generalized bayesian information criterion for source enumeration in array processing we investigate the problem of enumerating source signals impinging on an array of sensors in an information theoretic framework the conventional bayesian information criterion bic does not yield satisfactory performance for this problem because it only considers the density of the observations in order to remedy the limitations of the bic we propose a generalized bayesian information criterion gbic rule by incorporating the density of the sample eigenvalues or corresponding statistics such a density contains extra information and complements the density of the observations in constructing the gbic as a result two different expressions for the gbic are suggested simulation results validate the superiority of the proposed gbic over the conventional bic in terms of correctly determining the number of sources while their computational costs are comparable

control of unstable steady states by extended time delayed feedback time delayed feedback methods can be used to control unstable periodic orbits as well as unstable steady states we present an application of extended time delay autosynchronization introduced by socolar et al phys rev e 50 3245 1994 to an unstable focus this system represents a generic model of an unstable steady state which can be found for instance in hopf bifurcation in addition to the original controller design we investigate effects of control loop latency and a bandpass filter on the domain of control furthermore we consider coupling of the control force to the system via a rotational coupling matrix parametrized by a variable phase we present an analysis of the domain of control and support our results by numerical calculations

detection of signals by information theoretic criteria a new approach is presented to the problem of detecting the number of signals in a multichannel time series based on the application of the information theoretic criteria for model selection introduced by akaike aic and by schwartz and rissanen mdl unlike the conventional hypothesis testing based approach the new approach does not requite any subjective threshold settings the number of signals is obtained merely by minimizing the aic or the mdl criteria simulation results that illustrate the performance of the new method for the detection of the number of signals received by a sensor array are presented

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

multifractal analysis of ssec in chinese stock market a different empirical result from heng seng index abstract in this paper high frequency per 5 min data of shanghai stock exchange composite index ssec from january 1999 to july 2001 is analyzed by multifractal we find that the correlation of the parameters of the multifractal spectra with the variation of daily return z in ssec is noticeably different from that in previous studies of heng seng index in hong kong stock market sun et al phys a 291 2001 553 562 sun et al phys a 301 2001 473 482 so we suppose that there may not be a universal rule for the dependence of the parameters of the multifractal spectra with daily return of a stock index then we construct a new measurement of market risk based on multifractal spectra and test its ability of predicting index fluctuations with a more thorough method than that in sun et al phys a 301 2001 473 482

multifractal analysis of chinese stock volatilities based on the partition function approach abstract we have performed a detailed multifractal analysis on the 1 min volatility of two indexes and 1139 stocks in the chinese stock markets based on the partition function approach the partition function q s scales as a power law with respect to the box size s the scaling exponents q form a nonlinear function of q statistical tests based on bootstrapping show that the extracted multifractal nature is significant at the 1 significance level the individual securities can be well modeled by the p model in turbulence with p 0 40 0 02 based on the idea of ensemble averaging including quenched and annealed average we treat each stock exchange as a whole and confirm the existence of multifractal nature in the chinese stock markets

multifractal detrended cross correlation analysis for two nonstationary signals we propose a method called multifractal detrended cross correlation analysis to investigate the multifractal behaviors in the power law cross correlations between two time series or higher dimensional quantities recorded simultaneously which can be applied to diverse complex systems such as turbulence finance ecology physiology geophysics and so on the method is validated with cross correlated one and two dimensional binomial measures and multifractal random walks as an example we illustrate the method by analyzing two financial time series

using the sphericity test for source detection with narrow band passive arrays a new sphericity test statistic is proposed for the complex case with a distribution that approaches the asymptotic chi squared distribution much faster than previously proposed statistics especially for situations in which the sources are very difficult to detect such as closely spaced or weak sources consequently the probability of a correct estimate is superior to those resulting from other sphericity tests the capability of this new sphericity test to detect closely space sources is examined and compared to the resolution capabilities of bearing estimation algorithms as well as other well known source detection algorithms

multifractal detrended cross correlations between the csi 300 index futures and the spot markets based on high frequency data abstract the cross correlation between the china securities index 300 csi 300 index futures and the spot markets based on high frequency data is discussed in this paper we empirically analyze the cross correlation by using the multifractal detrended cross correlation analysis mf dcca and investigate further the characteristics of asymmetry frequency difference and transmission direction of the cross correlation the results indicate that the cross correlation between the two markets is significant and multifractal meanwhile weak asymmetries exist in the cross correlation and higher data frequency results in a lower multifractality degree of the cross correlation the causal relationship between the two markets is bidirectional but the csi 300 index futures market has greater impact on the spot market

