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

periodically forced ensemble of nonlinearly coupled oscillators from partial to full synchrony we analyze the dynamics of a periodically forced oscillator ensemble with global nonlinear coupling without forcing the system exhibits complicated collective dynamics even for the simplest case of identical phase oscillators due to nonlinearity the synchronous state becomes unstable for certain values of the coupling parameter and the system settles at the border between synchrony and asynchrony what can be denoted as partial synchrony we find that an external common forcing can result in two synchronous states i a weak forcing entrains only the mean field whereas the individual oscillators remain unlocked to the force and correspondingly to the mean field ii a strong forcing fully synchronizes the system making the phases of all oscillators identical analytical results are confirmed by numerics

limitations of robust stability of a linear delayed feedback control in this paper we consider the issue of robust stability of a linear delayed feedback control dfc mechanism in particular we consider a dfc for stabilizing fixed points of a smooth function f mathbb r m rightarrow mathbb r m of the form x k 1 f x k u k where u k is given by the formula u k sum j 1 n 1 epsilon j x k j x k j 1 we associate with each fixed point of f an explicit polynomial whose schur stability corresponds to the local asymptotic stability of the dfc at that fixed point this polynomial is the characteristic polynomial of the jacobian matrix of an auxiliary map from mathbb r mn to mathbb r mn and may be given in terms of the eigenvalues of the jacobian of f at the fixed point this enables us to evaluate the robustness of the control by considering over what possible sets of eigenvalues of the jacobian of f the associated characteristic polynomials are schur stable we will show that for a given control of the above form sta

tracking fixed point dynamics in an electrochemical system using delayed feedback control we report numerical and experimental results indicating successful tracking of stabilized fixed points solutions in an electrochemical system by applying a continuous delayed feedback technique periodic oscillations are suppressed via stabilization of a steady state fixed point subsequently using a simple continuation method involving an update term this stabilized fixed point is tracked through the bifurcation diagram as a system parameter is slowly varied under the influence of this tracking protocol inception of oscillatory dynamics is precluded over large parameter domains and through bifurcations

analytical properties and optimization of time delayed feedback control time delayed feedback control is an efficient method for stabilizing unstable periodic orbits of chaotic systems if the equations governing the system dynamics are known the success of the method can be predicted by a linear stability analysis of the desired orbit unfortunately the usual procedures for evaluating the floquet exponents of such systems are rather intricate we show that the main stability properties of the system controlled by time delayed feedback can be simply derived from a leading floquet exponent defining the system behavior under proportional feedback control optimal parameters of the delayed feedback controller can be evaluated without an explicit integration of delay differential equations the method is valid for low dimensional systems whose unstable periodic orbits are originated from a period doubling bifurcation and is demonstrated for the rossler system and the duffing oscillator

direct estimation of the fiber orientation density function from diffusion weighted mri data using spherical deconvolution diffusion weighted magnetic resonance imaging can provide information related to the arrangement of white matter fibers the diffusion tensor is the model most commonly used to derive the orientation of the fibers within a voxel however this model has been shown to fail in regions containing several fiber populations with distinct orientations a number of alternative models have been suggested such as multiple tensor fitting q space and q ball imaging however each of these has inherent limitations in this study we propose a novel method for estimating the fiber orientation distribution directly from high angular resolution diffusion weighted mr data without the need for prior assumptions regarding the number of fiber populations present we assume that all white matter fiber bundles in the brain share identical diffusion characteristics thus implicitly assigning any differences in diffusion anisotropy to partial volume effects the diffusion weighted signal attenuation measured over the surface of a sphere can then be expressed as the convolution over the sphere of a response function the diffusion weighted attenuation profile for a typical fiber bundle with the fiber orientation density function odf the fiber odf the distribution of fiber orientations within the voxel can therefore be obtained using spherical deconvolution the properties of the technique are demonstrated using simulations and on data acquired from a volunteer using a standard 1 5 t clinical scanner the technique can recover the fiber odf in regions of multiple fiber crossing and holds promise for applications such as tractography

