Showing papers by "Edward Ott published in 2010"
TL;DR: A flexible and modular delayed-feedback nonlinear oscillator that is capable of generating a wide range of dynamical behaviours, from periodic oscillations to high-dimensional chaos is described and a new adaptive control method is demonstrated that keeps two oscillators synchronized, even when the coupling between them is changing unpredictably.
Abstract: We describe a flexible and modular delayed-feedback nonlinear oscillator that is capable of generating a wide range of dynamical behaviours, from periodic oscillations to high-dimensional chaos. The oscillator uses electro-optic modulation and fibre-optic transmission, with feedback and filtering implemented through real-time digital signal processing. We consider two such oscillators that are coupled to one another, and we identify the conditions under which they will synchronize. By examining the rates of divergence or convergence between two coupled oscillators, we quantify the maximum Lyapunov exponents or transverse Lyapunov exponents of the system, and we present an experimental method to determine these rates that does not require a mathematical model of the system. Finally, we demonstrate a new adaptive control method that keeps two oscillators synchronized, even when the coupling between them is changing unpredictably.
76 citations
TL;DR: In this article, a general class of problems involving the evolution of large systems of globally coupled phase oscillators was considered and it was shown that the solutions to these problems are time asymptotically attracted toward a reduced manifold of system states (denoted M).
Abstract: A previous paper (arXiv:0902.2773, henceforth referred to as I) considered a general class of problems involving the evolution of large systems of globally coupled phase oscillators. It was shown there that, in an appropriate sense, the solutions to these problems are time asymptotically attracted toward a reduced manifold of system states (denoted M). This result has considerable utility in the analysis of these systems, as has been amply demonstrated in recent papers. In this note, we show that the analysis of I can be modified in a simple way that establishes significant extensions of the range of validity of our previous result. In particular, we generalize I in the following ways: (1) attraction to M is now shown for a very general class of oscillator frequency distribution functions g(\omega), and (2) a previous restriction on the allowed class of initial conditions is now substantially relaxed.
62 citations
TL;DR: It is shown that a suitably averaged value of the impedance can be computed from short ray trajectories in wave-chaotic systems open to outside scattering channels and that this can improve the ability to describe the statistical properties of the scattering systems.
Abstract: Predicting the statistics of realistic wave-chaotic scattering systems requires, in addition to random matrix theory, introduction of system-specific information. This paper investigates experimentally one aspect of system-specific behavior, namely, the effects of short ray trajectories in wave-chaotic systems open to outside scattering channels. In particular, we consider ray trajectories of limited length that enter a scattering region through a channel (port) and subsequently exit through a channel (port). We show that a suitably averaged value of the impedance can be computed from these trajectories and that this can improve the ability to describe the statistical properties of the scattering systems. We illustrate and test these points through experiments on a realistic two-port microwave scattering billiard.
56 citations
TL;DR: This model for oscillators, which adapt both their phases and frequencies, naturally reproduces some observed phenomena that are not qualitatively produced by the standard Kuramoto model, such as long waiting times before the synchronization of clapping audiences.
Abstract: We study the synchronization of Kuramoto oscillators with all-to-all coupling in the presence of slow, noisy frequency adaptation. In this paper, we develop a model for oscillators, which adapt both their phases and frequencies. It is found that this model naturally reproduces some observed phenomena that are not qualitatively produced by the standard Kuramoto model, such as long waiting times before the synchronization of clapping audiences. By assuming a self-consistent steady state solution, we find three stability regimes for the coupling constant $k$, separated by critical points ${k}_{1}$ and ${k}_{2}$: (i) for $kl{k}_{1}$ only the stable incoherent state exists; (ii) for $kg{k}_{2}$, the incoherent state becomes unstable and only the synchronized state exists; and (iii) for ${k}_{1}lkl{k}_{2}$ both the incoherent and synchronized states are stable. In the bistable regime spontaneous transitions between the incoherent and synchronized states are observed for finite ensembles. These transitions are well described as a stochastic process on the order parameter $r$ undergoing fluctuations due to the system's finite size, leading to the following conclusions: (a) in the bistable regime, the average waiting time of an $\text{incoherent}\ensuremath{\rightarrow}\text{coherent}$ transition can be predicted by using Kramer's escape time formula and grows exponentially with the number of oscillators; (b) when the incoherent state is unstable $(kg{k}_{2})$, the average waiting time grows logarithmically with the number of oscillators.