bifurcation analysis of a class of first order nonlinear delay differential equations with reflectional symmetry abstract we consider a general class of first order nonlinear delay differential equations ddes with reflectional symmetry and study completely the bifurcations of the trivial equilibrium under some generic conditions on the taylor coefficients of the dde our analysis reveals a hopf bifurcation curve terminating on a pitchfork bifurcation line at a codimension two takens bogdanov point in parameter space we compute the normal form coefficients of the reduced vector field on the centre manifold in terms of the taylor coefficients of the original dde and in contrast to many previous bifurcation analyses of ddes we also compute the unfolding parameters in terms of these coefficients for application purposes this is important since one can now identify the possible asymptotic dynamics of the dde near the bifurcation points by computing quantities which depend explicitly on the taylor coefficients of the original dde we illustrate these results using simple model systems relevant to the areas of neural networks and atmospheric physics and show that the results agree with numerical simulations

excitable systems with noise and delay with applications to control renewal theory approach we present an approach for the analytical treatment of excitable systems with noise induced dynamics in the presence of time delay an excitable system is modeled as a bistable system with a time delay while another delay enters as a control term taken after pyragas k pyragas phys lett a 170 421 1992 as a difference between the current system state and its state tau time units before this approach combines the elements of renewal theory to estimate the essential features of the resulting stochastic process as functions of the parameters of the controlling term

multifractal analysis of stock exchange crashes abstract we analyze the complexity of rare events of the djia index we reveal that the returns of the time series exhibit strong multifractal properties meaning that temporal correlations play a substantial role the effect of major stock market crashes can be best illustrated by the comparison of the multifractal spectra of the time series before and after the crash aftershock periods compared to foreshock periods exhibit richer and more complex dynamics compared to an average crash calculated by taking into account the larger 5 crashes of the djia index the 1929 event exhibits significantly more increase in multifractality than the 1987 crisis

power law cross correlations between price change and volume change of indian stocks abstract we study multifractal long range correlations and cross correlations of daily price change and volume change of 50 stocks that comprise nifty index of national stock exchange mumbai using mf dfa and mf dcca methods we find that the time series of price change are uncorrelated whereas anti persistent long range multifractal correlations are found in volume change series we also find antipersistent long range multifractal cross correlations between the time series of price change and volume change as multifractality is a signature of complexity we estimate complexity parameters of the time series of price change volume change and cross correlated price volume change by fitting the fourth degree polynomials to their multifractal spectra our results indicate that the time series of price change display high complexity whereas the time series of volume change and cross correlated price volume change display low complexity

a multifractal detrended fluctuation description of iranian rial us dollar exchange rate the miltifractal properties and scaling behaviour of the exchange rate variations of the iranian rial against the us dollar from a daily perspective is numerically investigated for this purpose the multifractal detrended fluctuation analysis mf dfa is used through multifractal analysis the scaling exponents generalized hurst exponents generalized fractal dimensions and singularity spectrum are derived moreover contribution of two major sources of multifractality that is fat tailed probability distributions and nonlinear temporal correlations are studied

multifractal detrended fluctuation analysis of nonstationary time series abstract we develop a method for the multifractal characterization of nonstationary time series which is based on a generalization of the detrended fluctuation analysis dfa we relate our multifractal dfa method to the standard partition function based multifractal formalism and prove that both approaches are equivalent for stationary signals with compact support by analyzing several examples we show that the new method can reliably determine the multifractal scaling behavior of time series by comparing the multifractal dfa results for original series with those for shuffled series we can distinguish multifractality due to long range correlations from multifractality due to a broad probability density function we also compare our results with the wavelet transform modulus maxima method and show that the results are equivalent

bootstrap multiple tests applied to sensor location a method for finding optimal locations of vibration sensors within a group of sensors for detecting knock in combustion engines is proposed it differs from other techniques in that only signal processing and statistical tests are used the method is based on linearly predicting the in cylinder pressure in a combustion chamber from the output signals of a group of vibration sensors being distributed on the engine wall the irrelevancy of a sensor in the group is characterized by the closeness to zero of a coherence gain explained by this sensor at some frequencies of interest we formulate multiple hypotheses define suitable statistics approximate their sampling distributions by the nonparametric bootstrap method and construct the generalized sequentially rejective bonferroni multiple test the level of accuracy of bootstrap tests is superior to that of asymptotic tests provided the test statistic used is asymptotically pivotal to achieve pivoting we transform the test statistic into a variance stable scale where we use a bootstrap technique to approximate the variance stabilizing transformation simulations results as well as results of an experiment performed on a test bed with a four cylinder engine emphasize the applicability of the method

high dimensional chaos in delayed dynamical systems abstract we introduce a general class of iterative delay maps to model high dimensional chaos in dynamical systems with delayed feedback the class includes as particular cases systems with a linear local dynamics we report analytic and numerical results on the scaling laws of lyapunov spectra with a number of degrees of freedom invariant measure is computed through a self consistent frobenius perron formalism which allows also a recalculation of the maximum lyapunov exponent in good agreement with the one measured directly

