synchronized chaotic intermittent and spiking behavior in coupled map chains we study phase synchronization effects in a chain of nonidentical chaotic oscillators with a type i intermittent behavior two types of parameter distribution linear and random are considered the typical phenomena are the onset and existence of global all to all and cluster partial synchronization with increase of coupling increase of coupling strength can also lead to desynchronization phenomena i e global or cluster synchronization is changed into a regime where synchronization is intermittent with incoherent states then a regime of a fully incoherent nonsynchronous state spatiotemporal intermittency appears synchronization desynchronization transitions with increase of coupling are also demonstrated for a system resembling an intermittent one a chain of coupled maps replicating the spiking behavior of neurobiological networks

partial synchronization from symmetry towards stability abstract in this paper we study the existence and stability of linear invariant manifolds in a network of coupled identical dynamical systems symmetry under permutation of different units of the network is helpful to construct explicit formulae for linear invariant manifolds of the network in order to classify them and to examine their stability through lyapunov s direct method

stability of weak solutions to equations of magnetohydrodynamics with lebesgue initial data abstract we prove the existence the uniqueness and the lipschitz continuous dependence on the initial data of global weak solutions to equations of magnetohydrodynamics mhd with the initial data in the lebesgue spaces

temporal autocorrelation in univariate linear modeling of fmri data in functional magnetic resonance imaging statistical analysis there are problems with accounting for temporal autocorrelations when assessing change within voxels techniques to date have utilized temporal filtering strategies to either shape these autocorrelations or remove them shaping or coloring attempts to negate the effects of not accurately knowing the intrinsic autocorrelations by imposing known autocorrelation via temporal filtering removing the autocorrelation or prewhitening gives the best linear unbiased estimator assuming that the autocorrelation is accurately known for single event designs the efficiency of the estimator is considerably higher for prewhitening compared with coloring however it has been suggested that sufficiently accurate estimates of the autocorrelation are currently not available to give prewhitening acceptable bias to overcome this we consider different ways to estimate the autocorrelation for use in prewhitening after high pass filtering is performed a tukey taper set to smooth the spectral density more than would normally be used in spectral density estimation performs best importantly estimation is further improved by using nonlinear spatial filtering to smooth the estimated autocorrelation but only within tissue type using this approach when prewhitening reduced bias to close to zero at probability levels as low as 1 x 10 5

robust bayesian general linear models we describe a bayesian learning algorithm for robust general linear models rglms the noise is modeled as a mixture of gaussians rather than the usual single gaussian this allows different data points to be associated with different noise levels and effectively provides a robust estimation of regression coefficients a variational inference framework is used to prevent overfitting and provides a model order selection criterion for noise model order this allows the rglm to default to the usual glm when robustness is not required the method is compared to other robust regression methods and applied to synthetic data and fmri

partial synchronization in coupled chemical chaotic oscillators in this paper we investigate the problem of partial synchronization in diffusively coupled chemical chaotic oscillators with zero flux boundary conditions the dynamical properties of the chemical system which oscillates with uniform phase evolution yet has chaotic amplitudes upca are first discussed by combining numerical and analytical methods the impossibility of full global synchronization in a network of two or three coupled chemical oscillators is discovered mathematically stable partial synchronization corresponds to convergence to a linear invariant manifold of the global state space the sufficient conditions for exponential stability of the invariant manifold in a network of three coupled chemical oscillators are obtained via the nonlinear contraction principle

outlier detection and robust regression for correlated data abstract outlier detection has attracted considerable interest in various areas existing outlier detection methods usually assume independence of the modeling errors among the data points but this assumption does not hold in a number of applications in this paper we propose a probabilistic method for outlier detection and robust updating of linear regression problems involving correlated data first suspicious data points will be identified using the minimum volume ellipsoid method and the maximum trimmed likelihood method then the outlierness of each suspicious data point will be determined according to the proposed outlier probability in consideration of possible correlation among the data points the proposed method is assessed and validated through simulated and real data

synchronization of impacting mechanical systems with a single constraint abstract this paper addresses the synchronization problem of mechanical systems subjected to a single geometric unilateral constraint the impacts of the individual systems induced by the unilateral constraint generally do not coincide even if the solutions are arbitrarily close to each other the mismatch in the impact time instants demands a careful choice of the distance function to allow for an intuitively correct comparison of the discontinuous solutions resulting from the impacts we propose a distance function induced by the quotient metric which is based on an equivalence relation using the impact map the distance function obtained in this way is continuous in time when evaluated along jumping solutions the property of maximal monotonicity which is fulfilled by most commonly used impact laws is used to significantly reduce the complexity of the distance function based on the simplified distance function a lyapunov function is constructed to investigate the synchronization problem for two identical one dimensional mechanical systems sufficient conditions for the uncoupled individual systems are provided under which local synchronization is guaranteed furthermore we present an interaction law which ensures global synchronization also in the presence of grazing trajectories and accumulation points zeno behavior the results are illustrated using numerical examples of a 1 dof mechanical impact oscillator which serves as stepping stone in the direction of more general systems

global solutions of nonlinear magnetohydrodynamics with large initial data a free boundary problem for nonlinear magnetohydrodynamics with general large initial data is investigated the existence uniqueness and regularity of global solutions are established with large initial data in h1 it is shown that neither shock waves nor vacuum and concentration in the solutions are developed in a finite time although there is a complex interaction between the hydrodynamic and magnetodynamic effects an existence theorem of global solutions with large discontinuous initial data is also established