55 citations
TL;DR: It is shown that the average impedance matrix, which characterizes such system-specific properties, can be semiclassically calculated in terms of ray trajectories between ports.
Abstract: Prediction of the statistics of scattering in typical wave-chaotic systems requires combining system-specific information with universal aspects of chaotic scattering as described by random matrix theory. This Rapid Communication shows that the average impedance matrix, which characterizes such system-specific properties, can be semiclassically calculated in terms of ray trajectories between ports. Theoretical predictions are compared with experimental results for a microwave billiard, demonstrating that the theory successfully uncovered universal statistics of wave-chaotic scattering systems.
38 citations
TL;DR: In this paper, the authors present a deterministic continuum model of flocking and use it to investigate the linearized response of an infinite extent flock to an obstacle or an attacking predator, showing that the steady-state flock response is in the form of density disturbances that resemble Mach cones whose configuration is determined by the anisotropic propagation of waves through the flock.
33 citations
TL;DR: In this article, an extension of the master stability function (MSF) was developed to study the stability of chaotic systems with adaptive couplings in the presence of a priori unknown slow temporal drift in the couplings.
Abstract: In past works, various schemes for adaptive synchronization of chaotic systems have been proposed. The stability of such schemes is central to their utilization. As an example addressing this issue, we consider a recently proposed adaptive scheme for maintaining the synchronized state of identical coupled chaotic systems in the presence of a priori unknown slow temporal drift in the couplings. For this illustrative example, we develop an extension of the master stability function technique to study synchronization stability with adaptive coupling. Using this formulation, we examine the local stability of synchronization for typical chaotic orbits and for unstable periodic orbits within the synchronized chaotic attractor (bubbling). Numerical experiments illustrating the results are presented. We observe that the stable range of synchronism can be sensitively dependent on the adaptation parameters, and we discuss the strong implication of bubbling for practically achievable adaptive synchronization. We also find that for our coupled systems with adaptation, bubbling can be caused by a slow temporal drift in the coupling strength.
28 citations
TL;DR: In this paper, classical analogs of the quantum mechanical concepts of the Loschmidt Echo and quantum fidelity are developed with the goal of detecting small perturbations in a closed wave chaotic region.
Abstract: Classical analogs of the quantum mechanical concepts of the Loschmidt Echo and quantum fidelity are developed with the goal of detecting small perturbations in a closed wave chaotic region. Sensing techniques that employ a one-recording-channel time-reversal-mirror, which in turn relies on time reversal invariance and spatial reciprocity of the classical wave equation, are introduced. In analogy with quantum fidelity, we employ scattering fidelity techniques which work by comparing response signals of the scattering region, by means of cross correlation and mutual information of signals. The performance of the sensing techniques is compared for various perturbations induced experimentally in an acoustic resonant cavity. The acoustic signals are parametrically processed to mitigate the effect of dissipation and to vary the spatial diversity of the sensing schemes. In addition to static boundary condition perturbations at specified locations, perturbations to the medium of wave propagation are shown to be detectable, opening up various real world sensing applications in which a false negative cannot be tolerated.
19 citations
TL;DR: In this paper, a technique for achieving and maintaining a global state of identical synchrony of an arbitrary network of chaotic oscillators even when the coupling strengths are unknown and time-varying is presented.
Abstract: We present and experimentally demonstrate a technique for achieving and maintaining a global state of identical synchrony of an arbitrary network of chaotic oscillators even when the coupling strengths are unknown and time-varying. At each node an adaptive synchronization algorithm dynamically estimates the current strength of the net coupling signal to that node. We experimentally demonstrate this scheme in a network of three bidirectionally coupled chaotic optoelectronic feedback loops and we present numerical simulations showing its application in larger networks. The stability of the synchronous state for arbitrary coupling topologies is analyzed via a master stability function approach.
16 citations
TL;DR: In this paper, the role played by chaotic wave dynamics in the propagation of information and the resulting impact on forecasts was investigated using numerical experiments on a toy atmospheric model introduced by Lorenz in 2005, and it was found that the spatial correlation function obtained at each forecast cycle by averaging over the background ensemble members is short-range.