correlation theory of delayed feedback in stochastic systems below andronov hopf bifurcation here we address the effect of large delay on the statistical characteristics of noise induced oscillations in a nonlinear system below andronov hopf bifurcation in particular we introduce a theory of these oscillations that does not involve the eigenmode expansion and can therefore be used for arbitrary delay time in particular we show that the correlation matrix cm oscillates on two different time scales on the scale of the main period of noise induced oscillations and on the scale close to the delay time at large values of the delay time the cm is shown to decay exponentially only for large values of its argument while for the arguments comparable with the value of the delay the cm remains finite disregarding the delay time the definition of the correlation time of the system with delay is discussed

quantifying and modeling long range cross correlations in multiple time series with applications to world stock indices we propose a modified time lag random matrix theory in order to study time lag cross correlations in multiple time series we apply the method to 48 world indices one for each of 48 different countries we find long range power law cross correlations in the absolute values of returns that quantify risk and find that they decay much more slowly than cross correlations between the returns the magnitude of the cross correlations constitutes bad news for international investment managers who may believe that risk is reduced by diversifying across countries we find that when a market shock is transmitted around the world the risk decays very slowly we explain these time lag cross correlations by introducing a global factor model gfm in which all index returns fluctuate in response to a single global factor for each pair of individual time series of returns the cross correlations between returns or magnitudes can be modeled with the autocorrelations of the global factor returns or magnitudes we estimate the global factor using principal component analysis which minimizes the variance of the residuals after removing the global trend using random matrix theory a significant fraction of the world index cross correlations can be explained by the global factor which supports the utility of the gfm we demonstrate applications of the gfm in forecasting risks at the world level and infinding uncorrelated individual indices we find ten indices that are practically uncorrelated with the global factor and with the remainder of the world indices which is relevant information for world managers in reducing their portfolio risk finally we argue that this general method can be applied to a wide range of phenomena in which time series are measured ranging from seismology and physiology to atmospheric geophysics

estimation of the number of sources in unbalanced arrays via information theoretic criteria estimating the number of sources impinging on an array of sensors is a well known and well investigated problem a common approach for solving this problem is to use an information theoretic criterion such as minimum description length mdl or the akaike information criterion aic the mdl estimator is known to be a consistent estimator robust against deviations from the gaussian assumption and nonrobust against deviations from the point source and or temporally or spatially white additive noise assumptions over the years several alternative estimation algorithms have been proposed and tested usually these algorithms are shown using computer simulations to have improved performance over the mdl estimator and to be robust against deviations from the assumed spatial model nevertheless these robust algorithms have high computational complexity requiring several multidimensional searches in this paper which is motivated by real life problems a systematic approach toward the problem of robust estimation of the number of sources using information theoretic criteria is taken an mdl type estimator that is robust against deviation from assumption of equal noise level across the array is studied the consistency of this estimator even when deviations from the equal noise level assumption occur is proven a novel low complexity implementation method avoiding the need for multidimensional searches is presented as well making this estimator a favorable choice for practical applications

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

dynamical singularities in adaptive delayed feedback control we demonstrate the dynamical characteristics of adaptive delayed feedback control systems exploiting a discrete time adaptive control method derived for carrying out detailed analysis in particular the systems exhibit singularities such as power law decay of the distribution of transient times and almost zero finite time lyapunov exponents we can explain these results by characterizing such systems as having 1 a jacobian matrix with unity eigenvalue in the whole phase space and 2 parameters approaching a stability boundary proven to be identical with that of nonadaptive delayed feedback control

multifractal analysis of shanghai and hong kong stock markets before and after the connect program abstract in this paper we study the multifractal scaling behaviour in shanghai and hong kong stock markets by means of multifractal detrended fluctuation analysis mf dfa and multifractal detrended cross correlation analysis mf dcca the results show that the multifractal degrees of each stock market are larger after the shanghai hong kong stock connect program shscp than before scaling analysis demonstrates that multifractality exists in cross correlations and the cross correlation coefficients after the shscp are larger than those before the shscp moreover an analysis of the origin of multifractality indicates that long range correlation and fat tailed distribution play important roles in the contributions of multifractality finally the results via the sliding window procedure indicate that the multifractal degrees after the shscp are not significantly affected by the stock market turbulence in 2015

negative fractal dimensions and multifractals abstract a new notion of fractal dimension is defined when it is positive it effectively falls back on known definitions but its motivating virtue is that it can take negative values which measure usefully the degree of emptiness of empty sets the main use concerns random multifractals for which f

beyond the odd number limitation a bifurcation analysis of time delayed feedback control we investigate the normal form of a subcritical hopf bifurcation subjected to time delayed feedback control bifurcation diagrams which cover time dependent states as well are obtained by analytical means the computations show that unstable limit cycles with an odd number of positive floquet exponents can be stabilized by time delayed feedback control contrary to incorrect claims in the literature the model system constitutes one of the few examples where a nonlinear time delay system can be treated entirely by analytical means