symmetry invariance of multiagent formations in self pursuit structure in the interconnection topology among individuals of a multiagent system plays a fundamental role in the system s steady state and transient behaviors this paper explores how certain interconnection topologies influence symmetry in a multiagent system s trajectories it is shown how circulant connectivity preserves rotation and in particular instances dihedral group symmetries in a formation of locally interacting planar integrators moreover it is revealed to what extent circulant connectivity is also necessary in order that symmetric formations remain symmetric under the multiagent system s dynamics

synchronization conditions and desynchronizing patterns in coupled limit cycle and chaotic systems many coupling schemes for both limit cycle and chaotic systems involve adding linear combinations of dynamical variables from various oscillators in an array of identical oscillators to each oscillator node of the array examples of such couplings are nearest neighbor diffusive coupling all to all coupling star coupling and random linear couplings we show that for a given oscillator type and a given choice of oscillator variables to use in the coupling arrangement the stability of each linear coupling scheme can be calculated from the stability of any other for symmetric coupling schemes in particular when there are desynchronization bifurcations our approach reveals interesting patterns and relations between desynchronous modes including the situation in which for some systems there is a limit on the number of oscillators that can be coupled and still retain synchronous chaotic behavior

cluster synchronization in directed networks of partial state coupled linear systems under pinning control this paper investigates the cluster synchronization for network of linear systems via a generalized pinning control strategy which allows the network of each cluster to take relaxed topological structure for the case with fixed topology it is shown that a feasible feedback controller can be designed to achieve the given cluster synchronization pattern if the induced network topology of each cluster has a directed spanning tree and further compared to the couplings among different clusters the couplings within the each cluster are sufficiently strong an extra balanced condition is imposed on the network topology of each cluster to allow for the cluster synchronization under arbitrary switching network topologies such a balanced condition can be removed via the use of dwell time technique for all the cases the lower bounds for such strengths of couplings within each cluster that secure the synchronization as well as cluster synchronization rate are explicitly specified finally some illustrative examples are provided to demonstrate the effectiveness of the theoretical findings

non linear elliptic and parabolic equations involving measure data in this paper we prove the existence of solutions for equations of the type div a du f in a bounded open set u 0 on where a is a possibly non linear function satisfying some coerciveness and monotonicity assumptions and f is a bounded measure we also consider the equation div a du g u f in u 0 on with f l1 or f m u u 0 and the parabolic equivalent of the first elliptic equation

on the unfolding of a blowout bifurcation abstract suppose a chaotic attractor a in an invariant subspace loses stability on varying a parameter at the point of loss of stability the most positive lyapunov exponent of the natural measure on a crosses zero at what has been called a blowout bifurcation we introduce the notion of an essential basin of an attractor a this is the set of points x such that accumulation points of the sequence of measures 1 n n 1 k 0 f k x are supported on a we characterise supercritical and subcritical scenarios according to whether the lebesgue measure of the essential basin of a is positive or zero we study a drift diffusion model and a model class of piecewise linear mappings of the plane in the supercritical case we find examples where a lyapunov exponent of the branch of attractors may be positive hyperchaos or negative depending purely on the dynamics far from the invariant subspace for the mappings we find asymptotically linear scaling of lyapunov exponents average distance from the subspace and basin size on varying a parameter we conjecture that these are general characteristics of blowout bifurcations

networks of diffusively time delay coupled systems conditions for synchronization and its relation to the network topology abstract we consider networks of time delayed diffusively coupled systems and relate conditions for synchronization of the systems in the network to the topology of the network first we present sufficient conditions for the solutions of the time delayed coupled systems to be bounded next we give conditions for local synchronization and we show that the values of the coupling strength and time delay for which there is local synchronization in any network can be determined from these conditions in addition we present results on global synchronization in relation to the network topology for networks of a class of nonlinear systems we illustrate our results with examples of synchronization in networks with fitzhugh nagumo model neurons and hindmarsh rose neurons

optimal periodic orbits of chaotic systems occur at low period invariant sets embedded in a chaotic attractor can generate time averages that differ from the average generated by typical orbits on the attractor motivated by two different topics namely controlling chaos and riddled basins of attraction we consider the question of which invariant set yields the largest optimal value of an average of a given smooth function of the system state we present numerical evidence and analysis that indicate that the optimal average is typically achieved by a low period unstable periodic orbit embedded in the chaotic attractor in particular our results indicate that if we consider that the function to be optimized depends on a parameter gamma then the lebesgue measure in gamma corresponding to optimal periodic orbits of period ital p or greater decreases exponentially with increasing ital p furthermore the set of parameter values for which optimal orbits are nonperiodic typically has zero lebesgue measure copyright ital 1996 the american physical society

general multilevel linear modeling for group analysis in fmri this article discusses general modeling of multisubject and or multisession fmri data in particular we show that a two level mixed effects model where parameters of interest at the group level are estimated from parameter and variance estimates from the single session level can be made equivalent to a single complete mixed effects model where parameters of interest at the group level are estimated directly from all of the original single sessions time series data if the co variance at the second level is set equal to the sum of the co variances in the single level form using the blue with known covariances this result has significant implications for group studies in fmri since it shows that the group analysis requires only values of the parameter estimates and their co variance from the first level generalizing the well established summary statistics approach in fmri the simple and generalized framework allows different prewhitening and different first level regressors to be used for each subject the framework incorporates multiple levels and cases such as repeated measures paired or unpaired t tests and f tests at the group level explicit examples of such models are given in the article using numerical simulations based on typical first level covariance structures from real fmri data we demonstrate that by taking into account lower level covariances and heterogeneity a substantial increase in higher level z score is possible

