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Contraction of monotone phase-coupled oscillators

A. Mauroy, R. Sepulchre
2012 Systems & control letters (Print)  
This paper establishes a global contraction property for networks of phase-coupled oscillators characterized by a monotone coupling function. The contraction measure is a total variation distance.  ...  The contraction property determines the asymptotic behavior of the network, which is either finite-time synchronization or asymptotic convergence to a splay state.  ...  Acknowledgments This paper presents research results of the Belgian Network DYSCO (Dynamical Systems, Control, and Optimization), funded by the Interuniversity Attraction Poles Programme, initiated by  ... 
doi:10.1016/j.sysconle.2012.08.007 fatcat:br6ixi5rkfdznoriag7g7dw3ra

Kick synchronization versus diffusive synchronization [article]

Alexandre Mauroy, Pierre Sacré, Rodolphe Sepulchre
2013 arXiv   pre-print
coupling.  ...  The paper provides an introductory discussion about two fundamental models of oscillator synchronization: the (continuous-time) diffusive model, that dominates the mathematical literature on synchronization  ...  Acknowledgments This paper presents research results of the Belgian Network DYSCO (Dynamical Systems, Control, and Optimization), funded by the Interuniversity Attraction Poles Programme, initiated by  ... 
arXiv:1209.4970v3 fatcat:lj2hla3iqjgrzkhkufecljvnu4

Kick synchronization versus diffusive synchronization

Alexandre Mauroy, Pierre Sacre, Rodolphe Sepulchre
2012 2012 IEEE 51st IEEE Conference on Decision and Control (CDC)  
coupling.  ...  The paper provides an introductory discussion about two fundamental models of oscillator synchronization: the (continuous-time) diffusive model, that dominates the mathematical literature on synchronization  ...  A corollary of the contraction property of Theorem 3 is that networks of oscillators coupled through a monotone coupling function display two behaviors (for almost every initial condition): • If Γ is monotone  ... 
doi:10.1109/cdc.2012.6425821 dblp:conf/cdc/MauroySS12 fatcat:rbwgvlbllbf4nlumzddp5m67we

Global Analysis of a Continuum Model for Monotone Pulse-Coupled Oscillators

Alexandre Mauroy, Rodolphe J. Sepulchre
2013 IEEE Transactions on Automatic Control  
We consider a continuum of phase oscillators on the circle interacting through an impulsive instantaneous coupling.  ...  The monotone time evolution of the Lyapunov function completely characterizes the dichotomic behavior of the oscillators: either the oscillators converge in finite time to a synchronous state or they asymptotically  ...  A PHASE DENSITY EQUATION FOR PULSE-COUPLED OSCILLATORS In this section, we introduce the model of (monotone) integrate-and-fire oscillators with an (instantaneous) impulsive coupling.  ... 
doi:10.1109/tac.2012.2229811 fatcat:tqr73qnhfngxdidc4q643fxdz4

Spontaneous oscillations from turnover of an elastic contractile material [article]

Kai Dierkes and Angughali Sumi and Jérôme Solon and Guillaume Salbreux
2014 arXiv   pre-print
We show here that a generic model of a contractile material, which is turning over and contracts against an elastic element, exhibits spontaneous oscillations.  ...  We investigate the collective dynamics of an ensemble of such oscillators and show that the relative contribution of viscous and friction losses yield different regimes of collective oscillations.  ...  Mechanically coupling the oscillators introduces a repulsive coupling, as the contraction of one unit has to be balanced by expansion of the other units.  ... 
arXiv:1402.5390v1 fatcat:jop7o62rsvb3zkl3l77s54b6ge

Convergence to the critical attractor of dissipative maps: Log-periodic oscillations, fractality, and nonextensivity

F. A. B. F. de Moura, U. Tirnakli, M. L. Lyra
2000 Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics  
We found that the phase space volume occupied by the ensemble W(t) depicts a power-law decay with log-periodic oscillations reflecting the multifractal character of the critical attractor.  ...  For a family of logistic-like maps, we investigate the rate of convergence to the critical attractor when an ensemble of initial conditions is uniformly spread over the entire phase space.  ...  oscillations [13] .The amplitude of the oscillations was found to depict a monotonic parametric dependence on d f .  ... 
doi:10.1103/physreve.62.6361 pmid:11101970 fatcat:w3366nyydzb5hez52ablcl3gbi

Bifurcation and chaos in a periodically stimulated cardiac oscillator

Leon Glass, Michael R. Guevara, Alvin Shrier, Rafael Perez
1983 Physica D : Non-linear phenomena  
Periodic stimulation of an aggregate of spontaneously beating cultured cardiac cells displays phase locking, period-doubling bifurcations and aperiodic "chaotic" dynamics at different values of the stimulation  ...  A simplified version of the experimentally determined Poincar6 map is proposed, and several features of the bifurcations of this map are described.  ...  Acknowledgments This research has been supported by grants from the Natural Sciences and Engineering Research Council of Canada and the Canadian Heart Foundation.  ... 
doi:10.1016/0167-2789(83)90119-7 fatcat:vk7uwer7zjaz3h35r67zuiyzsa

Sparse Control for Dynamic Movement Primitives [article]

Patrick M. Wensing, Jean-Jacques Slotine
2016 arXiv   pre-print
New analytical results on the coupling of oscillators with diverse natural frequencies are also discussed.  ...  The dynamics of DMPs are analyzed through the framework of contraction theory as networked hierarchies of contracting or transversely contracting systems.  ...  Sangbae Kim for use of the MIT Cheetah robot to conduct experiments.  ... 
arXiv:1611.05066v2 fatcat:ekovb4yty5cz3fniomm4of7qlq