impact of heterogeneous delays on cluster synchronization we investigate cluster synchronization in coupled map networks in the presence of heterogeneous delays we find that while the parity of heterogeneous delays plays a crucial role in determining the mechanism of cluster formation the cluster synchronizability of the network gets affected by the amount of heterogeneity in addition heterogeneity in delays induces a rich cluster pattern as compared to homogeneous delays the complete bipartite network stands as an extreme example of this richness where robust ideal driven clusters observed for the undelayed and homogeneously delayed cases dismantle yielding versatile cluster patterns as heterogeneity in the delay is introduced we provide arguments behind this behavior using a lyapunov function analysis furthermore the interplay between the number of connections in the network and the amount of heterogeneity plays an important role in deciding the cluster formation

entire solutions for a class of variational problems involving the biharmonic operator and rellich potentials abstract we study existence multiplicity and qualitative properties of entire solutions for a noncompact problem related to second order interpolation inequalities with weights more precisely we deal with the following family of equations 2 u x 4 u x u q 2 u in r n where n 5 q 2 n q n 4 2 and r is smaller than the rellich constant

pyragas stabilizability via delayed feedback with periodic control gain abstract in this paper for the unstable periodic solution of nonlinear differential equation pyragas stabilizability problem is studied an algorithm of stabilization via periodical delayed feedback is obtained the consideration is based on the theory of nonstationary stabilization

fast global oscillations in networks of integrate and fire neurons with low firing rates we study analytically the dynamics of a network of sparsely connected inhibitory integrate and fire neurons in a regime where individual neurons emit spikes irregularly and at a low rate in the limit when the number of neurons n 1 the network exhibits a sharp transition between a stationary and an oscillatory global activity regime where neurons are weakly synchronized the activity becomes oscillatory when the inhibitory feedback is strong enough the period of the global oscillation is found to be mainly controlled by synaptic times but depends also on the characteristics of the external input in large but finite networks the analysis shows that global oscillations of finite coherence time generically exist both above and below the critical inhibition threshold their characteristics are determined as functions of systems parameters in these two different regimes the results are found to be in good agreement with numerical simulations

towards easier realization of time delayed feedback control of odd number orbits we develop generalized time delayed feedback schemes for the stabilization of periodic orbits with an odd number of positive floquet exponents which are particularly well suited for experimental realization we construct the parameter regimes of successful control and validate these by numerical simulations and numerical continuation methods in particular it is shown how periodic orbits can be stabilized with symmetric feedback matrices by introducing an additional latency time in the control loop finally we show using normal form analysis and numerical simulations how our results could be implemented in a laser setup using optoelectronic feedback

melnikov s criteria and chaos in systems with fractional order deflection in this paper a qualitative analysis of the dynamic systems described with the second order differential equation with fractional order deflection function is considered the existence of fixed points closed orbits and the unions of fixed points and the trajectories connecting them is shown the homoclinic orbit which connects a fixed point with itself and the corresponding stable and unstable manifolds are given in the closed analytical form melnikov s procedure for defining the criteria for transversal intersection of the stable and unstable manifolds is extended for the systems with fractional order deflection function the critical parameter values for chaos are obtained analytically and proved numerically using the lyapunov exponents the bifurcation diagrams are plotted for various values of fractional order and the transition to chaos by period doubling is shown the phase plane diagrams and the poincare maps for certain fractional orders are obtained the control of chaos and the transformation to periodic motion is considered

delayed feedback control of the lorenz system an analytical treatment at a subcritical hopf bifurcation we develop an analytical approach for the delayed feedback control of the lorenz system close to a subcritical hopf bifurcation the periodic orbits arising at this bifurcation have no torsion and cannot be stabilized by a conventional delayed feedback control technique we utilize a modification based on an unstable delayed feedback controller the analytical approach employs the center manifold theory and the near identity transformation we derive the characteristic equation for the floquet exponents of the controlled orbit in an analytical form and obtain simple expressions for the threshold of stability as well as for an optimal value of the control gain the analytical results are supported by numerical analysis of the original system of nonlinear differential difference equations