technical communique adaptive control for nonlinear nonnegative dynamical systems nonnegative and compartmental models are widespread in engineering systems and life sciences and play a key role in the understanding of these systems in this paper we develop a direct adaptive control framework for nonlinear uncertain nonnegative and compartmental dynamical systems the proposed framework is lyapunov based and guarantees partial asymptotic set point regulation that is asymptotic set point regulation with respect to part of the closed loop system states associated with the plant in addition the adaptive controller guarantees that the physical system states remain in the nonnegative orthant of the state space

robust group analysis using outlier inference neuroimaging group studies are typically performed with the assumption that subjects used are randomly drawn from a population of subjects the population of subjects is assumed to have a distribution of effect sizes associated with it that are gaussian distributed however in practice group studies can include outlier subjects whose effect sizes are completely at odds with the general population for reasons that are not of experimental interest if ignored these outliers can dramatically affect the inference results to solve this problem we propose a group inference approach which includes inference of outliers using a robust general linear model glm approach this approach models the errors as being a mixture of two gaussian distributions one for the normal population and one for the outliers crucially the robust glm is part of a traditional hierarchical group model which uses glms at each level of the hierarchy this combines the benefits of outlier inference with the benefits of using variance information from lower levels in the hierarchy a bayesian inference framework is used to infer on the robust glm while using the lower level variance information the performance of the method is demonstrated on simulated and fmri data and is compared with iterative reweighted least squares and permutation testing

a comprehensive review of group level model performance in the presence of heteroscedasticity can a single model control type i errors in the presence of outliers even after thorough preprocessing and a careful time series analysis of functional magnetic resonance imaging fmri data artifact and other issues can lead to violations of the assumption that the variance is constant across subjects in the group level model this is especially concerning when modeling a continuous covariate at the group level as the slope is easily biased by outliers various models have been proposed to deal with outliers including models that use the first level variance or that use the group level residual magnitude to differentially weight subjects the most typically used robust regression implementing a robust estimator of the regression slope has been previously studied in the context of fmri studies and was found to perform well in some scenarios but a loss of type i error control can occur for some outlier settings a second type of robust regression using a heteroscedastic autocorrelation consistent hac estimator which produces robust slope and variance estimates has been shown to perform well with better type i error control but with large sample sizes 500 1000 subjects the type i error control with smaller sample sizes has not been studied in this model and has not been compared to other modeling approaches that handle outliers such as fsl s flame 1 and fsl s outlier de weighting focusing on group level inference with a continuous covariate over a range of sample sizes and degree of heteroscedasticity which can be driven either by the within or between subject variability both styles of robust regression are compared to ordinary least squares ols fsl s flame 1 flame 1 with outlier de weighting algorithm and kendall s tau additionally subject omission using the cook s distance measure with ols and nonparametric inference with the ols statistic are studied pros and cons of these models as well as general strategies for detecting outliers in data and taking precaution to avoid inflated type i error rates are discussed

generation of clusters in complex dynamical networks via pinning control many real world networks show community structure i e groups or clusters of nodes that have a high density of links within them but with a lower density of links between them in this paper by applying feedback injections to a fraction of network nodes various clusters are synchronized independently according to the community structure generated by the group partition of the network cluster synchronization this control is achieved by pinning i e applying linear feedback control to a subset of the network nodes those pinned nodes are selected not randomly but according to the topological structure of communities of a given network specifically for a given group partition of a network those nodes with direct connections between groups must be pinned in order to achieve cluster synchronization both the local stability and global stability of cluster synchronization are investigated taking the tree shaped network and the most modular network as two particular examples we illustrate in detail how the pinning strategy influences the generation of clusters the simulations verify the efficiency of the pinning schemes used in this paper

blow up of smooth solutions to the compressible magnetohydrodynamic flows abstract in this paper we prove the blow up phenomena of smooth solutions to the cauchy problem for the full compressible magnetohydrodynamic equations and isentropic compressible magnetohydrodynamic equations with constant and degenerate viscosities under some restrictions on the initial data in particular our results do not require that the initial data have compact support or contain vacuum in any finite region

connection graph stability method for synchronized coupled chaotic systems this paper elucidates the relation between network dynamics and graph theory a new general method to determine global stability of total synchronization in networks with different topologies is proposed this method combines the lyapunov function approach with graph theoretical reasoning in this context the main step is to establish a bound on the total length of all paths passing through an edge on the network connection graph in particular the method is applied to the study of synchronization in rings of 2k nearest neighbor coupled oscillators a rigorous bound is given for the minimum coupling strength sufficient for global synchronization of all oscillators this bound is explicitly linked with the average path length of the coupling graph contrary to the master stability function approach developed by pecora and carroll the connection graph stability method leads to global stability of synchronization and it permits not only constant but also time dependent interaction coefficients in a companion paper blinking model and synchronization in small world networks with a time varying coupling see this issue this method is extended to the blinking model of small world networks where in addition to the fixed 2 k nearest neighbor interactions all the remaining links are rapidly switched on and off independently of each other

