## Featured Projects

## Asymmetry-Induced Symmetry

### Asymmetry-induced synchronization in oscillator networks

It is generally assumed that individual entities are more likely to exhibit the same or similar behavior if they are equal to each other: think of lasers pulsing at the same frequency, animals using the same gait, agents reaching consensus. In a recent PRL paper we have shown that this assumption is in fact false in networks of interacting entities. Our central discovery is a network phenomenon we term “asymmetry-induced symmetry” (AIS), in which the state of the system can be symmetric only when the system itself is not symmetric. Using synchronization as a model process, we demonstrate that the state in which all nodes synchronize and exhibit identical dynamics (a state of maximum symmetry, as it remains unchanged after swapping any two nodes), such as when lasers pulse together, can only be realized when the nodes themselves are not identical. Asymmetry-induced symmetry can be seen as the converse of the well-studied phenomenon of symmetry breaking, where the state has less symmetry than the system. AIS has far-reaching implications for processes that involve converging to uniform states; in particular, it offers a mechanism for yet-to-be-explained convergent forms of pattern formation, in which an asymmetric structure develops into a symmetric one. AIS also has implications for consensus dynamics, where it gives rise to the scenario in which interacting agents only reach consensus when they are sufficiently different from each other. See also AIS Demo and AIS-Inspired Dance Outreach Video.

### Main publications

T. Nishikawa and A.E. Motter,

Symmetric states requiring system asymmetry,

Phys. Rev. Lett. **117**, 114101 (2016).

doi:10.1103/PhysRevLett.117.114101 - Synopsis

arXiv:1608.05419

Y. Zhang, T. Nishikawa, and A.E. Motter,

Asymmetry-induced synchronization in oscillator networks,

Phys. Rev. E **95**, 062215 (2017).

doi:10.1103/PhysRevE.95.062215

arXiv:1705.07907

Y. Zhang and A.E. Motter,

Identical synchronization of nonidentical oscillators: When only birds of different feathers flock together,

Nonlinearity **31**, R1 (2018).

doi:10.1088/1361-6544/aa8fe7

arXiv:1712.03245

J.D. Hart, Y. Zhang, R. Roy, and A.E. Motter,

Topological control of synchronization patterns: Trading symmetry for stability,

Phys. Rev. Lett. **122**, 058301 (2019).

doi:10.1103/PhysRevLett.122.058301

arXiv:1902.03255

Z.G. Nicolaou, D. Eroglu, and A.E. Motter,

Multifaceted dynamics of Janus oscillator networks,

Phys. Rev. X **9**, 011017 (2019).

doi:10.1103/PhysRevX.9.011017 - Synopsis - Animated summary

arXiv:1810.06576 - Explorable Iterative Interface

F. Molnar, T. Nishikawa, and A.E. Motter,

Network experiment demonstrates converse symmetry breaking,

Nature Physics **16**, 351–356 (2020).

doi:10.1038/s41567-019-0742-y - Supplemental Material

arXiv:2009.05582 - Animated summary

Z.G. Nicolaou, M. Sebek, I.Z. Kiss, and A.E. Motter,

Coherent dynamics enhanced by uncorrelated noise,

Phys. Rev. Lett. **125**, 094101 (2020).

doi:10.1103/PhysRevLett.125.094101

arXiv:2008.10654

F. Molnar, T. Nishikawa, and A.E. Motter,

Asymmetry underlies stability in power grids,

Nature Communications **12**, 1457 (2021).

doi:10.1038/s41467-021-21290-5

arXiv:2103.10952

Y. Sugitani, Y. Zhang, and A.E. Motter,

Synchronizing Chaos with Imperfections,

Phys. Rev. Lett. **126**, 164101 (2021).

doi:10.1103/PhysRevLett.126.164101

arXiv:2104.13376

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).

doi.org/10.1073/pnas.2024299118