Abstract: Several localized versions of the ensemble Kalman filter have been proposed. Although tests applying such schemes have proven them to be extremely promising, a full basic understanding of the rationale and limitations of localization is currently lacking. It is one of the goals of this paper to contribute toward addressing this issue. The second goal is to elucidate the role played by chaotic wave dynamics in the propagation of information and the resulting impact on forecasts. To accomplish these goals, the principal tool used here will be analysis and interpretation of numerical experiments on a toy atmospheric model introduced by Lorenz in 2005. Propagation of the wave packets of this model is shown. It is found that, when an ensemble Kalman filter scheme is employed, the spatial correlation function obtained at each forecast cycle by averaging over the background ensemble members is short ranged, and this is in strong contrast to the much longer range correlation function obtained by averagin...
10 citations
TL;DR: A discrete time map model is considered for the study of the effects of noise, oscillation frequency diversity, and network topology, particularly community structure in synchronization of many coupled oscillators.
Abstract: Synchronization of many coupled oscillators is a generic issue in a wide variety of natural situations. We consider a discrete time map model for the study of such problems. Issues addressed include the effects of noise, oscillation frequency diversity, and network topology, particularly community structure.
TL;DR: In this paper, classical analogs of the quantum mechanical concepts of the Loschmidt Echo and quantum fidelity are developed with the goal of detecting small perturbations in a closed wave chaotic region.
Abstract: Classical analogs of the quantum mechanical concepts of the Loschmidt Echo and quantum fidelity are developed with the goal of detecting small perturbations in a closed wave chaotic region. Sensing techniques that employ a one-recording-channel time-reversal-mirror, which in turn relies on time reversal invariance and spatial reciprocity of the classical wave equation, are introduced. In analogy with quantum fidelity, we employ Scattering Fidelity techniques which work by comparing response signals of the scattering region, by means of cross correlation and mutual information of signals. The performance of the sensing techniques is compared for various perturbations induced experimentally in an acoustic resonant cavity. The acoustic signals are parametrically processed to mitigate the effect of dissipation and to vary the spatial diversity of the sensing schemes. In addition to static boundary condition perturbations at specified locations, perturbations to the medium of wave propagation are shown to be detectable, opening up various real world sensing applications in which a false negative cannot be tolerated.
Journal Article•
TL;DR: In this article, classical analogs of the quantum mechanical concepts of the Loschmidt Echo and quantum fidelity are developed with the goal of detecting small perturbations in a closed wave chaotic region.
Abstract: Classical analogs of the quantum mechanical concepts of the Loschmidt Echo and quantum fidelity are developed with the goal of detecting small perturbations in a closed wave chaotic region. Sensing techniques that employ a one-recording-channel time-reversal-mirror, which in turn relies on time reversal invariance and spatial reciprocity of the classical wave equation, are introduced. In analogy with quantum fidelity, we employ scattering fidelity techniques which work by comparing response signals of the scattering region, by means of cross correlation and mutual information of signals. The performance of the sensing techniques is compared for various perturbations induced experimentally in an acoustic resonant cavity. The acoustic signals are parametrically processed to mitigate the effect of dissipation and to vary the spatial diversity of the sensing schemes. In addition to static boundary condition perturbations at specified locations, perturbations to the medium of wave propagation are shown to be detectable, opening up various real world sensing applications in which a false negative cannot be tolerated. © 2010 American Institute of Physics. doi:10.1063/1.3518047
12 Oct 2010
TL;DR: In this paper, an extension of the previously developed Random Coupling Model statistical description of wave coupling into enclosures to describe the coupling through apertures, coupling to mixed systems for which only part of the ray phase space is chaotic, and coupling to systems of systems in which the components have varying degrees of isolation, for example chains of cavities.
Abstract: : We performed research in the field of electromagnetic wave chaos and High Power Microwave (HPM) effects in electronic systems. Our emphasis was on issues likely to be most relevant to the coupling of electromagnetic radiation into systems and its effects on systems, as in electromagnetic attacks of military electronics.. Our program addressed the following issues of relevance to the understanding of HPM effects on electronic systems: The extension of the previously developed Random Coupling Model statistical description of wave coupling into enclosures to describe a) the coupling through apertures, b) the coupling to mixed systems for which only part of the ray phase space is chaotic, and c) the coupling to systems of systems in which the components have varying degrees of isolation, for example chains of cavities. The further development of time domain models for the response of systems excited by pulses of wave energy, including nonlinear effects The Extension of HPM upset experimentation and modeling to complex networks of interconnected circuits. Our aim is to develop a generalized approach for modeling HPM effects in electronic circuits, systems and infrastructures. Examination of fading, power-delay profiles, and small-signal discrimination in reverberant electromagnetic environments containing short-ray trajectories.