Drawing on Locality to Control Large Networks

localized The control of large networks is a pressing problem of relevance to numerous natural and engineered systems. In a recent PNAS publication, we show that most complex networks are highly localized, and that exploiting this property dramatically improves our ability to control large-scale systems. It follows that large networks can be controlled with computation and communication costs comparable to those for small ones. An open access copy of the paper is available here and ready-to-use control codes are available on GitHub.

Creating Programmable Microfluidic Networks

“microfluidics” Microfluidic systems are now being designed with precision as miniaturized fluid manipulation devices that can execute increasingly complex tasks. However, their operation often requires numerous external control devices. In our recent Nature article, we design microfluidic networks whose behavior can be harnessed to create a fluid analogue of Braess’s paradox and switch the direction of internal flows solely by manipulating the input and/or output pressures. These findings can be used to create built-in control mechanisms, thereby facilitating the development of portable systems and enabling novel applications, ranging from wearable healthcare technologies to deployable space systems.

Demonstrating Converse Symmetry Breaking

network analog butterfly Symmetry breaking—the phenomenon in which the symmetry of a system is not inherited by its stable states—underlies pattern formation, superconductivity, and numerous other effects. Theoretical work has established the possibility of converse symmetry breaking, a phenomenon in which the stable states are symmetric only when the system itself is not. This includes scenarios in which interacting entities are required to be non-identical in order to exhibit identical behavior, such as in reaching consensus. In our recent Nature Physics article, we present an experimental demonstration of this phenomenon using a network of electromechanical oscillators. An animated summary of the work is available here and you can view our cover on the issue here.


Cascade vulnerability

Cascade Vulnerability of the North American Power Grid

Janus oscillators video

Janus Oscillator Networks


Levitation of Heavy Particles in Downward Flows

Network Analog Butterfly Effect

Network Analog of the Butterfly Effect








Transient chaos

Fractal Geometry of Doubly Transient Chaos

Adilson Motter video

Outreach: What is Entropy?

Dance Outreach video

Outreach: Syncing Up Without Sameness

Self-siphoning beads

Outreach: Self-Siphoning Beads








Recent Publications

C. Duan, T. Nishikawa, and A.E. Motter,
Prevalence and scalable control of localized networks,
Proc. Natl. Acad. Sci. USA 119(32), e2122566119 (2022).
doi:10.1073/pnas.2122566119 - Supplemental Material

C. Duan, T. Nishikawa, D. Eroglu, and A.E. Motter,
Network structural origin of instabilities in large complex systems,
Science Advances 8(28), eabm8310 (2022).
doi:10.1126/sciadv.abm8310 - Supplemental Material

A.N. Montanari, C. Duan, L.A. Aguirre, and A.E. Motter,
Functional observability and target state estimation in large-scale networks,
Proc. Natl. Acad. Sci. USA 119(1), e2113750119 (2022).

A.E. Motter,
Whom is real science for?
Science 377(6612), 1270 (2022).

A. E. Motter,
Control Theory for Physicists [Bookshelf],
IEEE Control Systems Magazine 42 (5), 114 (2022).

Y. Zhang, J.L. Ocampo-Espindola, I.Z. Kiss, and A.E. Motter,
Random heterogeneity outperforms design in network synchronization,
Proc. Natl. Acad. Sci. USA 118(21), e2024299118 (2021).

Z.G. Nicolaou, D.J. Case, E.B. van der Wee, M.M. Driscoll, and A.E. Motter,
Heterogeneity-stabilized homogeneous states in driven media,
Nature Communications 12, 4486 (2021).

Y. Zhang, V. Latora, and A.E. Motter,
Unified treatment of synchronization patterns in generalized networks with higher-order, multilayer, and temporal interactions,
Communications Physics 4, 195 (2021).

C. Duan, G. Bharati, P. Chakraborty, B. Chen, T. Nishikawa, and A.E. Motter,
Practical challenges in real-time demand response,
IEEE Transactions on Smart Grid 12, 4573 (2021).