hierarchy and stability of partially synchronous oscillations of diffusively coupled dynamical systems the paper presents a qualitative analysis of an array of diffusively coupled identical continuous time dynamical systems the effects of full partial anti phase and in phase anti phase chaotic synchronization are investigated via the linear invariant manifolds of the corresponding differential equations existence of various invariant manifolds a self similar behavior a hierarchy and embedding of the manifolds of the coupled system are discovered sufficient conditions for the stability of the invariant manifolds are obtained via the method of lyapunov functions conditions under which full global synchronization can not be achieved even for the largest coupling constant are defined the general rigorous results are illustrated through examples of coupled lorenz like and coupled rossler systems

brief paper stability and robustness analysis of nonlinear systems via contraction metrics and sos programming a wide variety of stability and performance questions about linear dynamical systems can be reformulated as convex optimization problems involving linear matrix inequalities lmis these techniques have been recently extended to nonlinear systems with polynomial or rational dynamics through the use of sum of squares sos programming in this paper we further extend the class of systems that can be analyzed with convexity based methods we show how to analyze the robust stability properties of uncertain nonlinear systems with polynomial or rational dynamics via contraction analysis and sos programming since the existence of a global contraction metric is a sufficient condition for global stability of an autonomous system we develop an algorithm for finding such contraction metrics using sos programming the search process is made computationally tractable by relaxing matrix definiteness constraints the feasibility of which indicates the existence of a contraction metric to sos constraints on polynomial matrices we illustrate our results through examples from the literature and show how our contraction based approach offers advantages when compared with traditional lyapunov analysis

a contraction theory approach to stochastic incremental stability we investigate the incremental stability properties of ito stochastic dynamical systems specifically we derive a stochastic version of nonlinear contraction theory that provides a bound on the mean square distance between any two trajectories of a stochastically contracting system this bound can be expressed as a function of the noise intensity and the contraction rate of the noise free system we illustrate these results in the contexts of nonlinear observers design and stochastic synchronization

synchronization of networks of nonidentical euler lagrange systems with uncertain parameters and communication delays this paper addresses the problem of synchronizing networks of nonidentical nonlinear dynamical systems described by euler lagrange equations which are assumed fully actuated with their states available for measurement but with unknown parameters the only assumption made on the communication graph is that it is connected moreover the communication is subject to constant time delays which are also unknown the main result of the paper is the construction of an adaptive controller that achieves global full state synchronization i e the difference between the agents positions and velocities asymptotically converges to zero if a desired trajectory for all systems is given a slight modification to the proposed scheme achieves also full state synchronization simulations using a ten robot manipulator network are used to illustrate the performance of the proposed schemes

comparing probabilistic methods for outlier detection in linear models summary this paper compares the use of two posterior probability methods to deal with outliers in linear models we show that putting together diagnostics that come from the mean shift and variance shift models yields a procedure that seems to be more effective than the use of probabilities computed from the posterior distributions of actual realized residuals the relation of the suggested procedure to the use of a certain predictive distribution for diagnostics is derived two main procedures for outlier detection have emerged when using the bayesian approach the first of these confines itself to postulating a null model for the generation of the data and then seeks identification methods for outliers with no alternative model to the null entertained examples of work in the category are i use of the predictive distribution for detection ii using the posterior probabilities of various unobserved perturbations and iii looking at the change in a posterior of interest when some observations are deleted these methods will be discussed in 3 of this paper after the basic model is set out in 2 the second procedure takes into account an alternative model for the generation of a subset of the sample as examples various authors have proposed and utilized the mean shift model and the variance inflation model these methods are discussed in 4 of this paper we show in this paper that these procedures can be classified as those which identify outliers by looking at some functions of the predictive density ordinate and those that look at the posterior probabilities of the unobserved residuals the first seems to be effective in overcoming the problem of high leverage outliers in contrast to the latter where outliers are masked by high leverage these results are illustrated by examples in 5

controlling synchronous patterns in complex networks although the set of permutation symmetries of a complex network could be very large few of them give rise to stable synchronous patterns here we present a general framework and develop techniques for controlling synchronization patterns in complex network of coupled chaotic oscillators specifically according to the network permutation symmetry we design a small size and weighted network namely the control network and use it to control the large size complex network by means of pinning coupling we argue mathematically that for any of the network symmetries there always exists a critical pinning strength beyond which the unstable synchronous pattern associated to this symmetry can be stabilized the feasibility of the control method is verified by numerical simulations of both artificial and real world networks and demonstrated experimentally in systems of coupled chaotic circuits our studies show the controllability of synchronous patterns in complex networks of coupled chaotic oscillators

a re defined and generalized percent overlap of activation measure for studies of fmri reproducibility and its use in identifying outlier activation maps functional magnetic resonance imaging fmri is a popular noninvasive modality to investigate activation in the human brain the end result of most fmri experiments is an activation map corresponding to the given paradigm these maps can vary greatly from one study to the next so quantifying the reliability of identified activation over several fmri studies is important the percent overlap of activation rombouts et al 1998 machielsen et al 2000 is a global reliability measure between activation maps drawn from any two fmri studies a slightly modified but more intuitive measure is provided by the jaccard 1901 coefficient of similarity whose use we study in this paper a generalization of these measures is also proposed to comprehensively summarize the reliability of multiple fmri studies finally a testing mechanism to flag potentially anomalous studies is developed the methodology is illustrated on studies involving left and right hand motor task paradigms performed by a right hand dominant male subject several times over a period of two months with excellent results