simple and efficient nonparametric method for estimating the number of signals without eigendecomposition inspired by the computational simplicity and numerical stability of qr decomposition a nonparametric method for estimating the number of signals without eigendecomposition mense is proposed for the coherent narrowband signals impinging on a uniform linear array ula by exploiting the array geometry and its shift invariance property to decorrelate the coherency of signals through subarray averaging the number of signals is revealed in the rank of the qr upper trapezoidal factor of the autoproduct of a combined hankel matrix formed from the cross correlations between some sensor data since the infection of additive noise is defused signal detection capability is improved a new detection criterion is then formulated in terms of the row elements of the qr upper triangular factor when finite array data are available and the number of signals is determined as a value of the running index for which this ratio criterion is maximized where the qr decomposition with column pivoting is also used to improve detection performance the statistical analysis clarifies that the mense detection criterion is asymptotically consistent furthermore the proposed mense algorithm is robust against the array uncertainties including sensor gain and phase errors and mutual coupling and against the deviations from the spatial homogeneity of noise model the effectiveness of the mense is verified through numerical examples and the simulation results show that the mense is superior in detecting closely spaced signals with a small number of snapshots and or at relatively low signal to noise ratio snr

statistical properties of the volatility of price fluctuations we study the statistical properties of volatility measured by locally averaging over a time window t the absolute value of price changes over a short time interval ensuremath delta t we analyze the s 500 stock index for the 13 year period jan 1984 to dec 1996 we find that the cumulative distribution of the volatility is consistent with a power law asymptotic behavior characterized by an exponent ensuremath mu ensuremath approx 3 similar to what is found for the distribution of price changes the volatility distribution retains the same functional form for a range of values of t further we study the volatility correlations by using the power spectrum analysis both methods support a power law decay of the correlation function and give consistent estimates of the relevant scaling exponents also both methods show the presence of a crossover at approximately 1 5 days in addition we extend these results to the volatility of individual companies by analyzing a data base comprising all trades for the largest 500 u s companies over the two year period jan 1994 to dec 1995

performance analysis of the decentralized eigendecomposition and esprit algorithm in this paper we consider performance analysis of the decentralized power method for the eigendecomposition of the sample covariance matrix based on the averaging consensus protocol an analytical expression of the second order statistics of the eigenvectors obtained from the decentralized power method which is required for computing the mean square error mse of subspace based estimators is presented we show that the decentralized power method is not an asymptotically consistent estimator of the eigenvectors of the true measurement covariance matrix unless the averaging consensus protocol is carried out over an infinitely large number of iterations moreover we introduce the decentralized esprit algorithm which yields fully decentralized direction of arrival doa estimates based on the performance analysis of the decentralized power method we derive an analytical expression of the mse of doa estimators using the decentralized esprit algorithm the validity of our asymptotic results is demonstrated by simulations

predictability of multifractal analysis of hang seng stock index in hong kong in this paper the daily hang seng index in hong kong stock market is studied by multifractal analysis the main parameter of multifractal spectra used is f which can be used to characterize the ratio of number of highest index moments to that of lowest ones the dependence of today s gain probability g and the day s index increase probability n with f of the previous 3 days are studied it is found that g and n can reach 70 80 at the large positive f region and can be very close to 20 at the big negative f region the predictability decreases with the increasing number of the previous days

on global properties of time delayed feedback control weakly nonlinear analysis we address the problem which type of initial state yields successful stabilisation when time delayed feedback control is applied using well known concepts from bifurcation theory we provide a general mechanism that limits the corresponding basins of attraction application of normal form analysis to general delay differential equations proves the universality of our results the empirical criteria which determine the prospective size of the basin are easily accessible and a demonstration in terms of a simple numerical simulation is provided

bifurcation to large period oscillations in physical systems controlled by delay an unusual bifurcation to time periodic oscillations of a class of delay differential equations is investigated as we approach the bifurcation point both the amplitude and the frequency of the oscillations go to zero the class of delay differential equations is a nonlinear extension of a nonevasive control method and is motivated by a recent study of the foreign exchange rate oscillations by using asymptotic methods we determine the bifurcation scaling laws for the amplitude and the period of the oscillations

a cucker smale model with noise and delay a generalization of the cucker smale model for collective animal behavior is investigated the model is formulated as a system of delayed stochastic differential equations it incorporates two additional processes which are present in animal decision making but are often neglected in modeling i stochasticity imperfections of individual behavior and ii delayed responses of individuals to signals in their environment sufficient conditions for flocking for the generalized cucker smale model are derived by using a suitable lyapunov functional as a by product a new result regarding the asymptotic behavior of delayed geometric brownian motion is obtained in the second part of the paper results of systematic numerical simulations are presented they not only illustrate the analytical results but hint at a somehow surprising behavior of the system namely that the introduction of an intermediate time delay may facilitate flocking

varieties of long memory models long memory is defined as a series having a slowly declining correlogram or equivalently an infinite spectrum at zero frequency fractional integrated processes have such properties but here it is pointed out that a number of other processes can also be long memory including generalized fractionally integrated models arising from aggregation time changing coefficient models and possibly nonlinear models it seems that there are many classes of processes that deserve further study the relevance of long memory is illustrated using absolute returns from a daily stock market index