conversion of stability in systems close to a hopf bifurcation by time delayed coupling we propose a control method with time delayed coupling which makes it possible to convert the stability features of systems close to a hopf bifurcation we consider two delay coupled normal forms for hopf bifurcation and demonstrate the conversion of stability i e an interchange between the sub and supercritical hopf bifurcation the control system provides us with an unified method for stabilizing both the unstable periodic orbit and the unstable steady state and reveals typical effects like amplitude death and phase locking the main method and the results are applicable to a wide class of systems showing hopf bifurcations for example the van der pol oscillator the analytical theory is supported by numerical simulations of two delay coupled van der pol oscillators which show good agreement with the theory

improvement of time delayed feedback control by periodic modulation analytical theory of floquet mode control scheme we investigate time delayed feedback control schemes which are based on the unstable modes of the target state to stabilize unstable periodic orbits the periodic time dependence of these modes introduces an external time scale in the control process phase shifts that develop between these modes and the controlled periodic orbit may lead to a huge increase of the control performance we illustrate such a feature on a nonlinear reaction diffusion system with global coupling and give a detailed investigation for the rossler model in addition we provide the analytical explanation for the observed control features

complex dynamics of an oscillator ensemble with uniformly distributed natural frequencies and global nonlinear coupling we consider large populations of phase oscillators with global nonlinear coupling for identical oscillators such populations are known to demonstrate a transition from completely synchronized state to the state of self organized quasiperiodicity in this state phases of all units differ yet the population is not completely incoherent but produces a nonzero mean field the frequency of the latter differs from the frequency of individual units here we analyze the dynamics of such populations in case of uniformly distributed natural frequencies we demonstrate numerically and describe theoretically i states of complete synchrony ii regimes with coexistence of a synchronous cluster and a drifting subpopulation and iii self organized quasiperiodic states with nonzero mean field and all oscillators drifting with respect to it we analyze transitions between different states with the increase of the coupling strength in particular we show that the mean field arises via a discontinuous transition for a further illustration we compare the results for the nonlinear model with those for the kuramoto sakaguchi model

synchronization analysis of linearly coupled systems described by differential equations with a coupling delay when a transmission delay occurs in the interconnection of linearly coupled systems described by ordinary differential equations lcodes both synchronization and the final synchronized state will vary in this paper mathematical analysis is presented on the synchronization phenomena of lcodes with a single coupling delay criteria are derived for both local and global synchronization it is known that in addition to the dynamical behaviors of the underlying uncoupled system and the coupling configuration the coupling strength and the coupling delay also play key roles on the stability of synchronization both theoretical and numerical analysis indicate that under some conditions if the coupling strength is large enough the coupled system can be completely synchronized for any coupling delay on the other hand in some cases the coupled system can be synchronized if the coupling delay is small enough

reproducibility of tract segmentation between sessions using an unsupervised modelling based approach abstract this work describes a reproducibility analysis of scalar water diffusion parameters measured within white matter tracts segmented using a probabilistic shape modelling method in common with previously reported neighbourhood tractography nt work the technique optimises seed point placement for fibre tracking by matching the tracts generated using a number of candidate points against a reference tract which is derived from a white matter atlas in the present study no direct constraints are applied to the fibre tracking results an expectation maximisation algorithm is used to fully automate the procedure and make dramatically more efficient use of data than earlier nt methods within subject and between subject variances for fractional anisotropy and mean diffusivity within the tracts are then separated using a random effects model we find test retest coefficients of variation cvs similar to those reported in another study using landmark guided single seed points and subject to subject cvs similar to a constraint based multiple roi method we conclude that our approach is at least as effective as other methods for tract segmentation using tractography whilst also having some additional benefits such as its provision of a goodness of match measure for each segmentation

limit cycle oscillators subject to a delayed feedback the coexistence of two stable limit cycles exhibiting different periods is examined for a nonlinear oscillator subject to a delayed feedback for the case of a weakly nonlinear oscillator we discuss the validity of a previously determined phase equation for the case of a strongly nonlinear oscillator we derive a phase equation and analyze its bifurcation diagram our analysis is motivated by previous experimental studies of chemical oscillators controlled by a delayed feedback