semi passivity and synchronization of diffusively coupled neuronal oscillators abstract we discuss synchronization in networks of neuronal oscillators which are interconnected via diffusive coupling i e linearly coupled via gap junctions in particular we present sufficient conditions for synchronization in these networks using the theory of semi passive and passive systems we show that the conductance based neuronal models of hodgkin huxley morris lecar and the popular reduced models of fitzhugh nagumo and hindmarsh rose all satisfy a semi passivity property i e that is the state trajectories of such a model remain oscillatory but bounded provided that the supplied electrical energy is bounded as a result for a wide range of coupling configurations networks of these oscillators are guaranteed to possess ultimately bounded solutions moreover we demonstrate that when the coupling is strong enough the oscillators become synchronized our theoretical conclusions are confirmed by computer simulations with coupled hindmarsh rose and morris lecar oscillators finally we discuss possible instabilities in networks of oscillators induced by the diffusive coupling

multilevel linear modelling for fmri group analysis using bayesian inference functional magnetic resonance imaging studies often involve the acquisition of data from multiple sessions and or multiple subjects a hierarchical approach can be taken to modelling such data with a general linear model glm at each level of the hierarchy introducing different random effects variance components inferring on these models is nontrivial with frequentist solutions being unavailable a solution is to use a bayesian framework one important ingredient in this is the choice of prior on the variance components and top level regression parameters due to the typically small numbers of sessions or subjects in neuroimaging the choice of prior is critical to alleviate this problem we introduce to neuroimage modelling the approach of reference priors which drives the choice of prior such that it is noninformative in an information theoretic sense we propose two inference techniques at the top level for multilevel hierarchies a fast approach and a slower more accurate approach we also demonstrate that we can infer on the top level of multilevel hierarchies by inferring on the levels of the hierarchy separately and passing summary statistics of a noncentral multivariate t distribution between them

to smooth or not to smooth bias and efficiency in fmri time series analysis this paper concerns temporal filtering in fmri time series analysis whitening serially correlated data is the most efficient approach to parameter estimation however if there is a discrepancy between the assumed and the actual correlations whitening can render the analysis exquisitely sensitive to bias when estimating the standard error of the ensuing parameter estimates this bias although not expressed in terms of the estimated responses has profound effects on any statistic used for inference the special constraints of fmri analysis ensure that there will always be a misspecification of the assumed serial correlations one resolution of this problem is to filter the data to minimize bias while maintaining a reasonable degree of efficiency in this paper we present expressions for efficiency of parameter estimation and bias in estimating standard error in terms of assumed and actual correlation structures in the context of the general linear model we show that i whitening strategies can result in profound bias and are therefore probably precluded in parametric fmri data analyses ii band pass filtering and implicitly smoothing has an important role in protecting against inferential bias

synchronization and symmetry breaking bifurcations in constructive networks of coupled chaotic oscillators the spatiotemporal dynamics of networks based on a ring of coupled oscillators with regular shortcuts beyond the nearest neighbor couplings is studied by using master stability equations and numerical simulations the generic criterion for dynamic synchronization has been extended to arbitrary network topologies with zero row sum the symmetry breaking oscillation patterns that resulted from the hopf bifurcation from synchronous states are analyzed by the symmetry group theory

stability of synchronized network of chaotic electromechanical devices with nearest and all to all couplings abstract a shift invariant set of n mutually nearest neighbour or all to all coupled moving coil electromechanical devices is analytically and numerically investigated the study of the stability of synchronization process is undertaken using the master stability function msf approach the emanating properties of this method make it possible to have a general study of the network dynamics and to explain de synchronization phenomena appearing in the synchronization stability parametric areas a detailed attention is paid to the effects of the dissipative component of the dispersive dissipative coupling tested here

synchronized states in a ring of mutually coupled self sustained electrical oscillators we investigate in this paper different states of synchronization in a ring of mutually coupled self sustained electrical oscillators the good coupling parameters leading to complete and partial synchronization or disordered states are calculated using the properties of the variational equations of stability a stability map showing domains of synchronization to an external excitation locally injected in the ring is also obtained in both cases the numerical simulation validates and complements the results of the analytical investigation

loss of synchronization in coupled rossler systems this paper considers the loss of synchronization for a system of two coupled rossler oscillators bifurcation curves for the transverse destabilization of low periodic orbits embedded in the synchronized chaotic state are obtained and we show that desynchronization for a pair of symmetrically coupled identical rossler systems is associated with different orbits undergoing transverse pitchfork or period doubling bifurcations the transverse destabilization of the period 1 orbit is examined in detail and we follow the sequence of bifurcations that the asynchronous periodic cycles undergo in the presence of an asymmetry in the coupling the transverse period doubling bifurcation remains essentially the same the transverse pitchfork bifurcation on the other hand is transformed into a transcritical riddling bifurcation if the interacting rossler oscillators have different parameter values the non generic character of the pitchfork bifurcation leads it to be replaced by a saddle node bifurcation occurring off the symmetric sub space finally we show how the transverse stability properties of the equilibrium point can be used to obtain approximative analytical results for the transverse stability of the coupled chaotic oscillators 2001 elsevier science b v all rights reserved

coupling schemes for cluster synchronization in coupled josephson equations abstract we propose an approach to constructing different coupling schemes to stabilize selected cluster synchronization patterns for coupled josephson equations in particular we select a coupling scheme to create synchronization with frequency ratio m 1 m 2 m n which can be arbitrarily chosen and is independent of the frequencies of the uncoupled oscillators we also discuss coupled discrete systems

