Topological Control of Synchronization Patterns: Trading Symmetry for Stability

Hart, Joseph D.; Zhang, Yuanzhao; Roy, Rajarshi; Motter, Adilson E.

doi:10.1103/physrevlett.122.058301

Cited by 56 publications

(42 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Using a generalization of the master stability function formalism developed in Ref. [8], we can calculate the maximum transverse Lyapunov exponent associated with chimera states efficiently (Appendix A). In particular, we find parameters under which i) the two clusters cannot be simultaneously in stable synchronous states (i.e., any solution satisfying x (1)…”

Section: Computational Observation Of Switching Chimerasmentioning

confidence: 99%

“…This can be done efficiently using a generalization of the master stability function formalism developed in Ref. [8], which is tailored to describe the synchronization stability of individual clusters.…”

Section: Appendix A: Linear Stability Analysis Of Chimera Statesmentioning

confidence: 99%

“…The relationship between symmetry and synchronization underlies many recent discoveries in network dynamics. Symmetries influence the possible dynamical patterns in a network [1,2], and can either facilitate [3][4][5] or inhibit [6][7][8] synchronization. A particularly interesting symmetry phenomenon in networks is the coexistence of coherent and incoherent clusters in populations of identically coupled identical oscillators [9,10]-the so-called chimera states [11].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Critical Switching in Globally Attractive Chimeras

et al. 2020

Self Cite

View full text Add to dashboard Cite

We report on a new type of chimera state that attracts almost all initial conditions and exhibits power-law switching behavior in networks of coupled oscillators. Such switching chimeras consist of two symmetric configurations, which we refer to as subchimeras, in which one cluster is synchronized and the other is incoherent. Despite each subchimera being linearly stable, switching chimeras are extremely sensitive to noise: arbitrarily small noise triggers and sustains persistent switching between the two symmetric subchimeras. The average switching frequency increases as a power law with the noise intensity, which is in contrast with the exponential scaling observed in typical stochastic transitions. Rigorous numerical analysis reveals that the power-law switching behavior originates from intermingled basins of attraction associated with the two subchimeras, which in turn are induced by chaos and symmetry in the system. The theoretical results are supported by experiments on coupled optoelectronic oscillators, which demonstrate the generality and robustness of switching chimeras. arXiv:1911.07871v1 [cond-mat.dis-nn]

show abstract

Section: Computational Observation Of Switching Chimerasmentioning

confidence: 99%

Section: Appendix A: Linear Stability Analysis Of Chimera Statesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Critical Switching in Globally Attractive Chimeras

et al. 2020

Self Cite

View full text Add to dashboard Cite

show abstract

“…In the left-hand panels, we show the actual network used to couple the optoelectronic oscillators in Ref. [52] as adjacency matrix in (a) and graph representation in (d). In the middle panels, we show the reconstruction of the network by a functional network analysis in terms of its adjacency matrix in (b) and graph representation in (e).…”

Section: Experimental Data Of Optoelectronic Oscillatorsmentioning

confidence: 99%

Revealing Dynamics, Communities, and Criticality from Data

et al. 2020

View full text Add to dashboard Cite

Complex systems such as ecological communities and neuron networks are essential parts of our everyday lives. These systems are composed of units which interact through intricate networks. The ability to predict sudden changes in the dynamics of these networks, known as critical transitions, from data is important to avert disastrous consequences of major disruptions. Predicting such changes is a major challenge as it requires forecasting the behavior for parameter ranges for which no data on the system are available. We address this issue for networks with weak individual interactions and chaotic local dynamics. We do this by building a model network, termed an effective network, consisting of the underlying local dynamics and a statistical description of their interactions. We show that behavior of such networks can be decomposed in terms of an emergent deterministic component and a fluctuation term. Traditionally, such fluctuations are filtered out. However, as we show, they are key to accessing the interaction structure. We illustrate this approach on synthetic time series of realistic neuronal interaction networks of the cat cerebral cortex and on experimental multivariate data of optoelectronic oscillators. We reconstruct the community structure by analyzing the stochastic fluctuations generated by the network and predict critical transitions for coupling parameters outside the observed range.

show abstract

“…统处于集团同步态时, 同一集团内的振子运动行为有着非常强的关联, 而不同集团间的振子运动则关联非常弱甚至无关联; 同步的振子之间可以存在直接耦合, 也可能不存在直接的耦合, 而是通过第三者的间接耦合相互达到同步(也称远程同步(Remote Synchronization)或接力同步(Relay Syn-量过于庞大, 现有条件下很难对大尺寸复杂网络的对称性进行计算 [65,66] . 同时人们也注意到, 虽然复杂网络中存在着数目众多的置换对称性, 但能够产生稳定同步斑图的却寥寥无几 [64][65][66][67] , 并由此带来了同步斑图的控制问题 [58,65,66,68] . 总体来讲, 虽然结构对称性为复杂网络同步斑图的研究提供了一个新的途径, 但目前该套方法仍处于发展阶段, 很多技术和理论问题尚待解决.…”

unclassified

Synchronous patterns in complex networks

Wang¹

2019

Sci. Sin.-Phys. Mech. Astron.

View full text Add to dashboard Cite

As a unique phenomenon in spatiotemporal nonlinear systems, dynamical patterns have been broadly interested by researchers from different fields. Recently, stimulated by the rapid progress in network science, the collective behaviors of coupled oscillators in complex networks have received continuous interest, in which the crucial roles of network structure on dynamics have been revealed and emphasized. Despite the significance of dynamical patterns to the functionality of realistic systems, it remains not very clear how patterns are generated in complex networks. Here, from the standingpoint of cluster synchronization, we give a brief introduction on the recent progress achieved on the formation of robust dynamical patterns in complex networks of coupled chaotic oscillators, including the identification of synchronous patterns, their dynamical properties, the impact of network symmetry on pattern generation, the theoretical framework for analyzing pattern stability, and methods for controlling synchronous patterns. Implications of synchronous patterns to the functionality of realistic systems will be also discussed, as well as the open questions to be addressed.

show abstract

Topological Control of Synchronization Patterns: Trading Symmetry for Stability

Cited by 56 publications

References 34 publications

Critical Switching in Globally Attractive Chimeras

Critical Switching in Globally Attractive Chimeras

Revealing Dynamics, Communities, and Criticality from Data

Synchronous patterns in complex networks

Contact Info

Product

Resources

About