brain behaviour and mathematics are we using the right approaches mathematics are used in biological sciences mostly as a quantifying tool for it is the science of numbers after all there is a long standing interest in the application of mathematical methods and concepts to neuroscience in attempts to decipher brain activity while there has been a very wide use of mathematical physical methodologies less effort has been made to formulate a comprehensive and integrative theory of brain function this review concentrates on recent developments uses and abuses of mathematical formalisms and techniques that are being applied in brain research particularly the current trend of using dynamical system theory to unravel the global collective dynamics of brain activity it is worth emphasising that the theoretician neuroscientist eager to apply mathematical analysis to neuronal recordings has to consider carefully some crucial anatomo physiological assumptions that may not be as accurate as the specific methods require on the other hand the experimentalist neuro physicist with an inclination to implement mathematical thoughts in brain science has to make an effort to comprehend the bases of the theoretical concepts that can be used as frameworks or as analysis methods of brain electrophysiological recordings and to critically inspect the accuracy of the interpretations of the results based on the neurophysiological ground it is hoped that this brief overview of anatomical and physiological presumptions and their relation to theoretical paradigms will help clarify some particular points of interest in current trends in brain science and may provoke further reflections on how certain or uncertain it is to conceptualise brain function based on these theoretical frameworks if the physiological and experimental constraints are not as accurate as the models prescribe

collective dynamics of globally coupled phase oscillators under multisite delayed feedback stimulation recently multisite delayed feedback stimulation was proposed as a novel method for mild and effective deep brain stimulation in neurological diseases characterized by pathological cerebral synchronization to develop the mathematical background of this technique we propose a continuous medium model of globally coupled phase oscillators in the form of a delayed integro differential equation this model provides a convenient description of the spatial phase patterns depending on the stimulation topology we describe physically relevant phase locked solutions and analyze their linear stability considering different spatial stimulation profiles as well as delays and polarities we demonstrate that multisite delayed feedback is a robust soft and effective method for the control of spatio temporal synchronization patterns our results can be used for the optimization of parameters in applications of multisite delayed feedback stimulation to the therapy of neurological diseases with pathological synchronization and the therapy of defective central pattern generators

the onset of synchronization in systems of globally coupled chaotic and periodic oscillators abstract a general stability analysis is presented for the determination of the transition from incoherent to coherent behavior in an ensemble of globally coupled heterogeneous continuous time dynamical systems the formalism allows for the simultaneous presence of ensemble members exhibiting chaotic and periodic behavior and in a special case yields the kuramoto model for globally coupled periodic oscillators described by a phase numerical experiments using different types of ensembles of lorenz equations with a distribution of parameters are presented

existence and symmetry of positive ground states for a doubly critical schrodinger system n n 2 and 1 1 satisfying 2 this problem is related to coupled nonlinear schrodinger equations with critical exponent for bose einstein condensate for different ranges of n and 0 we obtain positive ground state solutions via some quite different methods which are all radially symmetric it turns out that the least energy level depends heavily on the relations among and 2 besides for sufficiently small 0 positive solutions are also obtained via a variational perturbation approach note that the palais smale condition can not hold for any positive energy level which makes the study via variational methods rather complicated

time delayed feedback control of unstable periodic orbits near a subcritical hopf bifurcation we show that the pyragas delayed feedback control can stabilize an unstable periodic orbit upo that arises from a generic subcritical hopf bifurcation of a stable equilibrium in an n dimensional dynamical system this extends results of fiedler et al b fiedler v flunkert m georgi p hovel e scholl refuting the odd number limitation of time delayed feedback control phys rev lett 98 11 2007 114101 who demonstrated that such a feedback control can stabilize the upo associated with a two dimensional subcritical hopf normal form the pyragas feedback requires an appropriate choice of a feedback gain matrix for stabilization as well as knowledge of the period of the targeted upo we apply feedback in the directions tangent to the two dimensional center manifold we parameterize the feedback gain by a modulus and a phase angle and give explicit formulae for choosing these two parameters given the period of the upo in a neighborhood of the bifurcation point we show first heuristically and then rigorously by a center manifold reduction for delay differential equations that the stabilization mechanism involves a highly degenerate hopf bifurcation problem that is induced by the time delayed feedback when the feedback gain modulus reaches a threshold for stabilization both of the genericity assumptions associated with a two dimensional hopf bifurcation are violated the eigenvalues of the linearized problem do not cross the imaginary axis as the bifurcation parameter is varied and the real part of the cubic coefficient of the normal form vanishes our analysis reveals two qualitatively distinct cases when the degenerate bifurcation is unfolded in a two parameter plane in each case the pyragas type feedback successfully stabilizes the branch of small amplitude upos in a neighborhood of the original bifurcation point provided that the feedback phase angle satisfies a certain restriction

