onset of cooperative entrainment in limit cycle oscillators with uniform all to all interactions bifurcation of the order function abstract the concept of order function was previously proposed as the key to a general theory of macroscopic mutual or cooperative entrainment in large populations of limit cycle oscillators with weak interactions such that every element is linked to all the other as well as with weakly dispersed intrinsic frequencies that is limit cycle oscillators that can be modeled by globally coupled phase oscillators with distributed frequencies following previous work a bifurcation theory of the order function is developed on the basis of its self consistent functional equation to elucidate in particular generic scaling behavior of such systems at the onset of cooperative entrainment among other results when the onset is not abrupt the critical exponent of fundamental order parameters turns out to generically differ from the conventional value 1 2 taken by the well studied sinusoidal coupling model as well as by typical mean fields models of thermodynamic phase transitions to which coupled oscillator models investigated here are analogous the theory also reveals what happens in nongeneric cases moreover a criterion is found of whether the bifurcation is normal or inverted all these analytical results and predictions are verified not only by numerically solving the equation of the order function but also by numerical simulations although this paper is mainly concerned with the critical behaviors noncritical regimes are also explored to demonstrate overall power of the order function theory by reproducing simulation results such as average frequency spectra the theory however keeps some room to be further generalized a finding which suggests this is put forth

synchronization in weighted scale free networks with degree degree correlation abstract we study synchronization phenomena in scale free networks of asymmetrically coupled dynamical systems featuring degree degree correlation in the topology of the connection wiring we show that when the interaction is dominant from the high degree to the low degree or from the low degree to the high degree nodes synchronization is enhanced for assortative or disassortative degree degree correlations

competition for synchronization in a phase oscillator system abstract a system of phase oscillators with a central oscillator co and a set of n peripheral oscillators pos is considered feed forward and feedback connections between the co and pos are determined by two interaction functions which are assumed to be smooth odd and periodic to describe the competition of pos for synchronization with the co we study the asymptotic stability of fixed points corresponding to in phase synchronization of a group of k pos while other pos are in anti phase with the co it is shown that stability conditions can be formulated in terms of four parameters that describe the slopes of the interaction functions at zero and half period points analytical description of stability in terms of the regions in 4 dimensional parameter space is given combining stability analysis with the detailed study of geometry of invariant manifolds the bifurcations of fixed points are investigated we show that various dynamical regimes such as multistability heteroclinic orbits and chaos are possible analytical stability conditions for global synchronization of pos with the co are formulated for the systems with local connections between pos it is shown that synchronization in a large system with local connections becomes unstable even under weak desynchronizing influence from the co the application of the results to modeling in neuroscience and in particular for modeling visual attention is discussed

a confidence limit for the empirical mode decomposition and hilbert spectral analysis the confidence limit is a standard measure of the accuracy of the result in any statistical analysis most of the confidence limits are derived as follows the data are first divided into subsections and then under the ergodic assumption the temporal mean is substituted for the ensemble mean next the confidence limit is defined as a range of standard deviations from this mean however such a confidence limit is valid only for linear and stationary processes furthermore in order for the ergodic assumption to be valid the subsections have to be statistically independent for non stationary and nonlinear processes such an analysis is no longer valid the confidence limit of the method here termed emd hsa for empirical mode decomposition hilbert spectral analysis is introduced by using various adjustable stopping criteria in the sifting processes of the emd step to generate a sample set of intrinsic mode functions imfs the emd technique acts as a pre processor for hsa on the original data producing a set of components imfs from the original data that equal the original data when added back together each imf represents a scale in the data from smallest to largest the ensemble mean and standard deviation of the imf sample sets obtained with different stopping criteria are calculated and these form a simple random sample set the confidence limit for emd hsa is then defined as a range of standard deviations from the ensemble mean without evoking the ergodic assumption subdivision of the data stream into short sections is unnecessary hence the results and the confidence limit retain the full frequency resolution of the full dataset this new confidence limit can be applied to the analysis of nonlinear and non stationary processes by these new techniques data from length of day measurements and a particularly violent recent earthquake are used to demonstrate how the confidence limit is obtained and applied by providing a confidence limit for this new approach a stable range of stopping criteria for the decomposition or sifting phase emd has been established making the results of the final processing with hsa and the entire emd hsa method more definitive

