Network Dynamics

Order out of disorder

Despite the common belief that individual differences are detrimental to uniform group dynamics, the opposite can be true and, in fact, quite common. One theme of my research is to understand when and why uniformity can grow out of diversity in coupled systems.

• Y. Zhang, J. L. Ocampo-Espindola, I. Z. Kiss, and A. E. Motter, Random heterogeneity outperforms design in network synchronization, Proc. Natl. Acad. Sci. U.S.A. 118, e2024299118 (2021)
• Y. Sugitani*, Y. Zhang*, and A. E. Motter, Synchronizing chaos with imperfections, Phys. Rev. Lett. 126, 164101 (2021)
• Y. Zhang and A. E. Motter, Identical synchronization of nonidentical oscillators: when only birds of different feathers flock together, Nonlinearity 31 R1-R23 (2018)
• Y. Zhang, T. Nishikawa and A. E. Motter, Asymmetry-induced synchronization in oscillator networks, Phys. Rev. E 95 062215 (2017)

Cluster synchronization

Complex networks often support complex synchronization patterns. Understanding such patterns will enable us to manipulate the behavior of numerous biological, social, and technological systems. I work on general theories and efficient algorithms to identify, characterize, and control synchronization patterns in both standard and generalized networks.

• Y. Zhang, V. Latora, and A. E. Motter, Unified treatment of synchronization patterns in generalized networks with higher-order, multilayer, and temporal interactions, Commun. Phys. 4, 195 (2021)
• Y. Zhang and A. E. Motter, Symmetry-independent stability analysis of synchronization patterns, SIAM Rev. 62, 817–836 (2020)
• 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)
• F. M. Brady*, Y. Zhang*, and A. E. Motter, Forget partitions: Cluster synchronization in directed networks generate hierarchies, arXiv:2106.13220

Chimera states

One particularly interesting type of synchronization patterns is chimera states, where a network of identically coupled identical oscillators spontaneously splits into coherent and incoherent clusters. It represents symmetry breaking phenomena in networks. I contribute to the understanding of chimera states by characterizing new chimeras and proposing general mechanisms giving rise to such states.

• Y. Zhang and A. E. Motter, Mechanism for strong chimeras, Phys. Rev. Lett. 126, 094101 (2021)
• Y. Zhang, Z. G. Nicolaou, J. D. Hart, R. Roy, and A. E. Motter, Critical switching in globally attractive chimeras, Phys. Rev. X 10, 011044 (2020)

Applications

Many real-world systems can be modelled as coupled oscillators. I work with domain experts to advance our understanding of systems such as circadian clocks and pancreatic islets.

• Y. Huang, Y. Zhang, and R. Braun, A minimal model of peripheral clocks reveals differential circadian re-entrainment in aging, Chaos 33, 093104 (2023)