time delay autosynchronization of the spatiotemporal dynamics in resonant tunneling diodes the double barrier resonant tunneling diode exhibits complex spatiotemporal patterns including low dimensional chaos when operated in an active external circuit we demonstrate how autosynchronization by time delayed feedback control can be used to select and stabilize specific current density patterns in a noninvasive way we compare the efficiency of different control schemes involving feedback in either local spatial or global degrees of freedom the numerically obtained floquet exponents are explained by analytical results from linear stability analysis

detection of the number of signals using the benjamini hochberg procedure this paper presents a novel approach to detect multiple signals embedded in noisy observations from a sensor array we formulate the detection problem as a multiple hypothesis test to control the global level of the multiple test we apply the false discovery rate fdr criterion proposed by benjamini and hochberg compared to the classical familywise error rate fwe criterion the fdr controling procedure leads to a significant gain in power for large size problems in addition we apply the bootstrap technique to estimate the observed significance level required by the fdr controling procedure simulations show that the fdr controling procedure always provides higher probability of correct detection than the fwe controling procedure furthermore the reliability of the proposed test procedure is not affected by the gain in power of the test

some basic remarks on eigenmode expansions of time delay dynamics abstract we describe in elementary terms how eigenmode expansions can be used to deal with differential difference equations as particular applications we present the full analytical solution of linear stochastic time delay systems and the weakly nonlinear analysis of nonlinear differential difference equations in the limit of large time delay our exposition is essentially based on an explicit analytical expression for the linear spectrum in terms of the lambert w function and on the explicit formula for the eigenfunctions of the adjoint equation

chaotic attractors of an infinite dimensional dynamical system abstract we study the chaotic attractors of a delay differential equation the dimension of several attractors computed directly from the definition agrees to experimental resolution with the dimension computed from the spectrum of lyapunov exponents according to a conjecture of kaplan and yorke assuming this conjecture to be valid as the delay parameter is varied from computations of the spectrum of lyapunov exponents we observe a roughly linear increase from two to twenty in the dimension while the metric entropy remains roughly constant these results are compared to a linear analysis and the asymptotic behavior of the lyapunov exponents is derived

multifractal detrending moving average cross correlation analysis there are a number of situations in which several signals are simultaneously recorded in complex systems which exhibit long term power law cross correlations the multifractal detrended cross correlation analysis mfdcca approaches can be used to quantify such cross correlations such as the mfdcca based on the detrended fluctuation analysis mfxdfa method we develop in this work a class of mfdcca algorithms based on the detrending moving average analysis called mfxdma the performances of the proposed mfxdma algorithms are compared with the mfxdfa method by extensive numerical experiments on pairs of time series generated from bivariate fractional brownian motions two component autoregressive fractionally integrated moving average processes and binomial measures which have theoretical expressions of the multifractal nature in all cases the scaling exponents h xy extracted from the mfxdma and mfxdfa algorithms are very close to the theoretical values for bivariate fractional brownian motions the scaling exponent of the cross correlation is independent of the cross correlation coefficient between two time series and the mfxdfa and centered mfxdma algorithms have comparative performances which outperform the forward and backward mfxdma algorithms for two component autoregressive fractionally integrated moving average processes we also find that the mfxdfa and centered mfxdma algorithms have comparative performances while the forward and backward mfxdma algorithms perform slightly worse for binomial measures the forward mfxdma algorithm exhibits the best performance the centered mfxdma algorithms performs worst and the backward mfxdma algorithm outperforms the mfxdfa algorithm when the moment order q 0 we apply these algorithms to the return time series of two stock market indexes and to their volatilities for the returns the centered mfxdma algorithm gives the best estimates of h xy q since its h xy 2 is closest to 0 5 as expected and the mfxdfa algorithm has the second best performance for the volatilities the forward and backward mfxdma algorithms give similar results while the centered mfxdma and the mfxdfa algorithms fail to extract rational multifractal nature

multifractality in stock indexes fact or fiction abstract multifractal analysis and extensive statistical tests are performed upon intraday minutely data within individual trading days for four stock market indexes including hsi szsc s p 500 and nasdaq to check whether the indexes instead of the returns possess multifractality we find that the mass exponent q is linear and the singularity q is close to 1 for all trading days and all indexes furthermore we find strong evidence showing that the scaling behaviors of the original data sets cannot be distinguished from those of shuffled time series hence the so called multifractality in the intraday stock market indexes is merely an illusion

analytical and numerical investigations of the phase locked loop with time delay we derive the normal form for the delay induced hopf bifurcation in the first order phase locked loop with time delay by the multiple scaling method the resulting periodic orbit is confirmed by numerical simulations further detailed numerical investigations demonstrate exemplarily that this system reveals a rich dynamical behavior with phase portraits fourier analysis and lyapunov spectra it is possible to analyze the scaling properties of the control parameter in the period doubling scenario both qualitatively and quantitatively within the numerical accuracy there is evidence that the scaling constant of the time delayed phase locked loop coincides with the feigenbaum constant delta approximately 4 669 in one dimensional discrete systems