physics based foundation for empirical mode decomposition we study the correspondence between analytical and empirical slow flow analyses given a sufficiently dense set of sensors measured time series recorded throughout a mechanical or structural system contains all information regarding the dynamics of that system empirical mode decomposition is a useful tool for decomposing the measured time series in terms of intrinsic mode functions which are oscillatory modes embedded in the data that fully reproduce the time series the equivalence of responses of the analytical slow flow models and the dominant intrinsic mode functions derived from empirical mode decomposition provides a physics based theoretical foundation for empirical mode decomposition which currently is performed formally in an ad hoc fashion to demonstrate correspondence between analytical and empirical slow flows we derive appropriate mathematical expressions governing the empirical slow flows and based on analyticity conditions several nonlinear dynamical systems are considered to demonstrate this correspondence and the agreement between the analytical and empirical slow dynamics proves the assertion

a fast approximation of the bilateral filter using a signal processing approach the bilateral filter is a nonlinear filter that smoothes a signal while preserving strong edges it has demonstrated great effectiveness for a variety of problems in computer vision and computer graphics and fast versions have been proposed unfortunately little is known about the accuracy of such accelerations in this paper we propose a new signal processing analysis of the bilateral filter which complements the recent studies that analyzed it as a pde or as a robust statistical estimator the key to our analysis is to express the filter in a higher dimensional space where the signal intensity is added to the original domain dimensions importantly this signal processing perspective allows us to develop a novel bilateral filtering acceleration using downsampling in space and intensity this affords a principled expression of accuracy in terms of bandwidth and sampling the bilateral filter can be expressed as linear convolutions in this augmented space followed by two simple nonlinearities this allows us to derive criteria for downsampling the key operations and achieving important acceleration of the bilateral filter we show that for the same running time our method is more accurate than previous acceleration techniques typically we are able to process a 2 megapixel image using our acceleration technique in less than a second and have the result be visually similar to the exact computation that takes several tens of minutes the acceleration is most effective with large spatial kernels furthermore this approach extends naturally to color images and cross bilateral filtering

hopf bifurcation with cubic symmetry and instability of abc flow we examine the dynamics of generic hopf bifurcation in a system that is symmetric under the action of the rotational symmetries of the cube we classify the generic branches of periodic solutions at bifurcation there are generically 27 branches corresponding to maximal symmetries organized into five symmetry types there are also up to 22 periodic solution branches of two other symmetry types these results are found by examination of the normal form with s 1 normal form symmetry for the bifurcation truncated at the third order in addition to the periodic branches whose branching and stability we find there are several branches of tori homoclinic bifurcations and chaotic attractors in the dynamics of the third order normal form since many of these features are not amenable to analysis we give some numerical examples on breaking the normal form symmetry there may be breakup of the branches of tori but the predictions for the periodic solutions will be reliable for the navier stokes equations with a particular forcing an abc flow is a dynamically stable solution for small reynolds numbers r for the most symmetric case a b c 1 the first instability of this system is a hopf bifurcation at r 13 04 with rotational symmetry of the cube we use our normal form analysis to explain the observed behaviour of solutions at this primary instability numerical simulations show that there is supercritical branching to rotating waves that alternate between the three axes which undergo secondary hopf bifurcation to a 2 torus at approximately r 13 09 the eight symmetrically related tori break up and then merge to form a chaotic attractor with full symmetry we can explain all these features by use of the generic third order normal form and s 1 normal form symmetry breaking terms

desynchronization transitions in nonlinearly coupled phase oscillators abstract we consider the nonlinear extension of the kuramoto model of globally coupled phase oscillators where the phase shift in the coupling function depends on the order parameter a bifurcation analysis of the transition from fully synchronous state to partial synchrony is performed we demonstrate that for small ensembles it is typically mediated by stable cluster states that disappear with creation of heteroclinic cycles while for a larger number of oscillators a direct transition from full synchrony to a periodic or a quasiperiodic regime occurs

the empirical mode decomposition and the hilbert spectrum for nonlinear and non stationary time series analysis a new method for analysing nonlinear and non stationary data has been developed the key part of the method is the empirical mode decomposition method with which any complicated data set can be dec

emd revisited a new understanding of the envelope and resolving the mode mixing problem in am fm signals empirical mode decomposition emd is an adaptive and data driven approach for analyzing multicomponent nonlinear and nonstationary signals the stop criterion envelope technique and mode mixing problem are the most important topics that need to be addressed in order to improve the emd algorithm in this paper we study the envelope technique and the mode mixing problem caused by separating multicomponent am fm signals with the emd algorithm we present a new necessary condition on the envelope that questions the current assumption that the envelope passes through the extreme points of an intrinsic mode function imf then we present a solution to the mode mixing problem that occurs when multicomponent am fm signals are separated we experiment on several signals including simulated signals and real life signals to demonstrate the efficacy of the proposed method in resolving the mode mixing problem