spatial normalization and averaging of diffusion tensor mri data sets diffusion tensor magnetic resonance imaging dt mri is unique in providing information about both the structural integrity and the orientation of white matter fibers in vivo and through tractography revealing the trajectories of white matter tracts dt mri is therefore a promising technique for detecting differences in white matter architecture between different subject populations however while studies involving analyses of group averages of scalar quantities derived from dt mri data have been performed as yet there have been no similar studies involving the whole tensor here we present the first step towards realizing such a study i e the spatial normalization of whole tensor data sets the approach is illustrated by spatial normalization of 10 dt mri data sets to a standard anatomical template both qualitative and quantitative approaches are described for assessing the results of spatial normalization techniques are then described for combining the spatially normalized data sets according to three definitions of average i e the mean median and mode of a distribution of tensors the current absence of and hence need for appropriate statistical tests for comparison of results derived from group averaged dt mri data sets is then discussed finally the feasibility of performing tractography on the group averaged dt mri data set is investigated and the possibility and implications of generating a generic map of brain connectivity from a group of subjects is considered

delayed feedback control of forced self sustained oscillations we consider a weakly nonlinear van der pol oscillator subjected to a periodic force and delayed feedback control without control the oscillator can be synchronized by the periodic force only in a certain domain of parameters however outside of this domain the system possesses unstable periodic orbits that can be stabilized by delayed feedback perturbation the feedback perturbation vanishes if the stabilization is successful and thus the domain of synchronization can be extended with only small control force we take advantage of the fact that the system is close to a hopf bifurcation and derive a simplified averaged equation which we are able to treat analytically even in the presence of the delayed feedback as a result we obtain simple analytical expressions defining the domain of synchronization of the controlled system as well as an optimal value of the control gain the analytical theory is supported by numerical simulations of the original delay differential equations

dynamics of a limit cycle oscillator under time delayed linear and nonlinear feedbacks abstract we study the effects of time delayed linear and nonlinear feedbacks on the dynamics of a single hopf bifurcation oscillator our numerical and analytic investigations reveal a host of complex temporal phenomena such as phase slips frequency suppression multiple periodic states and chaos such phenomena are frequently observed in the collective behavior of a large number of coupled limit cycle oscillators our time delayed feedback model offers a simple paradigm for obtaining and investigating these temporal states in a single oscillator we construct a detailed bifurcation diagram of the oscillator as a function of the time delay parameter and the driving strengths of the feedback terms we find some new states in the presence of the quadratic nonlinear feedback term with interesting characteristics like birhythmicity phase reversals radial trapping phase jumps and spiraling patterns in the amplitude space our results may find useful applications in physical chemical or biological systems

controlling coherence of noisy and chaotic oscillators by a linear feedback abstract we analyze the dynamics of a noisy limit cycle oscillator coupled to a general passive linear system we analytically demonstrate that the phase diffusion constant which characterizes the coherence of the oscillations can be efficiently controlled theoretical analysis is performed in the framework of linear and gaussian approximations and is supported by numerical simulations we also demonstrate numerically the coherence control of a chaotic system

