Synchronization of Coupled Oscillators is a Game

Yin, Huibing; Mehta, Prashant G.; Meyn, Sean; Shanbhag, Uday V.

doi:10.1109/tac.2011.2168082

Cited by 132 publications

(127 citation statements)

References 20 publications

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“…The continuum-limit model has enjoyed a considerable amount of attention by the physics and dynamics communities. Related controltheoretical applications of the continuum-limit model are estimation of gait cycles (Tilton et al, 2012), spatial power grid modeling and analysis (Mangesius et al, 2012), and game theoretic approaches (Yin et al, 2012).…”

Section: Synchronization In Infinite-dimensional Networkmentioning

confidence: 99%

Synchronization in complex networks of phase oscillators: A survey

2014

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The emergence of synchronization in a network of coupled oscillators is a fascinating subject of multidisciplinary research. This survey reviews the vast literature on the theory and the applications of complex oscillator networks. We focus on phase oscillator models that are widespread in real-world synchronization phenomena, that generalize the celebrated Kuramoto model, and that feature a rich phenomenology. We review the history and the countless applications of this model throughout science and engineering. We justify the importance of the widespread coupled oscillator model as a locally canonical model and describe some selected applications relevant to control scientists, including vehicle coordination, electric power networks, and clock synchronization. We introduce the reader to several synchronization notions and performance estimates. We propose analysis approaches to phase and frequency synchronization, phase balancing, pattern formation, and partial synchronization. We present the sharpest known results about synchronization in networks of homogeneous and heterogeneous oscillators, with complete or sparse interconnection topologies, and in finite-dimensional and infinite-dimensional settings. We conclude by summarizing the limitations of existing analysis methods and by highlighting some directions for future research.

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Section: Synchronization In Infinite-dimensional Networkmentioning

confidence: 99%

Synchronization in complex networks of phase oscillators: A survey

2014

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“…In the context of stochastic games, mean field equilibrium and related approaches have been proposed under a variety of monikers across economics and engineering; see, for example, studies of anonymous sequential games (Jovanovic and Rosenthal 1988, Bergin and Bernhardt 1995, Chakrabarti 2003; stationary equilibrium (Hopenhayn 1992); dynamic stochastic general equilibrium in macroeconomic modeling (Stokey et al 1989); Nash certainty equivalent control (Huang et al 2006(Huang et al , 2007; mean field games (Lasry and Lions 2007); oblivious equilibrium (Weintraub et al 2008(Weintraub et al , 2011; and dynamic user equilibrium (Friesz et al 1993, Wunderlich et al 2000. Mean field equilibrium has also been studied in recent works on information percolation models (Duffie et al 2009), sensitivity analysis in aggregate games (Acemoglu and Jensen 2013), coupling of oscillators (Yin et al 2010), scaling behavior of markets (Bodoh-Creed 2012), and on power control in wireless communications (Wiecek et al 2011). Most closely related to our paper is the work of Sleet (2001), who considers mean field equilibria of a dynamic price-setting game with stochastic, exogenous firm-specific demand shocks per period, that exhibits strategic complementarities.…”

Section: Introductionmentioning

confidence: 99%

Mean Field Equilibrium in Dynamic Games with Strategic Complementarities

Adlakha

Johari

2013

Operations Research

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We study a class of stochastic dynamic games that exhibit strategic complementarities between players; formally, in the games we consider, the payoff of a player has increasing differences between her own state and the empirical distribution of the states of other players. Such games can be used to model a diverse set of applications, including network security models, recommender systems, and dynamic search in markets. Stochastic games are generally difficult to analyze, and these difficulties are only exacerbated when the number of players is large (as might be the case in the preceding examples).We consider an approximation methodology called mean field equilibrium to study these games. In such an equilibrium, each player reacts to only the long-run average state of other players. We find necessary conditions for the existence of a mean field equilibrium in such games. Furthermore, as a simple consequence of this existence theorem, we obtain several natural monotonicity properties. We show that there exist a "largest" and a "smallest" equilibrium among all those where the equilibrium strategy used by a player is nondecreasing, and we also show that players converge to each of these equilibria via natural myopic learning dynamics; as we argue, these dynamics are more reasonable than the standard best-response dynamics. We also provide sensitivity results, where we quantify how the equilibria of such games move in response to changes in parameters of the game (for example, the introduction of incentives to players).

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“…Note that by substituting the mean-field equilibrium strategies u * = − 1 c 1 (φ(t)X + h(t)) and w * = 1 γ 2 (φ(t)X + h(t)) as given in (18) in the openloop microscopic dynamics dX(t) = (u(t) + w(t))dt + σdB(t) as defined in (15), the closed-loop microscopic dynamics is Let V (X(t)) = dist(X(t), X ), where dist(X(t), X ) denotes the Euclidean distance of X(t) from the set X . The next result establishes a condition under which the above dynamics converges asymptotically to the set of equilibrium points in a stochastic sense [11].…”

Section: Mean-field Equilibriummentioning

confidence: 99%

“…For a survey see [4]. Modeling synchronization as a game is also in [15]. Game theoretic learning is also discussed in [16].…”

Section: Introductionmentioning

confidence: 99%

Consensus via multi-population robust mean-field games

Bauso

2017

Systems & Control Letters

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In less prescriptive environments where individuals are told 'what to do' but not 'how to do', synchronization can be a byproduct of strategic thinking, prediction, and local interactions. We prove this in the context of multipopulation robust mean-field games. The model sheds light on a multi-scale phenomenon involving fast synchronization within the same population and slow inter-cluster oscillation between different populations.

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Synchronization of Coupled Oscillators is a Game

Cited by 132 publications

References 20 publications

Synchronization in complex networks of phase oscillators: A survey

Synchronization in complex networks of phase oscillators: A survey

Mean Field Equilibrium in Dynamic Games with Strategic Complementarities

Consensus via multi-population robust mean-field games

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