dynamics of a globally coupled oscillator array abstract we study a set of n globally coupled ordinary differential equations of the form encountered in circuit analysis of superconducting josephson junction arrays particular attention is paid to two kinds of simple time periodic behavior known as in phase and splay phase states some results valid for general n as well as further results for n 2 and n are presented a recurring theme is the appearance of very weak dynamics near the periodic states the implications for josephson junction arrays are discussed

identification of weakly nonlinearities in multiple coupled oscillators this paper considers the analysis of free nonlinear response of multi degree of freedom mdof vibration systems demonstrating that system skeleton curves are significantly changed in the presence of coupling the hilbert transform vibration decomposition together with the modal spatial coordinate transform allow precise identification of initial nonlinear characteristics

nonlinear vibration characterization by signal decomposition abstract methods for nonlinear vibration characterization by decomposing dynamic responses using the hilbert huang transform and a sliding window fitting technique are presented numerical results show that hilbert huang transform can be used for decomposing nonlinear non stationary signals in order to reveal and estimate nonlinear effects major nonlinear phenomena that can be extracted from transient and or steady state dynamic responses include different nonlinearities softening and hardening effects intrawave amplitude and phase modulation distorted harmonic responses under a single frequency harmonic excitation interwave amplitude and phase modulation and multiple mode vibrations caused by internal external resonances however the discontinuity induced gibbs phenomenon makes hilbert huang transform analysis inaccurate around the two data ends on the other hand the sliding window fitting analysis has no gibbs phenomenon at the two data ends but it cannot extract accurate modulation frequencies due to the use of non orthogonal basis functions in the sliding window least squares curve fitting process

bifurcations in phase oscillator networks with a central element abstract a system of phase oscillators with identical natural frequencies and the star like architecture of connections is considered interaction functions are described by two terms of fourier expansion bifurcation analysis of small systems containing 3 or 4 oscillators has been performed the results are summarized in bifurcation diagrams that provide a full description of the boundaries between regions with different dynamics and the types of bifurcations that lead to the changes in the topology of phase space the bifurcations include changes of fixed point stability and formation destruction of limit and heteroclinic cycles for the system with 4 oscillators chaotic behaviour has been investigated the results can be useful to control system dynamics through an appropriate choice and variation of parameter values the generalization of the results to the systems with an arbitrary number of oscillators and application of the results in computational neuroscience are discussed

on the non linear stability of the 1 1 1 abc flow abstract abc flows which can be considered as prototypes for the study of the onset of three dimensional spatio temporal turbulence are known both analytically and numerically to be linearly unstable we analyze the nonlinear evolution of the abc flow a 1 with a b c 1 and with characteristic wavenumber k0 1 in the interval of reynolds number 13 r 50 we solve numerically the forced navier stokes equations with periodic boundary conditions for up to 9 9 104 eddy turnover times bifurcations towards progressively more complex flows obtain with a relaminarization window loss of symmetries and chaotic oscillations probably revealing an underlying heteroclinic structure in the chaotic regime only three steady solutions emerge besides a1 they consist of a perturbed abc flow a 2 with a b c plus cyclic permutations at 23 r 50 an unstructured temporal chaos is observed with the flow still dominated by the largest scales

bifurcation to heteroclinic cycles and sensitivity in three and four coupled phase oscillators abstract we study the bifurcation and dynamical behaviour of the system of n globally coupled identical phase oscillators introduced by hansel mato and meunier in the cases n 3 and n 4 this model has been found to exhibit robust slow switching oscillations that are caused by the presence of robust heteroclinic attractors this paper presents a bifurcation analysis of the system in an attempt to better understand the creation of such attractors we consider bifurcations that occur in a system of identical oscillators on varying the parameters in the coupling function these bifurcations preserve the permutation symmetry of the system we then investigate the implications of these bifurcations for the sensitivity to detuning i e the size of the smallest perturbations that give rise to loss of frequency locking for n 3 we find three types of heteroclinic bifurcation that are codimension one with symmetry on varying two parameters in the coupling function we find three curves giving a an s 3 transcritical homoclinic bifurcation b a saddle node heteroclinic bifurcation and c a z 3 heteroclinic bifurcation we also identify several global bifurcations with symmetry that organize the bifurcation diagram these are codimension two with symmetry for n 4 oscillators we determine many but not all codimension one bifurcations with symmetry including those that lead to a robust heteroclinic cycle a robust heteroclinic cycle is stable in an open region of parameter space and unstable in another open region furthermore we verify that there is a subregion where the heteroclinic cycle is the only attractor of the system while for other parts of the phase plane it can coexist with stable limit cycles we finish with a discussion of bifurcations that appear for this coupling function and general n as well as for more general coupling functions