cross correlations between volume change and price change in finance one usually deals not with prices but with growth rates r defined as the difference in logarithm between two consecutive prices here we consider not the trading volume but rather the volume growth rate r the difference in logarithm between two consecutive values of trading volume to this end we use several methods to analyze the properties of volume changes r and their relationship to price changes r we analyze 14 981 daily recordings of the standard and poor s s p 500 index over the 59 year period 1950 2009 and find power law cross correlations between r and r by using detrended cross correlation analysis dcca we introduce a joint stochastic process that models these cross correlations motivated by the relationship between r and r we estimate the tail exponent of the probability density function p r r 1 for both the s p 500 index as well as the collection of 1819 constituents of the new york stock exchange composite index on 17 july 2009 as a new method to estimate we calculate the time intervals q between events where r q we demonstrate that q the average of q obeys q q we find 3 furthermore by aggregating all q values of 28 global financial indices we also observe an approximate inverse cubic law

exact dynamics of stochastic linear delayed systems application to spatiotemporal coordination of comoving agents delayed dynamics result from finite transmission speeds of a signal in the form of energy mass or information in stochastic systems the resulting lagged dynamics challenge our understanding due to the rich behavioral repertoire encompassing monotonic oscillatory and unstable evolution despite the vast literature quantifying this rich behavior is limited by a lack of explicit analytic studies of high dimensional stochastic delay systems here we fill this gap for systems governed by a linear langevin equation of any number of delays and spatial dimensions with additive gaussian noise by exploiting laplace transforms we are able to derive an exact time dependent analytic solution of the langevin equation by using characteristic functionals we are able to construct the full time dependence of the multivariate probability distribution of the stochastic process as a function of the delayed and nondelayed random variables as an application we consider interactions in animal collective movement that go beyond the traditional assumption of instantaneous alignment we propose models for coordinated maneuvers of comoving agents applicable to recent empirical findings in pigeons and bats whereby individuals copy the heading of their neighbors with some delay we highlight possible strategies that individual pairs may adopt to reduce the variance in their velocity difference and or in their spatial separation we also show that a minimum in the variance of the spatial separation at long times can be achieved with certain ratios of measurement to reaction delay

multiple scale analysis of delayed dynamical systems abstract the model equations of a semiconductor laser with delayed feeback are studied as a prototype of general delayed systems in the case of long delay thermodynamic limit it is shown that its behaviour in the vicinity of the hopf bifurcation can be described by suitable amplitude equations the derivation of the final model follows naturally from the space time representation of the evolution and by the corresponding re formulation of the linear stability problem regions characterized by both direct and inverse hopf bifurcations are found and in particular parameter values are identified for which a chaotic evolution is expected

statistical volatility duration and complexity of financial dynamics on sierpinski gasket lattice percolation abstract a novel agent based financial dynamics is established based on the percolation system on sierpinski gasket lattice to reproduce the statistical characteristics of financial markets sierpinski gasket lattice is a fractal like graph which corresponds to the fractal well known sierpinski gasket modeling a financial dynamics on sierpinski gasket lattice is a new approach in financial micro mechanism construction in an attempt to investigate the statistical properties of returns and prove the feasibility of the proposed model two new nonlinear statistics maximum and average monotonous volatility duration are introduced in this work for the first time which describe the trend of volatility of return time series in financial markets furthermore a new method cmcid is proposed to measure the synchronization and similarity behaviors of return volatility duration in multiscale the results show that the pairs of real data and simulated data have synchronization and the synchronization becomes stronger when the scale increases and the power law distribution is employed to investigate the corresponding statistical properties which shows that the proposed model shares a common power law distribution with regard to monotonous volatility duration the empirical results show that the simulated series from the financial model and the historical data share common statistical properties which indicate that the proposed model is reasonable in terms of volatility behavior

functional characterization of linear delay langevin equations we present an exact functional characterization of linear delay langevin equations driven by any noise structure defined through its characteristic functional this method relies on the possibility of finding an explicitly analytical expression for each realization of the delayed stochastic process in terms of those of the driving noise general properties of the transient dissipative dynamics are analyzed the corresponding interplay with a color gaussian noise is presented as a full application of our functional method we study a model for population growth with non gaussian fluctuations the gompertz model driven by multiplicative white shot noise