global variational solutions to the compressible magnetohydrodynamic equations abstract we prove the existence of globally defined variational solutions to the compressible magnetohydrodynamic mhd equations with the coefficients depending on the temperature as a by product we give a simple proof for the nonexistence of nontrivial weak time periodic solutions by the entropy principle of clausius duhem and a new poincare type inequality

synchronized clusters in coupled map networks i numerical studies we study the synchronization of coupled maps on a variety of networks including regular one and two dimensional networks scale free networks small world networks tree networks and random networks for small coupling strengths nodes show turbulent behavior but form phase synchronized clusters as coupling increases when nodes show synchronized behavior we observe two interesting phenomena first there are some nodes of the floating type that show intermittent behavior between getting attached to some clusters and evolving independently second we identify two different ways of cluster formation namely self organized clusters which have mostly intracluster couplings and driven clusters which have mostly intercluster couplings the synchronized clusters may be of dominant self organized type dominant driven type or mixed type depending on the type of network and the parameters of the dynamics we define different states of the coupled dynamics by considering the number and type of synchronized clusters for the local dynamics governed by the logistic map we study the phase diagram in the plane of the coupling constant and the logistic map parameter ensuremath mu for large coupling strengths and nonlinear coupling we find that the scale free networks and the caley tree networks lead to better cluster formation than the other types of networks with the same average connectivity for most of our study we use the number of connections of the order of the number of nodes as the number of connections increases the number of nodes forming clusters and the size of the clusters in general increase

increased sensitivity in neuroimaging analyses using robust regression robust regression techniques are a class of estimators that are relatively insensitive to the presence of one or more outliers in the data they are especially well suited to data that require large numbers of statistical tests and may contain outliers due to factors not of experimental interest both these issues apply particularly to neuroimaging data analysis we use simulations to compare several robust techniques against ordinary least squares ols regression and we apply robust regression to second level group brandom effectsq analyses in three fmri datasets our results show that robust iteratively reweighted least squares irls at the 2nd level is a computationally efficient technique that both increases statistical power and decreases false positive rates in the presence of outliers the benefits of irls are apparent with small samples n 10 and increase with larger sample sizes n 40 in the typical range of group neuroimaging experiments when no true effects are present irls controls false positive rates at an appropriate level we show that irls can have substantial benefits in analysis of group data and in estimating hemodynamic response shapes from time series data we provide software to implement irls in group neuroimaging analyses

group analysis in functional neuroimaging selecting subjects using similarity measures standard group analyses of fmri data rely on spatial and temporal averaging of individuals this averaging operation is only sensible when the mean is a good representation of the group this is not the case if subjects are not homogeneous and it is therefore a major concern in fmri studies to assess this group homogeneity we present a method that provides relevant distances or similarity measures between temporal series of brain functional images belonging to different subjects the method allows a multivariate comparison between data sets of several subjects in the time or in the space domain these analyses assess the global intersubject variability before averaging subjects and drawing conclusions across subjects at the population level we adapt the rv coefficient to measure meaningful spatial or temporal similarities and use multidimensional scaling to give a visual representation of each subject s position with respect to other subjects in the group we also provide a measure for detecting subjects that may be outliers results show that the method is a powerful tool to detect subjects with specific temporal or spatial patterns and that despite the apparent loss of information restricting the analysis to a homogeneous subgroup of subjects does not reduce the statistical sensitivity of standard group fmri analyses

bayesian density estimation and inference using mixtures abstract we describe and illustrate bayesian inference in models for density estimation using mixtures of dirichlet processes these models provide natural settings for density estimation and are exemplified by special cases where data are modeled as a sample from mixtures of normal distributions efficient simulation methods are used to approximate various prior posterior and predictive distributions this allows for direct inference on a variety of practical issues including problems of local versus global smoothing uncertainty about density estimates assessment of modality and the inference on the numbers of components also convergence results are established for a general class of normal mixture models

synchronization and dynamic consensus of heterogeneous networked systems we present an analysis framework for the study of synchronization of heterogeneous nonlinear systems interconnected over networks described by directed graphs heterogeneous systems may have totally different dynamical models albeit of the same dimension or may possess equal models with different lumped parameters we show that their behavior when network interconnected is fully characterized in terms of two properties whose study may be recasted in terms of the stability analysis of two corresponding interconnected dynamical systems that evolve in orthogonal spaces on one hand we have the so called emergent dynamics and on the other the synchronization error dynamics based on this premise we introduce the concept of dynamic consensus and we present results on robust stability which assess the conditions for practical asymptotic synchronization of networked systems and characterize their collective behavior to illustrate our main theoretical findings we broach a brief case study on mutual synchronization of heterogeneous chaotic oscillators

revisiting multi subject random effects in fmri advocating prevalence estimation abstract random effect analysis has been introduced into fmri research in order to generalize findings from the study group to the whole population generalizing findings is obviously harder than detecting activation within the study group since in order to be significant an activation has to be larger than the inter subject variability indeed detected regions are smaller when using random effect analysis versus fixed effects the statistical assumptions behind the classic random effect model are that the effect in each location is normally distributed over subjects and activation refers to a non null mean effect we argue that this model is unrealistic compared to the true population variability where due to function anatomy inconsistencies and registration anomalies some of the subjects are active and some are not at each brain location we propose a gaussian mixture random effect that amortizes between subject spatial disagreement and quantifies it using the prevalence of activation at each location we present a formal definition and an estimation procedure of this prevalence the end result of the proposed analysis is a map of the prevalence at locations with significant activation highlighting activation regions that are common over many brains prevalence estimation has several desirable properties a it is more informative than the typical active inactive paradigm b in contrast to the usual display of p values in activated regions which trivially converge to 0 for large sample sizes prevalence estimates converge to the true prevalence