efficient and robust specular highlight removal a robust and effective specular highlight removal method is proposed in this paper it is based on a key observation the maximum fraction of the diffuse colour component in diffuse local patches in colour images changes smoothly the specular pixels can thus be treated as noise in this case this property allows the specular highlights to be removed in an image denoising fashion an edge preserving low pass filter e g the bilateral filter can be used to smooth the maximum fraction of the colour components of the original image to remove the noise contributed by the specular pixels recent developments in fast bilateral filtering techniques enable the proposed method to run over 200 times faster than state of the art techniques on a standard cpu and differentiates it from previous work

a study of the characteristics of white noise using the empirical mode decomposition method based on numerical experiments on white noise using the empirical mode decomposition emd method we find empirically that the emd is effectively a dyadic filter the intrinsic mode function imf components are all normally distributed and the fourier spectra of the imf components are all identical and cover the same area on a semi logarithmic period scale expanding from these empirical findings we further deduce that the product of the energy density of imf and its corresponding averaged period is a constant and that the energy density function is chi squared distributed furthermore we derive the energy density spread function of the imf components through these results we establish a method of assigning statistical significance of information content for imf components from any noisy data southern oscillation index data are used to illustrate the methodology developed here

constants of motion for superconducting josephson arrays abstract we show that series arrays of n identical overdamped josephson junctions have extremely degenerate dynamics in particular we prove that such arrays have n 3 constants of motion for all n 3 the analysis is based on a coordinate transformation that reduces the governing equations to an n 3 parameter family of low dimensional systems in the weak coupling limit the reduced equations can be analyzed completely either all solutions approach the synchronous state or they converge to a continuous family of incoherent oscillations depending on a certain parameter value at the transitional value of this parameter the system becomes completely integrable then the phase space is foliated by invariant two dimensional tori for any n 3 the infinite n limit of the system is an integro partial differential equation with rigorously low dimensional dynamics it supports solitons in the integrable case and chaotic waves in the non integrable case

averaging of globally coupled oscillators abstract we study a specific system of symmetrically coupled oscillators using the method of averaging the equations describe a series array of josephson junctions we concentrate on the dynamics near the splay phase state also known as the antiphase state ponies on a merry go round or rotating wave we calculate the floquet exponents of the splay phase periodic orbit in the weak coupling limit and find that all of the floquet exponents are purely imaginary in fact all the floquet exponents are zero except for a single complex conjugate pair thus nested two tori of doubly periodic solutions surround the splay phase state in the linearized averaged equations we numerically integrate the original system and find startling agreement with the averaging results on two counts the observed ratio of frequencies is very close to the prediction and the solutions of the full equations appear to be either periodic or doubly periodic as they are in the averaged equations such behavior is quite surprising from the point of view of generic dynamical systems theory one expects higher dimensional tori and chaotic solutions we show that the functional form of the equations and not just their symmetry is responsible for this nongeneric behavior

separating reflection components of textured surfaces using a single image in inhomogeneous objects highlights are linear combinations of diffuse and specular reflection components to our knowledge all methods that use a single input image require explicit color segmentation to deal with multicolored surfaces unfortunately for complex textured images current color segmentation algorithms are still problematic to segment correctly consequently a method without explicit color segmentation becomes indispensable and this work presents such a method the method is based solely on colors particularly chromaticity without requiring any geometrical information one of the basic ideas is to iteratively compare the intensity logarithmic differentiation of an input image and its specular free image a specular free image is an image that has exactly the same geometrical profile as the diffuse component of the input image and that can be generated by shifting each pixel s intensity and maximum chromaticity nonlinearly unlike existing methods using a single image all processes in the proposed method are done locally involving a maximum of only two neighboring pixels this local operation is useful for handling textured objects with complex multicolored scenes evaluations by comparison with the results of polarizing filters demonstrate the effectiveness of the proposed method