Frequency gradients in heterogeneous oscillatory media can spatially localize self-organized wave sources that coordinate system-wide activity [article]

Ria Ghosh, Pavithraa Seenivasan, Shakti N. Menon, S. Sridhar, Nicolas B. Garnier, Alain Pumir, Sitabhra Sinha
2019 arXiv   pre-print
In the absence of centralized coordination by specialized cells (pacemakers), competing oscillating clusters impede this global synchrony.  ...  Such gradients, arising through heterogeneous inter-cellular coupling, may explain directed rhythmic activity during labor in the uterus despite the absence of pacemakers.  ...  The frequency of oscillations at each site (l, m) depends in a non-monotonic manner on n p (see Fig. 1 b of Ref.  ... 
arXiv:1912.07271v1 fatcat:ojwzirrtrjblfgonlchxhvsnc4

Locally and Globally Coupled Oscillators in Muscle

Katsuhiko Sato, Yoshiki Kuramoto, Masako Ohtaki, Yuta Shimamoto, Shin'ichi Ishiwata
2013 Physical Review Letters  
We further reduce the connected model to phase equations, revealing that the combination of local and global couplings is crucial to the emergence of these patterns.  ...  At an intermediate activation level, striated muscle exhibits autonomous oscillations called SPOC, in which the basic contractile units, sarcomeres, oscillate in length, and various oscillatory patterns  ...  Mikhailenko for his critical reading of manuscript. This work was supported by a RIKEN grant (to K.  ... 
doi:10.1103/physrevlett.111.108104 pmid:25166714 fatcat:lcwb4e563jbvhnodrrq6l7qu4y

Various oscillation patterns in phase models with locally attractive and globally repulsive couplings

Katsuhiko Sato, Shin-ichiro Shima
2015 Physical Review E  
Depending on the relative strengths of the local and global coupling and on the form of global coupling, the system can show a spatially uniform state (in-phase synchronization), a monotonically increasing  ...  state (traveling wave), and three types of oscillations of relative phase difference.  ...  The local coupling term in this oscillation orders the phases.  ... 
doi:10.1103/physreve.92.042922 pmid:26565319 fatcat:7ullcfo6inhuxfxdfdio72nlei

Non-monotonic population and coherence evolution in Markovian open-system dynamics [article]

Jan F. Haase, Andrea Smirne, Susana F. Huelga
2019 arXiv   pre-print
Namely, a non monotonic behavior both in the population and in the coherence evolution arises due to the presence of non-secular contributions, which break the phase covariance of the Lindbladian (semigroup  ...  We also show by an explicit construction how such a non-monotonic behaviour can be reproduced by a phase covariant evolution, but only at the price of inserting some state-dependent memory effects.  ...  Neither the population nor the coherence show a monotonic behavior but, instead, we can observe damped oscillating evolutions, which are even different for the two chosen initial phases.  ... 
arXiv:1903.11118v1 fatcat:uqzl5x5or5dgxpdtbjslk7fjxi

Relaxation dynamics of the Kuramoto model with uniformly distributed natural frequencies

Anandamohan Ghosh, Shamik Gupta
2013 Physica A: Statistical Mechanics and its Applications  
The model in the steady state exhibits a phase transition as a function of the coupling strength, between a low-coupling incoherent phase in which the oscillators oscillate independently and a high-coupling  ...  The Kuramoto model describes a system of globally coupled phase-only oscillators with distributed natural frequencies.  ...  G. acknowledges support of the French contract LORIS (ANR-10-CEXC-010-01). We thank Deepak Dhar, David Mukamel, Antonio Politi, and Stefano Ruffo for useful discussions and comments on the manuscript.  ... 
doi:10.1016/j.physa.2013.03.037 fatcat:3hbho3ce5vhy3acja5gza2g7n4

Macroscopic quantum self-trapping and Josephson oscillations of exciton polaritons

M. Abbarchi, A. Amo, V. G. Sala, D. D. Solnyshkov, H. Flayac, L. Ferrier, I. Sagnes, E. Galopin, A. Lemaître, G. Malpuech, J. Bloch
2013 Nature Physics  
The finite lifetime of polaritons results in a dynamical transition from self-trapping to oscillations with pi phase.  ...  We report on the observation of non-linear Josephson oscillations of two coupled polariton condensates confined in a photonic molecule etched in a semiconductor microcavity.  ...  Senellart for the lithography of the sample and T. Jacqmin for his experimental help.  ... 
doi:10.1038/nphys2609 fatcat:fxlio2vjufhjrbej6dsb5is5w4

TRANSIENT TIME IN UNIDIRECTIONAL SYNCHRONIZATION

GIOVANNI SANTOBONI, STEVEN R. BISHOP, ALBERTO VARONE
1999 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering  
We consider here the behaviour of a dynamical system consisting of unidirectionally coupled Du ng oscillators.  ...  Under certain conditions the subsystems may become synchronised corresponding to a stable invariant subset of the full dimensional phase space.  ...  Carretero-Gonz alez and G.H.M. van der Heijden for many invaluable comments and for a critical reading of the manuscript.  ... 
doi:10.1142/s0218127499001851 fatcat:bot34gnn5zdn5ao2xn46zaixli
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