Z. G. Nicolaou and A. E. Motter,
Anharmonic classical time crystals: A coresonance pattern formation mechanism,
Phys. Rev. Research 3, 023106 (2021).
doi:10.1103/PhysRevResearch.3.023106 - Animated summary

Y. Sugitani, Y. Zhang, and A.E. Motter,
Synchronizing Chaos with Imperfections,
Phys. Rev. Lett. 126, 164101 (2021).

F. Molnar, T. Nishikawa, and A.E. Motter,
Asymmetry underlies stability in power grids,
Nature Communications 12, 1457 (2021).

C. Duan, P. Chakraborty, T. Nishikawa, and A.E. Motter,
Hierarchical power flow control in smart grids: Enhancing rotor angle and frequency stability with demand-side flexibility,
IEEE Trans. Control Netw. Syst. 8(3), 1046 (2021).

Y. Zhang and A.E. Motter,
Mechanism for strong chimeras,
Phys. Rev. Lett. 126, 094101 (2021).

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. Current projects include quantum networks, machine learning applications to network problems, and data-driven discovery in network science. More...

Twitter - Google Scholar - ORCID
YouTube Channel

Postdoctoral Positions

The Motter group is currently recruiting postdoctoral researchers in mechanical metamaterial networks, quantum network science, and other areas of complex systems and networks.

“Janus Bunch” Complexity Explorable

Explore the wealth of dynamical states exhibited in a network of Janus oscillators. “Janus




Group News

October 2022: Adilson E. Motter receives the Senior Scientific Award from the Complex Systems Society.

September 2022: Adilson E. Motter and Renaud Lambiotte chair the 2022 SIAM Workshop on Network Science.

September 2022: Ana Elisa D. Barioni and Thomas Mckenzie-Smith are awarded Data Science Fellowships from Northwestern University’s Data Science Initiative.

July 2022: Adilson E. Motter starts his term as President of the Network Science Society.

March 2022: Yuanzhao Zhang is awarded the 2021 Dissertation Award in Statistical and Nonlinear Physics.

September 2021: Jorin Graham is awarded an NIH Physical Genomics Predoctoral Training Program Fellowship.

July 2021: Yuanzhao Zhang has just been selected as one of the three winners of the 2021 SIAM Student Paper Prize for the paper "Symmetry-Independent Stability Analysis of Synchronization Patterns."

June 2021: Yanxuan (Charlotte) Shao receives the 2020-21 outstanding teaching assistant award.

March 2021: Chloe T. Calderon is awarded an NSF Graduate Research Fellowship.

November 2020: Our work on extreme gene-environment antagonism is featured in the cover image of the Biophysical Journal.

September 2020: Adilson E. Motter is elected Fellow of the Network Science Society.

June 2020: Fiona Brady receives the departmental award for Outstanding Senior Thesis in Physics and Astronomy.

Selected Press

Failures in large networks can be prevented with local focus
Northwestern Now (August 8, 2022)

T&D HIL for Demand Response
FLEXLAB (November, 2021)

New tool untangles complex dynamics on hypergraphs
Santa Fe Institute (October 26, 2021)

Diversity can prevent failures in large power grids
Northwestern Now (April 1, 2021)

This Is The Reason American Politics Are So Polarized
Forbes (October 27, 2020)

The Dominance of Chaos
Mashable (September 2, 2020)

Student Videos

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

Phalguni Shah video

Phalguni Shah
Untangling the nets: The paradox of network complexity and stability

Yuanzhao Zhang video

Yuanzhao Zhang
Network, Synchronization, and the Paradox of Heterogeneity

Thomas Wytock video

Thomas Wytock
Anarchists or Authoritarians? Probing the Internal Politics of E. coli

Alex Mercanti video

Alex Mercanti
Protecting Your Privacy Using Randomness

Department of Physics & Astronomy | Northwestern University
2145 Sheridan Rd, Evanston, IL 60208 USA
World Wide Web Disclaimer | University Policy Statements
© 2012 The Motter Group