oblique projection based enumeration of mixed noncoherent and coherent narrowband signals in many application scenarios the signals impinging on the array of sensors comprise the noncoherent uncorrelated and or partially correlated signals and the coherent signals with several groups due to multipath propagation in this paper we consider the problem of estimating the number of noncoherent narrowband signals and that of coherent narrowband signals with multiple groups impinging on a planar sensor array composed of two parallel uniform linear arrays ulas and an oblique projection based enumerator for the mixed signals opems is proposed by utilizing the qr decomposition based ratio criterion qrrc for rank determination of a matrix in the opems the number of noncoherent signals and that of coherent signals in each group are estimated separately where only the elevation angles of noncoherent signals are estimated to isolate the coherent signals from the noncoherent ones and the computationally intensive and time consuming eigendecomposition procedure is avoided the consistency of the proposed opems is analyzed and its effectiveness is verified through numerical examples

comparison of time delayed feedback schemes for spatiotemporal control of chaos in a reaction diffusion system with global coupling time delayed feedback control for stabilizing time periodic spatial patterns is investigated in a generic reaction diffusion system with global coupling we focus on the case of low dimensional chaos where unstable patterns admit only a single unstable mode spatial degrees of freedom are taken into account to define different control schemes the efficiency of these schemes is discussed where control forces are motivated by physical requirements as well as by the possibility of obtaining analytically exact results we find that control schemes that contain the full feedback of the inhibitor variable may finally destroy the control performance thus schemes that omit the inhibitor might be more efficient our numerical findings are explained in terms of floquet spectra and compared with analytical solutions of particular coupling schemes

the complexity and fractal structures of csi300 before and after the introduction of csi300if abstract this paper employs multifractal detrended fluctuation analysis mf dfa approach to analyze the complexity and fractal structures of china securities index 300 csi300 which covers the period from april 5 2006 to may 9 2014 through comparing the statistic properties before and after the introduction of csi300 index futures csi300if we find that 1 the price return series exhibits multifractal properties for the two periods 2 by comparing the efficient measure based on the general hurst exponent we find the market becomes more efficient after the introduction of csi300if 3 the width of multifractal spectrum becomes narrower which means the complexity of the market is decreased therefore the introduction of csi300if is beneficial to reduce the risk and increase the efficiency of chinese securities market furthermore the main sources of multifractality of these time series are examined through the shuffle method and the results show that before csi300if the multifractality is mainly due to the long range correlation properties between small and large fluctuations while after csi300if it is more due to fat tailed probability distributions

on the eigenvalue spectrum for time delayed floquet problems abstract a linear homogeneous scalar differential difference equation with harmonic time dependence is investigated the associated eigenvalue problem is solved in terms of a continued fraction expansion for the characteristic equation the dependence of the largest eigenvalue on the system parameters being relevant for stability of periodic states in delay systems is discussed in detail the competition between the two timescales the delay and the external period cause intricate structures the result suggests features to improve control of chaos by time delayed feedback schemes with time dependent control amplitudes

testing for nonlinearity in time series the method of surrogate data we describe a statistical approach for identifying nonlinearity in time series the method first specifies some linear process as a null hypothesis then generates surrogate data sets which are consistent with this null hypothesis and finally computes a discriminating statistic for the original and for each of the surrogate data sets if the value computed for the original data is significantly different than the ensemble of values computed for the surrogate data then the null hypothesis is rejected and nonlinearity is detected we discuss various null hypotheses and discriminating statistics the method is demonstrated for numerical data generated by known chaotic systems and applied to a number of experimental time series which arise in the measurement of superfluids brain waves and sunspots we evaluate the statistical significance of the evidence for nonlinear structure in each case and illustrate aspects of the data which this approach identifies

study of a high dimensional chaotic attractor the nature of a very high dimensional chaotic attractor in an infinite dimensional phase space is examined for the purpose of studying the relationships between the physical processes occurring in the real space and the characteristics of high dimensional attractor in the phase space we introduce two complementary bases from which the attractor is observed one the lyapunov basis composed of the lyapunov vectors and the another the fourier basis composed of the fourier modes we introduce the exterior subspaces on the basis of the lyapunov vectors and observe the chaotic motion projected onto these exteriors it is shown that a certain statistical property of the projected motion changes markedly as the exterior subspace goes out of the attractor the origin of such a phenomenon is attributed to more fundamental features of our attractor which become manifest when the attractor is observed from the lyapunov basis a counterpart of the phenomenon can be observed also on the fourier basis because there is a statistical one to one correspondence between the lyapunov vectors and the fourier modes in particular a statistical property of the high pass filtered time series reflects clearly the difference between the interior and the exterior of the attractor

source enumeration in array processing using a two step test we investigate the problem of enumerating source signals impinging on an array of sensors given noisy limited observations the assumption of a large sample size is indispensable for most of the existing approaches so that they suffer significant performance degradation when only a small number of samples is available random matrix theory can capture the asymptotic distributions of the eigenvalues accurately and provide good approximations even for a finite sample size in this paper we take into account the relationship and distributions of the noise and signal eigenvalues based on random matrix theory and derive a simple two step test numerical simulations demonstrate that it is capable of correctly determining the number of sources in the case of small sample sizes

