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On the Stability of the Kuramoto Model of Coupled Nonlinear Oscillators
, 2005
"... We provide an analysis of the classic Kuramoto model of coupled nonlinear oscillators that goes beyond the existing results for alltoall networks of identical oscillators. Our work is applicable to oscillator networks of arbitrary interconnection topology with uncertain natural frequencies. Using ..."
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We provide an analysis of the classic Kuramoto model of coupled nonlinear oscillators that goes beyond the existing results for alltoall networks of identical oscillators. Our work is applicable to oscillator networks of arbitrary interconnection topology with uncertain natural frequencies. Using tools from spectral graph theory and control theory, we prove that for couplings above a critical value, the synchronized state is locally asymptotically stable, resulting in convergence of all phase differences to a constant value, both in the case of identical natural frequencies as well as uncertain ones. We further explain the behavior of the system as the number of oscillators grows to infinity.
Exploring Synchronization in Complex Oscillator Networks
"... Abstract — The emergence of synchronization in a network of coupled oscillators is a pervasive topic in various scientific disciplines ranging from biology, physics, and chemistry to social networks and engineering applications. A coupled oscillator network is characterized by a population of hetero ..."
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Cited by 10 (1 self)
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Abstract — The emergence of synchronization in a network of coupled oscillators is a pervasive topic in various scientific disciplines ranging from biology, physics, and chemistry to social networks and engineering applications. A coupled oscillator network is characterized by a population of heterogeneous oscillators and a graph describing the interaction among the oscillators. These two ingredients give rise to a rich dynamic behavior that keeps on fascinating the scientific community. In this article, we present a tutorial introduction to coupled oscillator networks, we review the vast literature on theory and applications, and we present a collection of different synchronization notions, conditions, and analysis approaches. We focus on the canonical phase oscillator models occurring in countless realworld synchronization phenomena, and present their rich phenomenology. We review a set of applications relevant to control scientists. We explore different approaches to phase and frequency synchronization, and we present a collection of synchronization conditions and performance estimates. For all results we present selfcontained proofs that illustrate a sample of different analysis methods in a tutorial style. I.
Synchronization in Complex Networks of Phase Oscillators: A Survey
, 2014
"... 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 realworl ..."
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Cited by 10 (0 self)
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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 realworld 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 finitedimensional and infinitedimensional settings. We conclude by summarizing the limitations of existing analysis methods and by highlighting some directions for future research.
Electromagnetic Modeling Of QuasiOptical Power Combiners
, 1996
"... A fullwave electromagnetic simulator is developed for the analysis of finite antenna elements and grid arrays in quasioptical systems. This electromagnetic simulator employs an efficient Galerkin moment method technique with subdomain sinusoidal basis functions. What makes this moment method anal ..."
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Cited by 8 (0 self)
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A fullwave electromagnetic simulator is developed for the analysis of finite antenna elements and grid arrays in quasioptical systems. This electromagnetic simulator employs an efficient Galerkin moment method technique with subdomain sinusoidal basis functions. What makes this moment method analysis unique is that it is formulated using a combination of spatial and spectral domains taking full advantage of the strengths of each method to ensure accurate and efficient evaluation of the moment matrix elements. Incorporated into the moment method simulator are quasioptical dyadic Green's functions which are derived by separately considering paraxial fields (quasioptical modes) which are largely responsible for distant interactions in the quasioptical system and the corrected open space (nonmodal) interactions responsible for near neighbor coupling. Two types of q...
Beam Scanning With Coupled VCOs
 In Proc. Antennas Propagation Soc. Int. Symp
, 1994
"... Abstract An eight element beam scanning array using strongly coupled voltage controlled oscillators (VCOs) is described. A constant, progressive phase shift between elements can be synthesized by adjusting the natural frequencies of the end elements [6]. The VCOs in the array are used to implement ..."
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Cited by 7 (0 self)
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Abstract An eight element beam scanning array using strongly coupled voltage controlled oscillators (VCOs) is described. A constant, progressive phase shift between elements can be synthesized by adjusting the natural frequencies of the end elements [6]. The VCOs in the array are used to implement this frequency detuning. Measured radiation patterns indicate continuous scanning from15 " to +30 " off broadside with an effective radiated power (ERP) of 8.5W at 8.1GHz. I.
Dynamics of two coupled van der Pol oscillators with delay coupling
 In Proceedings of ASME Design Engineering Technical Conference
, 1997
"... In this work, we investigate the dynamics of two weakly coupled van der Pol oscillators in which the coupling terms have time delay τ. Our work is motivated by applications to laser dynamics and the coupling of microwave oscillators. The governing equations are ¨x1 + x1 − ɛ (1 − x 2 1)˙x1 = ɛα ˙x2 ( ..."
