On Exponential Synchronization of Kuramoto Oscillators

By Nikhil Chopra, Mark W. Spong. 2009

424 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Computer Networks and Communications

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Citations in the corpus

An Overview of Recent Progress in the Study of Distributed Multi-Agent Coordination (2012, background): “(9) Clearly, (8) refers to the case when only communication delay is considered while (9) refers to the case when only input delay is considered.”
Asymptotic formation and orbital stability of phase-locked states for the Kuramoto model (2012, result): “This improves previous results on the formation of phase-locked states by Chopra-Spong [1] and Ha-Ha-Kim [2] where their attention were focused only on the latter relaxation stage.”
Synchronization in complex networks of phase oscillators: A survey (2014, methodology): “The following tighter lower bound has been constructed by Chopra and Spong (2009). Here, we report a refined formulation of their necessary condition.”
On the Critical Coupling for Kuramoto Oscillators (2010, neutral): “…(cid:107) , ω i − ω j , . . . ) (cid:107) ∞ , that is, for V ω being the vector of all n ( n − 1) / 2 frequency diﬀerences and p = ∞ in condition (3.4) Lyapunov 14 − Lemma 9], and a geometric argument leads to the scale-free bound f ( γ ) = 1 / (2 sin( γ/ 2) cos( γ )) [19, proof of Proposition 1].”
Distributed Asynchronous Constrained Stochastic Optimization (2011, methodology): “The algorithms for reaching consensus have proven useful in a wide variety of contexts from formation control [3], distributed parameter estimation [12], [13], load balancing [14], to synchronization of Kuramoto oscillators [15].”
Effects of Delay in Multi-Agent Consensus and Oscillator Synchronization (2010, neutral): “See also [34].”
Distributed Control of Robotic Networks: A Mathematical Approach to Motion Coordination Algorithms (2009, background): “(2004), Chopra and Spong (2009), Triplett et al. (2006), Papachristodoulou and Jadbabaie (2006), Wang and Slotine (2006).”
Distributed adaptive control for synchronization of unknown nonlinear networked systems (2010, methodology): “Synchronization to timevarying trajectories has been studied based on physical or natural systems by Chopra and Spong (2009), Kuramoto (1975), Strogatz (2000), and Vicsek et al. (1995). Synchronization of nonlinear passive dynamical systems has been studied by Chopra and Spong (2006). Consensus usin”
Synchronization and transient stability in power networks and non-uniform Kuramoto oscillators (2009, methodology): “Note also that the Lyapunov function W(θ) reduces to the one used in [23], [24] and can be used to prove [23, Theorem 4.”
Distributed Adaptive Tracking Control for Synchronization of Unknown Networked Lagrangian Systems (2011, background): “Synchronization to the time-varying trajectories has been studied, based on physical or natural systems, by Chopra and Spong [7], Lu and Chen [15], Vicsek et al. [20], and Wu [27], to name a few.”