adaptive tuning to bifurcation for time varying nonlinear systems adaptive output feedback control algorithm providing exact tuning of adjustable parameters to unknown values which ensure desired bifurcation properties of the system is proposed design of the algorithm is based on passification and adaptive observer application examples like neural integrator resonant pendulum and three dimensional oscillator are presented and illustrated by simulation results

control systems analysis for the fornasini marchesini 2d systems model progress after four decades the development of a control systems theory for multidimensional linear systems i e systems with more than one independent variable is an area where a very significant volume of research is based

automatic control of phase synchronization in coupled complex oscillators abstract we present an automatic control method for phase locking of regular and chaotic nonidentical oscillations when all subsystems interact via feedback this method is based on the well known principle of feedback control which takes place in nature and is successfully used in engineering in contrast to unidirectional and bidirectional coupling the approach presented here supposes the existence of a special controller which allows to change the parameters of the controlled systems first we discuss general principles of automatic phase synchronization ps for arbitrary coupled systems with a controller whose input is given by a special quadratic form of coordinates of the individual systems and its output is a result of the application of a linear differential operator we demonstrate the effectiveness of our approach for controlled ps on several examples i two coupled regular oscillators ii coupled regular and chaotic oscillators iii two coupled chaotic rossler oscillators iv two coupled foodweb models v coupled chaotic rossler and lorenz oscillators vi ensembles of locally coupled regular oscillators vii ensembles of locally coupled chaotic oscillators and viii ensembles of globally coupled chaotic oscillators

asymptotic stabilization of minimum phase nonlinear systems how a class of multivariable nonlinear systems can be stabilized about an equilibrium via smooth state feedback is shown more precisely conditions under which for every compact set of initial states it is possible to design a feedback law which drives to the equilibrium all initial states in this compact set are described the theory includes the development of globally defined transformations of the system equations to their global normal form

state agreement for continuous time coupled nonlinear systems two related problems are treated in continuous time first the state agreement problem is studied for coupled nonlinear differential equations the vector fields can switch within a finite family associated to each vector field is a directed graph based in a natural way on the interaction structure of the subsystems generalizing the work of moreau under the assumption that the vector fields satisfy a certain subtangentiality condition it is proved that asymptotic state agreement is achieved if and only if the dynamic interaction digraph has the property of being sufficiently connected over time the proof uses nonsmooth analysis second the rendezvous problem for kinematic point mass mobile robots is studied when the robots fields of view have a fixed radius the circumcenter control law of ando e ieee trans robotics automation 15 1999 pp 818 828 is shown to solve the problem the rendezvous problem is a kind of state agreement problem but the interaction structure is state dependent

mixed effect statistics for group analysis in fmri a nonparametric maximum likelihood approach this technical note describes a collection of test statistics accounting for estimation uncertainties at the within subject level that can be used as alternatives to the standard t statistic in one sample random effect analyses i e when testing the mean effect of a population we build such test statistics by estimating the across subject distribution of the effects using maximum likelihood under a nonparametric mixed effect model for inference purposes the statistics are calibrated using permutation tests to achieve exact false positive control under a symmetry assumption regarding the across subject distribution the new tests are implemented in a freely available toolbox for spm called distance

a new augmented lyapunov krasovskii functional approach to exponential passivity for neural networks with time varying delays abstract in this paper the problem of exponential passivity analysis for uncertain neural networks with time varying delays is considered by constructing new augmented lyapunov krasovskii s functionals and some novel analysis techniques improved delay dependent criteria for checking the exponential passivity of the neural networks are established the proposed criteria are represented in terms of linear matrix inequalities lmis which can be easily solved by various convex optimization algorithms a numerical example is included to show the superiority of our results

synchronization of complex dynamical networks by the incremental iss approach abstract we apply the theory of incremental input to state stability to the problem of synchronization in a complex dynamical network of identical nodes using chaotic nodes as a typical platform the proposed technique can achieve chaos synchronization using only partial state output information in the sense that it does not require all nodes to have access to the state output information from the seed node that produces the reference orbit for network synchronization examples and simulations demonstrate the applicability and effectiveness of the new synchronization method

exponential feedback passivity and stabilizability of nonlinear systems abstract motivated by n krasovskii s characterisation of exponential stability the concept of exponential passivity is introduced it is shown that to make a nonlinear system with factorisable high frequency gain matrix exponentially passive via either state or output feedback exponential minimum phaseness and invertibility conditions are necessary and sufficient these conditions also guarantee exponential output feedback stabilisability this result extends previous results concerning linear systems

partial synchronization and spontaneous spatial ordering in coupled chaotic systems a model of many symmetrically and locally coupled chaotic oscillators is studied partial chaotic synchronizations associated with spontaneous spatial ordering are demonstrated very rich patterns of the system are revealed based on partial synchronization analysis the stabilities of different partially synchronous spatiotemporal structures and some dynamical behaviors of these states are discussed both numerically and analytically