zero delay synchronization of chaos in coupled map lattices we show that two coupled map lattices that are mutually coupled to one another with a delay can display zero delay synchronization if they are driven by a third coupled map lattice we analytically estimate the parametric regimes that lead to synchronization and show that the presence of mutual delays enhances synchronization to some extent the zero delay or isochronal synchronization is reasonably robust against mismatches in the internal parameters of the coupled map lattices and we analytically estimate the synchronization error bounds

global mu synchronization of linearly coupled unbounded time varying delayed neural networks with unbounded delayed coupling in this brief we study the global synchronization of linearly coupled neural networks with delayed couplings where the intrinsic systems are recurrently connected neural networks with unbounded time varying delays and the couplings include instant couplings and unbounded delayed couplings the concept of mu synchronization is introduced some sufficient conditions are derived for the global mu synchronization for the underlined coupled systems

controlling limit cycle behaviors of brain activity the limit cycles of brain activity are studied using a compact continuum model that reproduces the main features of electroencephalographic signals including bifurcations of fixed points and limit cycles in seizures frequencies and amplitudes are predicted analytically and related to physiology gaussian stimuli yield two distinct evoked responses in the linearly stable zone consistent with experiment limit cycles can be initiated or suppressed by control signals or stimuli

locating unstable periodic orbits when adaptation integrates into delayed feedback control finding unstable periodic orbits upos is always a challenging demand in biophysics and computational biology which needs efficient algorithms to meet this need an approach to locating unstable periodic orbits in chaotic dynamical system is presented the uniqueness of the approach lies in the introduction of adaptive rules for both feedback gain and time delay in the system without requiring any information of the targeted upo periods a priori this approach is theoretically validated under some mild conditions and successfully tested with some practical strategies in several typical chaotic systems with or without significant time delays

improved segmentation reproducibility in group tractography using a quantitative tract similarity measure abstract the field of tractography is rapidly developing and many automatic or semiautomatic algorithms have now been devised to segment and visualize neural white matter fasciculi in vivo however these algorithms typically need to be given a starting location as input and their output can be strongly dependent on the exact location of this seed point no robust method has yet been devised for placing these seed points so as to segment a comparable tract in a group of subjects here we develop a measure of tract similarity based on the shapes and lengths of the two tracts being compared and apply it to the problem of consistent seed point placement and tract segmentation in group data we demonstrate that using a single seed point transferred from standard space to each native space produces considerable variability in tractography output between scans however by seeding in a group of nearby candidate points and choosing the output with the greatest similarity to a reference tract chosen in advance a method we refer to as neighborhood tractography this variability can be significantly reduced

global view on a nonlinear oscillator subject to time delayed feedback control we apply time delayed feedback control to stabilise unstable periodic orbits of an amplitude phase oscillator the control acts on both the amplitude and the frequency of the oscillator and we show how the phase of the control signal influences the dynamics of the oscillator a comprehensive bifurcation analysis in terms of the control phase and the control strength reveals large stability regions of the target periodic orbit as well as an increasing number of unstable periodic orbits caused by the time delay of the feedback loop our results provide insight into the global features of time delayed control schemes

variability in diffusion kurtosis imaging impact on study design statistical power and interpretation diffusion kurtosis imaging dki is an emerging technique with the potential to quantify properties of tissue microstructure that may not be observable using diffusion tensor imaging dti in order to help design dki studies and improve interpretation of dki results we employed statistical power analysis to characterize three aspects of variability in four dki parameters the mean diffusivity fractional anisotropy mean kurtosis and radial kurtosis first we quantified the variability in terms of the group size required to obtain a statistical power of 0 9 second we investigated the relative contribution of imaging and post processing noise to the total variance in order to estimate the benefits of longer scan times versus the inclusion of more subjects third we evaluated the potential benefit of including additional covariates such as the size of the structure when testing for differences in group means the analysis was performed in three major white matter structures of the brain the superior cingulum the corticospinal tract and the mid sagittal corpus callosum extracted using diffusion tensor tractography and dki data acquired in a healthy cohort the results showed heterogeneous variability across and within the white matter structures thus the statistical power varies depending on parameter and location which is important to consider if a pathogenesis pattern is inferred from dki data in the data presented inter subject differences contributed more than imaging noise to the total variability making it more efficient to include more subjects rather than extending the scan time per subject finally strong correlations between dki parameters and the structure size were found for the cingulum and corpus callosum structure size should thus be considered when quantifying dki parameters either to control for its potentially confounding effect or as a means of reducing unexplained variance

