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.

Network Frontier Workshop 2015 - December 6-7, 2015

Ad for NFW 2015

The Network Frontier Workshop 2015 is a two-day event highlighting leading-edge research on complex networks. Presentations will emphasize physical principles underlying network control, collective behavior in networks of dynamical systems, and network problems in biological, ecological, social, and physical systems. The Workshop will be held at Northwestern University December 6-7, 2015. Seating is limited and registration is required.

MBI Workshop: Control and Observability of Network Dynamics

April 11-15, 2016 - Mathematical Biosciences Institute, The Ohio State University

Control and dynamical systems go hand in hand in biology. Dynamic networks and processes that occur on them can be used to describe many biological processes. Understanding the emergent properties of these systems, how they are influenced, and how one might influence them lends itself to ideas of mathematical control theory.

Despite many challenges, there has been significant progress on the modeling of network control mechanisms, as well as on the development of mathematical and computational control approaches in fields such as dynamical systems, network science, and life sciences. This workshop will stimulate progress by promoting interactions between experts working in these disparate fields, thereby facilitating the combination of approaches from different domains and the integration of system-specific knowledge about biological or bio-inspired networks.

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

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.


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,
Chaos 25, 097621 (2015).
doi: 10.1063/1.4931570

P. Gawand, F.S. Abukar, N. Venayak, S. Partow, A.E. Motter, and R. Mahadevan,
Sub-optimal phenotypes of double-knockout mutants of Escherichia coli depend on the order of gene deletions,
Integr. Biol., Advance Article (2015).

J. Sun, S.P. Cornelius, J. Janssen, K.A. Gray, and A.E. Motter,
Regularity underlies erratic population abundances in marine ecosystems,
J. R. Soc. Interface 12, 20150235 (2015).
arXiv:1505.03521 - doi:10.1098/rsif.2015.0235 - Supplementary Material

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

Adilson E. Motter

Motter photo

Photo by Eileen Molony

Professor Motter's research is focused on the dynamical behavior and control of complex systems and networks.


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 Z. Tytenicz to send your CV or to request more information.

Network Control

New Image

See the talk Advances on the Control of Nonlinear Network Dynamics by Adilson E. Motter at the 2015 SIAM Conference on Applications of Dynamical Systems and check out our featured control projects page to see a summary of our recent work in this area.

Group News

June 2015: Xiaowen Chen receives the Prize for Distinguished Honors Thesis for her senior thesis entitled "Fractal Geometry of Undriven Dissipative Systems".

March 2015: Adilson E. Motter is awarded a 2015 Simons Fellowship in Theoretical Physics.

The Best Writing on Mathematics cover

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.

Que Pasa cover

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

Selected Press

Network Control: Letting Noise Lead the Way
Science Daily (September 17, 2015)

The Answer Is the Network. What Is the Question?
Northwestern University Office of Research Annual Report 2014 (February 19, 2015)
http://... 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)

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