detection of sources using bootstrap techniques source detection in array processing can be viewed as a test for equality of eigenvalues such a test is proposed based on a multiple test procedure that considers all pairwise comparisons between eigenvalues using the bootstrap to estimate the null distributions of the test statistics results in a procedure with minimal assumptions on the nature of the signal simulations show that the proposed test is superior to information theoretic criteria such as the mdl which are based on gaussian signals and large sample sizes performance in most cases exceeds the more powerful sphericity test

bifurcations in a planar system of differential delay equations modeling neural activity abstract a planar system of differential delay equations modeling neural activity is investigated the stationary points and their saddle node bifurcations are estimated by an analysis of the associated characteristic equation hopf bifurcations are demonstrated at the intersection points of the saddle node and hopf bifurcation curves in an appropriate parameter plane the existence of bogdanov takens singularities is shown the properties of the bogdanov takens singularities are studied by applying the center manifold and normal form theory a numerical example illustrates the obtained results

flexible detection criterion for source enumeration in array processing two new procedures are proposed using random matrix theory to evaluate theoretically the performance of the bayesian information criterion bic for source enumeration in array processing the proposed procedures can predict precisely the estimation results of the bic also they shed light on the behavior of the bic in order to remedy the limitation of the bic that is the bic tends to underestimate the number of sources by one in most cases an extra parameter is introduced into the bic formulation which results in a new criterion for source enumeration referred to as the flexible detection criterion fdc by carefully choosing this parameter the fdc is capable of substantially reducing the probability of underestimation which is validated by theoretical analysis and simulations note that the fdc is consistent and has low computational complexity as the bic

an improved multifractal formalism and self similar measures abstract to characterize the geometry of a measure its generalized dimensions dq have been introduced recently the mathematically precise definition given by falconer fractal geometry 1990 turns out to be unsatisfactory for reasons of convergence as well as of undesired sensitivity to the particular choice of coordinates in the negative q range a new definition is introduced which is also based on box counting but which carries relevant information about for negative q also in particular the legendre connection between generalized dimensions and the multifractal spectrum is established using large deviations and rigorous proofs are provided for the implicit formula giving the generalized dimensions of selfsimilar measures which was until now known only for positive q

space representation of stochastic processes with delay we show that a time series x t evolving by a nonlocal update rule x t f x t ensuremath n x t ensuremath k with two different delays kln can be mapped onto a local process in two dimensions with special time delayed boundary conditions provided that n and k are coprime for certain stochastic update rules exhibiting a nonequilibrium phase transition this mapping implies that the critical behavior does not depend on the short delay k in these cases the autocorrelation function of the time series is related to the critical properties of the corresponding two dimensional model

universal and non universal properties of recurrence intervals of rare events abstract this paper is devoted to the statistical analysis on the recurrence intervals of rare events that are defined above a given threshold the memory property of original records is found to have significant effects on the distribution and the correlation structure of recurrence intervals so that some universal and non universal properties arise i for long range persistent records by the arfima processes where large values are likely to follow large values the recurrence intervals yield stretched exponential distributions and further show long range persistence ii for long range anti persistent records by the arfima processes the recurrence intervals obey exponential distributions also absence of autocorrelation iii for short range autocorrelated records the distribution and the correlation structure of recurrence intervals both depend on the parameters of the model and the threshold of rare events

fokker planck perspective on stochastic delay systems exact solutions and data analysis of biological systems stochastic delay systems with additive noise are examined from the perspective of fokker planck equations for a linear system the exact stationary probability density is derived by means of a delay fokker planck equation we show how to determine the delay equation of the linear system from experimental data and corroborate a fundamental result previously obtained by kuchler and mensch we also propose a method to derive delay equations of nonlinear systems from experimental data to this end the theory of multivariate fokker planck equations is used the applicability of this method is demonstrated for stochastic models describing tracking and pointing movements of humans

dcca cross correlation coefficient differentiation theoretical and practical approaches abstract we propose in this paper to establish a well defined relationship between d f a the long range auto correlation exponent and d c c a the long range cross correlation exponent respectively described by the dfa and dcca methods this relationship will be accomplished theoretically by differentiating the dcca cross correlation coefficient d c c a n also for some specific times series we apply this theory in order to establish its validity

computing unstable manifolds of periodic orbits in delay differential equations we present the first algorithm for computing unstable manifolds of saddle type periodic orbits with one unstable floquet multiplier in systems of autonomous delay differential equations ddes with one fixed delay specifically we grow the one dimensional unstable manifold wu q of an associated saddle fixed point q of a poincare map defined by a suitable poincare section starting close to q along the linear approximation to wu q given by the associated eigenfunction our algorithm grows the manifold as a sequence of points where the distance between points is governed by the curvature of the one dimensional intersection curve wu q of wu q with our algorithm makes it possible to study global bifurcations in ddes we illustrate this with the break up of an invariant torus and a subsequent crisis bifurcation to chaos in a dde model of a semiconductor laser with phase conjugate feedback