On partial contraction analysis for coupled nonlinear oscillators

By Wei Wang, Jean-Jacques E. Slotine. Biological cybernetics, 2004

606 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics, Cognitive Neuroscience, Computer Networks and Communications

View Paper: https://www.semanticscholar.org/paper/c0aec976e2e38a40f225ca11466fd64701c0cb92

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In Atomic and Molecular Physics, and Optics

In Cognitive Neuroscience

In Computer Networks and Communications

Citations in the corpus

A Differential Lyapunov Framework for Contraction Analysis (2012, methodology): “In what follows we revisit these results, showing that a particular application of Theorem 1 entails the sufficient conditions for convergent systems in [34], [35], and we formulate a proposition whose conditions parallels the relaxed contraction analysis proposed by [20], [55], through the notion o”
On the stability of the Kuramoto model of coupled nonlinear oscillators (2005, background): “) Interestingly, a few researchers in the control community have recently started to look into the problem of synchronization, coordination and reaching consensus among multi-agent systems [9, 20] as well as synchronization phenomena among nonlinear oscillators [11,18,32].”
A Weighted and Directed Interareal Connectivity Matrix for Macaque Cerebral Cortex (2012, background): “Sparse long-distance connections, conceivably via nonlinear phenomena such as “contraction dynamics”, may have disproportionate effects relative to the far more dense intrinsic and intermediatedistance connections (Wang and Slotine 2005).”
A Predictive Network Model of Cerebral Cortical Connectivity Based on a Distance Rule (2013, neutral): “One can speculate that the highly specific long-distance low-bandwidth connections between areas in different modules may coordinate activity via contraction dynamics (Wang and Slotine, 2005).”
Learning Partially Contracting Dynamical Systems from Demonstrations (2017, methodology): “[10]) is used to 1st Conference on Robot Learning (CoRL 2017), Mountain View, United States.”
Synchronization in complex networks of phase oscillators: A survey (2014, methodology): “We refer the reader to (Lohmiller and Slotine, 1998; Sontag , 2010) for a treatment of contraction analysis and to (Wang and Slotine, 2005; Russo et al., 2010; Forni and Sepulchre , 2014) for its extension to systems with symmetries.”
Decentralized, Adaptive Coverage Control for Networked Robots (2009, background): “However, they have only recently yielded to rigorous mathematical treatment; first in the distributed and parallel computing community [2, 3, 28, 29] in discrete time, and more recently in the controls community in continuous time [4, 7, 11, 15, 30–32].”
Control Principles of Complex Networks (2015, background): “…et al., 2006, 2005, 2004a,b; Chen, 2006, 2007, 2008; Li et al., 2009; Wu and Chua, 1994, 1995a,b,c) or contraction theory (Aminzare and Sontag, 2015; Li et al., 2007; Lohmiller and Slotine, 1998; Pham and Slotine, 2007; Russo and Di Bernardo, 2009; Tabareau et al., 2010; Wang and Slotine, 2005).”
On Exponential Synchronization of Kuramoto Oscillators (2009, methodology): “, N Recently, control theoretic methods have been used in [2], [3], [7], [8], [14], [15], [16], [21], [19] to address the synchronization phenomenon.”
Cooperative Robot Control and Concurrent Synchronization of Lagrangian Systems (2007, methodology): “The synchronization of a large network with a constant metric is already discussed in [10] using contraction analysis.”
A theoretical study of different leader roles in networks (2006, background): “• Synchronization conditions derived in Theorem 2 are very similar to those in [28], [33] for coupled networks without any leader or adaptation.”
Contractive Systems with Inputs (2010, background): “In control theory, contraction theory has been popularized and extended by Slotine and coworkers, see for instance [7], [6], [19] where applications to nonlinear control, observer problems, and synchronization and consensus problems in complex networks have been developed, as well as by Nijmejer and”
Application of Synchronization to Formation Flying Spacecraft: Lagrangian Approach (2008, methodology): “Consequently, the last (pth) satellite is connected with the first satellite to form a ring network as suggested in [28].”
Cortical High-Density Counterstream Architectures (2013, background): “The considerably more numerous long-distance connections are sparse and exhibit high binary specificity; we speculate that these connections serve to promote cortical communication by controlling oscillatory coherence (77) possibly via contraction dynamics (100).”