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.
Network Frontier Workshop 2015
The Network Frontier Workshop 2015 will be held at Northwestern University December 6-7, 2015. More information will be available soon.
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.
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.
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
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
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.
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.
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.
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.
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.
The Answer Is the Network. What Is the Question?
Northwestern University Office of Research Annual Report 2014 (February 19, 2015)
Chaos Reigns in Unexpected Places
Physics World (November 20, 2013)