existence and robustness of phase locking in coupled kuramoto oscillators under mean field feedback motivated by the recent development of deep brain stimulation dbs for neurological diseases we study a network of interconnected oscillators under the influence of mean field feedback and analyze the robustness of its phase locking with respect to general inputs under standard assumptions this system can be reduced to a modified version of the kuramoto model of coupled nonlinear oscillators in the first part of the paper we present an analytical study on the existence of phase locked solutions under generic interconnection and feedback configurations in particular we show that in general no oscillating phase locked solutions can co exist with any non zero proportional mean field feedback in the second part we prove some robustness properties of phase locked solutions namely total stability this general result allows in particular to justify the persistence of practically phase locked states if sufficiently small feedback gains are applied and to give explicit necessary conditions on the intensity of a desynchronizing mean field feedback furthermore the lyapunov function used in the analysis provides a new characterization of the robust phase locked configurations in the kuramoto system with symmetric interconnections

delayed feedback control of collective synchrony an approach to suppression of pathological brain rhythms we suggest a method for suppression of synchrony in a globally coupled oscillator network based on the time delayed feedback via the mean field having in mind possible applications for suppression of pathological rhythms in neural ensembles we present numerical results for different models of coupled bursting neurons a theory is developed based on the consideration of the synchronization transition as a hopf bifurcation

existence and nonexistence results for critical biharmonic systems involving multiple singularities abstract in this paper a system of biharmonic equations is investigated which involves critical sobolev nonlinearities and multiple singular points by variational methods and analytical techniques the best soblev constant corresponding to the system is investigated and the existence nonexistence of ground state solutions to the system is established

multi branch entrainment and multi peaked order functions in a phase model of limit cycle oscillators with uniform all to all coupling a peculiar type of mutual entrainment is found numerically in a phase model of a large population of limit cycle oscillators with uniform all to all coupling strongly modulated by higher harmonics in which more than one branch of mutually phase locked oscillators exists accompanied by a multi peaked order function for system size n at least en different entrained states are likely to coexist with almost identical order functions also discussed is how to extend the order function theory for dealing with such a phenomenon

controlling oscillator coherence by delayed feedback we demonstrate that the coherence of a noisy or chaotic self sustained oscillator can be efficiently controlled by the delayed feedback we develop a theory of this effect considering noisy systems in the gaussian approximation we obtain a closed equation system for the phase diffusion constant and the mean frequency of oscillation for weak feedback and strong noise the theory is in good agreement with the numerics we discuss possible applications of the effect for the synchronization control

delayed feedback control of dynamical systems at a subcritical hopf bifurcation we consider the delayed feedback control of a torsion free unstable periodic orbit originated in a dynamical system at a subcritical hopf bifurcation close to the bifurcation point the problem is treated analytically using the method of averaging we discuss the necessity of employing an unstable degree of freedom in the feedback loop as well as a nonlinear coupling between the controlled system and controller to demonstrate our analytical approach the specific example of a nonlinear electronic circuit is taken as a model of a subcritical hopf bifurcation

bootstrap white matter tractography boot trac white matter tractography is a noninvasive method for estimating and visualizing the white matter connectivity patterns in the human brain using diffusion tensor imaging dti data sources of experimental noise may induce errors in the measured fiber directions which will reduce the accuracy of the estimated white matter trajectories in this study a statistical nonparametric bootstrap method is described for estimating the dispersion and other errors in white matter tractography results prior studies have derived models of tractography error using the signal to noise ratio snr and diffusion anisotropy of the dti data tractography errors measured using bootstrap methods were generally consistent with an analytic model of tractography error except in areas where branching was evident white matter tractography with bootstrap resampling is also applied to estimate the probabilities of connection between brain regions the approach was used to generate probabilistic connectivity maps between the cerebral peduncles and specific cortical regions