partial synchronization in linearly and symmetrically coupled ordinary differential systems in this paper we discuss partial synchronization of linearly and symmetrically coupled ordinary differential equations lscodes the synchronization phenomena are investigated via invariant synchronization manifolds on the basis of geometrical analysis of the synchronization manifold several criteria for the global attractivity of the invariant synchronization manifold are obtained combining these criteria with some numerical examples we investigate how topological structure affects partial synchronization and give a valuable discussion about the possibility of partial synchronization with increasing coupling strength

universality for the parameter mismatching effect on weak synchronization in coupled chaotic systems to examine the universality for the parameter mismatching effect on weak chaotic synchronization we study coupled multidimensional invertible systems such as the coupled henon maps and coupled pendula by generalizing the method proposed in coupled one dimensional 1d noninvertible maps we introduce the parameter sensitivity exponent to measure the degree of the parameter sensitivity of a weakly stable synchronous chaotic attractor in terms of the parameter sensitivity exponents we characterize the effect of the parameter mismatch on the intermittent bursting and the basin riddling occurring in the regime of weak synchronization it is thus found that the scaling exponent for the average characteristic time i e the average interburst time and the average chaotic transient lifetime for both the bubbling and riddling cases is given by the reciprocal of the parameter sensitivity exponent as in the simple system of coupled 1d maps hence the reciprocal relation i e 1 seems to be universal in the sense that it holds in typical coupled chaotic systems of different nature

probabilistic model based functional parcellation reveals a robust fine grained subdivision of the striatum the striatum is involved in many different aspects of behaviour reflected by the variety of cortical areas that provide input to this structure this input is topographically organized and is likely to result in functionally specific signals such specificity can be examined using functional clustering approaches here we propose a bayesian model based functional clustering approach applied solely to resting state striatal functional mri timecourses to identify intrinsic striatal functional modules data from two sets of ten participants were used to obtain parcellations and examine their robustness this stable clustering was used to initialize a more constrained model in order to obtain individualized parcellations in 57 additional participants resulting cluster time courses were used to examine functional connectivity between clusters and related to the rest of the brain in a glm analysis we find six distinct clusters in each hemisphere with clear inter hemispheric correspondence and functional relevance these clusters exhibit functional connectivity profiles that further underscore their homologous nature and are consistent with existing notions on segregation and integration in parallel cortico basal ganglia loops our findings suggest that multiple territories within both the affective and motor regions can be distinguished solely using resting state functional mri from these regions

technical communique mitigation of symmetry condition in positive realness for adaptive control feasibility of nonlinear and adaptive control methodologies in multivariable linear time invariant systems with state space realization a b c is apparently limited by the standard strictly positive realness conditions that imply that the product cb must be positive definite symmetric this paper expands the applicability of the strictly positive realness conditions used for the proofs of stability of adaptive control or control with uncertainty by showing that the not necessarily symmetric cb is only required to have a diagonal jordan form and positive eigenvalues the paper also shows that under the new condition any minimum phase systems can be made strictly positive real via constant output feedback the paper illustrates the usefulness of these extended properties with an adaptive control example

passivity and disturbance attenuation via output feedback for uncertain nonlinear systems the authors address the problem of disturbance attenuation with internal stability via output feedback for a class of passive systems with uncertainties the problem is approached by means of adaptive output feedback control which does not require any state observer the results obtained extend an earlier result of steinberg and corless 1985 sufficient conditions are proposed under which a nonlinear system can be made locally or globally passive via output feedback

detecting and adjusting for artifacts in fmri time series data we present a new method to detect and adjust for noise and artifacts in functional mri time series data we note that the assumption of stationary variance which is central to the theoretical treatment of fmri time series data is often violated in practice sporadic events such as eye mouth or arm movements can increase noise in a spatially global pattern throughout an image leading to a non stationary noise process we derive a restricted maximum likelihood reml algorithm that estimates the variance of the noise for each image in the time series these variance parameters are then used to obtain a weighted least squares estimate of the regression parameters of a linear model we apply this approach to a typical fmri experiment with a block design and show that the noise estimates strongly vary across different images and that our method detects and appropriately weights images that are affected by artifacts furthermore we show that the noise process has a global spatial distribution and that the variance increase is multiplicative rather than additive the new algorithm results in significantly increased sensitivity in the ability to detect regions of activation the new method may be particularly useful for studies that involve special populations e g children or elderly where sporadic artifact generating events are more likely

global well posedness of the cauchy problem for the equations of a one dimensional viscous heat conducting gas with lebesgue initial data we study the cauchy problem for the one dimensional equations of a viscous heat conducting gas in the lagrangian mass coordinates with the initial data in the lebesgue spaces we prove the existence the uniqueness and the lipschitz continuous dependence on the initial data of global weak solutions 1 main theorems we study the existence the uniqueness and the lipschitz continuous dependence on initial data of global weak solutions to the cauchy problem for the system of one dimensional quasilinear equations of a viscous polytropic ideal gas in a strip qt r 0 t t vx

direct passivity of a class of mimo non linear systems using adaptive feedback in this paper an adaptive controller with adaptive laws specially designed is proposed to solve the problem of making a multi input multi output mimo non linear system with explicit linear parametric uncertainty equivalent to a passive system these results are an extension of those obtained by the authors for the siso case some stability issues associated to the resultant closed loop passive system are also discussed the results obtained are applied to models of dynamical mimo systems to illustrate the controller design methodology