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Cited by 7 (2 self)
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In this work, we investigate the dynamics of two weakly coupled van der Pol oscillators in which the coupling terms have time delay τ. Our work is motivated by applications to laser dynamics and the coupling of microwave oscillators. The governing equations are ¨x1 + x1 − ɛ (1 − x 2 1)˙x1 = ɛα ˙x2 (t − τ), ¨x2 + x2 − ɛ (1 − x 2 2)˙x2 = ɛα ˙x1 (t − τ), where the coupling is chosen to be through the damping terms because this form of coupling occurs in radiatively coupled microwave oscillator arrays. We use the method of averaging to obtain the approximate simplified system of three slowflow equations ˙R1 = 1 2 ˙R2 = 1
Progress in Active Integrated Antennas and Their Applications
 IEEE Trans. Microwave Theory Techn
, 1998
"... Active integrated antennas (AIA's) provide a new paradigm for designing modern microwave and millimeterwave architecture with desirable features such as compactness, light weight, low cost, low profile, minimum power consumption, and multiple functionality. This paper reviews recent research a ..."
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Cited by 5 (1 self)
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Active integrated antennas (AIA's) provide a new paradigm for designing modern microwave and millimeterwave architecture with desirable features such as compactness, light weight, low cost, low profile, minimum power consumption, and multiple functionality. This paper reviews recent research and development related to this emerging technology with emphasis on its applications in highefficiency radiofrequency (RF) frontend, millimeterwave power combining, beam steering, and retrodirective arrays, as well as wireless sensors. Optical controlling techniques for AIA's are also described.
Modeling and Simulation of Coupling Structures for QuasiOptical Systems
, 1993
"... Heron, Patrick Lascelles Modeling and Simulation of Coupling Structures for QuasiOptical Systems. Under the direction of Michael B. Steer and James W. Mink Sponsored research was directed toward developing millimeter wave power sources utilizing quasioptical techniques. A system consisting of ..."
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Heron, Patrick Lascelles Modeling and Simulation of Coupling Structures for QuasiOptical Systems. Under the direction of Michael B. Steer and James W. Mink Sponsored research was directed toward developing millimeter wave power sources utilizing quasioptical techniques. A system consisting of an array of oscillators that radiated into a quasioptical resonator was analyzed. Each oscillator was comprised of a solid state device and a radiating structure. A dyadic Green's function was developed for a FabryPerot resonator which consisted of a metallic planar reflector and a shallow spherical metallic reflector. The Green's function was applied to determine the driving point impedance matrix for an array of electrically small antennas within the resonator. An experimental Xband resonator was designed and fabricated, then one and twoport measurements were used to validate the theoretical calculations. A technique was determined for simulation of antennas that are not electrically ...
Enhanced scanning range of coupled oscillator arrays utilizing frequency multipliers
 in IEEE APS Int. Symp. Dig
, 1995
"... Abstract Scanning in arrays is conventionally achieved through phase shiften. Recent work has indicated that scanning can be achieved with significantly reduced complexity and cost using coupledoscillator techniques. However, the scan range has been somewhat limited using this tecbnique. This pape ..."
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Cited by 2 (0 self)
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Abstract Scanning in arrays is conventionally achieved through phase shiften. Recent work has indicated that scanning can be achieved with significantly reduced complexity and cost using coupledoscillator techniques. However, the scan range has been somewhat limited using this tecbnique. This paper describes a simple method to greatly enhance the scan range using varactor frequency doublers, which has the added advantage of simplifying the fimdamental mode oscillator design. In an effort to combine power in an efficient way the field of quasi optical power combining was born. [3][6] A large number of solid state oscillators can be integrated in such a way that their respective outputs coherently add in free space. The low loss properties of free space, especially at higher frequencies, along with the reliability of solid state devices make this approach particularly attractive. Extensive work, theoretical [1,7,8] and experimental [1,2] on the coupling dynamics of these discrete oscillators has already been performed. A significant breakthtough of this research was the discovery of a simple way to induce beam scanning in such an array of coupled oscillators[2]. This can be achieved by
Simulation Of Microwave And MillimeterWave Oscillators, Present Capability And Future Directions
 Proc. Workshop on Integrated Nonlinear Microwave and Millimeterwave Circuits
, 1992
"... The current stateofthe art of oscillator simulation techniques is presented. Candidate approaches for the next genertion of oscillator simulation techniques are reviewed. The method is presented which uses an e#cient and robust convolutionbased procedure to integrate frequencydomain modeling of ..."
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The current stateofthe art of oscillator simulation techniques is presented. Candidate approaches for the next genertion of oscillator simulation techniques are reviewed. The method is presented which uses an e#cient and robust convolutionbased procedure to integrate frequencydomain modeling of a distributed linear network in transient simulation. The impulse response of the entire linear distributed network is obtained and the algorithm presented herein ensures that aliasing e#ects are minimized by introducing a procedure that ensures that the interconnect network response is both timelimited and bandlimited. In particular, artificial filtering to bandlimit the response is not required. I. Introduction Large signal simulation of microwave oscillators is necessary to provide steadystate characterization of oscillator performance. Such quantities as power and harmonic content information are then readily available. This is particularly important in achieving first pass successf...