News

January 2015: **Motter and Campbell**'s article Chaos at Fifty is selected as a chapter of The Best Writing on Mathematics 2014.

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

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.

## Selected Press

The Answer Is the Network. What Is the Question?

Northwestern University Office of Research Annual Report 2014 (February 19, 2015)

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When not to Tackle Problems Head-on

New Scientist (January 18, 2014) - cover story

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http://..Full Article

Chaos Reigns in Unexpected Places

Physics World (November 20, 2013)

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Upgrading the US Grid - Building a Smart Self-Healing Grid

Power Technology (September 23, 2013)

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Tiny Trouble Spots can Fix Complex Networks

Futurity (July 9, 2013)

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How Network Monitoring Could be Like Fishing

Slashdot (June 28, 2013)

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