## Approaches to Control Large, Nonlinear Complex Networks

Nonlinearity, interconnectivity, and noise are common features of complex systems and have generally been regarded as obstacles to controlling their behavior. In a pair of recent papers we have shown how these properties can be harnessed to control a network and drive it to desired states by either manipulating the system's trajectories or the landscape through which these trajectories travel. Our new Physical Review X paper presents an action-based method to predict and control noise-induced switching between different states in a network, which can also be used to create bifurcation-induced transitions in the absence of noise. Our recent Nature Communications paper shows how to identify compensatory perturbations on networks away from equilibrium even under rather restrictive constraints on the possible interventions — see movie for step-by-step construction of the interventions in simple examples. These new approaches are highly scalable and can be used to identify control interventions in a range of large complex networks, from cells to power grids. Ready-to-use codes that can be applied to identify eligible control interventions in general systems described by coupled ODEs are available in PRX's Supplemental Material and Nature's Protocol Exchange, respectively. For a nontechnical discussion, see our Chaos review on control of nonlinear network dynamics published recently as part of the 25th anniversary issue of the journal.

## MBI Workshop: Control and Observability of Network Dynamics

April 11-15, 2016 - Mathematical Biosciences Institute (MBI), The Ohio State University, Columbus, OH

Organizers: Réka Albert, John Baillieul, and Adilson E. Motter

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. Throughout biology, it is important to use control to achieve desired dynamics and prevent undesired behaviors. Thus, the study of network control is significant both to reveal naturally evolved control mechanisms that underlie the functioning of biological systems and to develop human-designed control interventions to recover lost function, mitigate failures, or repurpose biological networks. Application areas include cell biology, neuroscience, and ecology as well as bioinspired engineering applications. 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 select Thursdays of each month at 2:00 PM in Tech F160.

## 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

D.K. Wells, W.L. Kath, and A.E. Motter,

Control of stochastic and induced switching in biophysical networks,

Phys. Rev. X **5**, 031036 (2015).

arXiv:1509.03349 -
doi: 10.1103/PhysRevX.5.031036

A.E. Motter,

Networkcontrology,

Chaos **25**, 097621 (2015).

arXiv:1510.08320 -
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., **7**, 930 (2015).

doi:10.1039/C5IB00096C

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

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

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

Photo by Eileen Molony

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

## Positions

(Dec 2015) The group has an opening for a postdoctoral researcher in the area of control of network dynamics as applied to complex chemical reaction networks. E-mail Prof. Motter to send your CV or to request more information.

## Network Control

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

April 2016: Daniel Case is awarded a Presidential Fellowship, which will support his graduate research on microfluidic networks.

March 2016: Yang (Angela) Yang receives the Topical Group on Statistical and Nonlinear Physics (GSNP) Student Speaker Award at the APS March Meeting 2016.

March 2016: Our group leads a Northwestern team receiving a $3.2 million ARPA-E Grant.

January 2016: Adilson E. Motter is selected Outstanding Referee of the APS.

December 2015: Group organizes the 3rd edition of the Network Frontier Workshop.

November 2015: Adilson E. Motter is elected Fellow of the American Association for the Advancement of Science (AAAS).

October 2015: Takashi Nishikawa and Corey Brady present "Networks All Around!" at the Jr. Science Café series of the Museum of Science and Industry of Chicago.

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.

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.

## Selected Press

Leveraging Noise to Control Complex Networks

SIAM News (January 19, 2016)

http://...

Network Control: Letting Noise Lead the Way

Science Daily (September 17, 2015)

http://...

The Answer Is the Network. What Is the Question?

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

http://...

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)

http://...