synchronization in general complex dynamical networks with coupling delays abstract complex networks have attracted increasing attention from various fields of science and engineering today due to the finite speeds of transmission and spreading as well as traffic congestions a signal or influence travelling through a complex network often is associated with time delays and this is very common in biological and physical networks in this paper we introduce complex dynamical network models with coupling delays for both continuous and discrete time cases and then investigate their synchronization phenomena and criteria based on these new complex network models we derive synchronization conditions for both delay independent and delay dependent asymptotical stabilities in terms of linear matrix inequalities lmi we finally use a network with a fixed delay and a specific coupling scheme as an example to illustrate the theoretical results

a new neural network for solving linear and quadratic programming problems a new neural network for solving linear and quadratic programming problems is presented and is shown to be globally convergent the new neural network improves existing neural networks for solving these problems it avoids the parameter turning problem it is capable of achieving the exact solutions and it uses only simple hardware in which no analog multipliers for variables are required furthermore the network solves both the primal problems and their dual problems simultaneously

synchronization of continuous dynamical networks with discrete time communications in this paper synchronization of continuous dynamical networks with discrete time communications is studied though the dynamical behavior of each node is continuous time the communications between every two different nodes are discrete time i e they are active only at some discrete time instants moreover the communication intervals between every two communication instants can be uncertain and variable by choosing a piecewise lyapunov krasovskii functional to govern the characteristics of the discrete communication instants and by utilizing a convex combination technique a synchronization criterion is derived in terms of linear matrix inequalities with an upper bound for the communication intervals obtained the results extend and improve upon earlier work simulation results show the effectiveness of the proposed communication scheme some relationships between the allowable upper bound of communication intervals and the coupling strength of the network are illustrated through simulations on a fully connected network a star like network and a nearest neighbor network

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

stability and synchronization analysis of neural networks via halanay type inequality in this paper not only some novel sufficient criteria for stability of discrete delay neural networks but also a new discriminant method for self synchronization of hopfield neural networks are considered some novel stability criteria for discrete delay neural networks are obtained if the time average of the difference for two coefficients on some fixed lengths is lower bounded by some positive numbers moreover a new discrete halanay inequality is given which extends the existing results based on the halanay inequality a novel sufficient criterion on self synchronization of hopfield neural networks with time delay is obtained two numerical examples are given to demonstrate the effectiveness of proposed methods

uniqueness of the stationary wave for the extended fisher kolmogorov equation abstract the extended fisher kolmogorov equation ut uxxxx uxx u u3 0 models a binary system near the lifshitz critical point and is known to exhibit a stationary heteroclinic solution joining the equilibria 1 for the classical case 0 the heteroclinic is u x tanh x 2 and is unique up to the obvious symmetries we prove the conjecture that the uniqueness persists all the way to 1 8 where the onset of spatial chaos associated with the loss of monotonicity of the stationary wave is known to occur our methods are non perturbative and employ a global cross section to the hamiltonian flow of the stationary fourth order equation on the energy level of 1 we also prove uniform a priori bounds on all bounded stationary solutions valid for any 0

scaling in currency exchange we study the scaling behavior in currency exchange rates our results suggest that they satisfy scaling with an exponent close to 0 5 but that it differs qualitatively from that of a simple random walk indeed price variations cannot be considered as independent variables and subtle correlations are present furthermore we introduce a novel statistical analysis for economic data which makes the physical properties of a signal more evident and eliminates the systematic effects of time periodicity

synchronization in complex dynamical networks with nonsymmetric coupling based on the work of nishikawa and motter who have extended the well known master stability framework to include non diagonalizable cases we develop another extension of the master stability framework to obtain criteria for global synchronization several criteria for global synchronization are provided which generalize some previous results the jordan canonical transformation method is used in stead of the matrix diagonalization method especially we show clearly that the synchronizability of a dynamical network with nonsymmetric coupling is not always characterized by its second largest eigenvalue even though all the eigenvalues of the nonsymmetric coupling matrix are real furthermore the effects of the asymmetry of coupling on synchronizability of networks with different structures are analyzed numerical simulations are also done to illustrate and verify the theoretical results on networks in which each node is a dynamical limit cycle oscillator consisting of a two cell cellular neural network

liouville type results for fourth order elliptic equations liouville type theorems are obtained for the solutions to elliptic equations of the form 2 u q x u p x f u 0 by means of two subharmonic functionals and green type inequalities

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

new approach to synchronization analysis of linearly coupled ordinary differential systems in this paper a general framework is presented for analyzing the synchronization stability of linearly coupled ordinary differential equations lcodes the uncoupled dynamical behavior at each node is general and can be chaotic or otherwise the coupling configuration is also general with the coupling matrix not assumed to be symmetric or irreducible on the basis of geometrical analysis of the synchronization manifold a new approach is proposed for investigating the stability of the synchronization manifold of coupled oscillators in this way criteria are obtained for both local and global synchronization these criteria indicate that the left and right eigenvectors corresponding to eigenvalue zero of the coupling matrix play key roles in the stability analysis of the synchronization manifold furthermore the roles of the uncoupled dynamical behavior on each node and the coupling configuration in the synchronization process are also studied

synchronous chaos in coupled oscillator systems we investigate the synchronization of chaotic oscillations in coupled oscillator systems both theoretically and in analog electronic circuits particular attention is paid to deriving and testing general conditions for the stability of synchronous chaotic behavior in cases where the coupled oscillator array possesses a shift invariant symmetry these cases include the well studied cases of nearest neighbor diffusive coupling and all to all or global coupling an approximate criterion is developed to predict the stability of synchronous chaotic oscillations in the strong coupling limit when the oscillators are coupled through a single coordinate scalar coupling this stability criterion is illustrated numerically in a set of coupled r ossler like oscillators synchronization experiments with coupled r ossler like oscillator circuits are also carried out to demonstrate the applicability of the theory to real systems

econophysics scaling and its breakdown in finance we discuss recent empirical results obtained by analyzing high frequency data of a stock market index the standard and poor s 500 we focus on the scaling properties and on its breakdown of the index dynamics a simple stochastic model the truncated levy flight is illustrated successes and limitations of this model are presented a discussion about similarities and differences between the scaling properties observed in financial markets and in fully developed turbulence is also provided

stock market dynamics abstract we elucidate on several empirical statistical observations of stock market returns moreover we find that these properties are recurrent and are also present in invariant measures of low dimensional dynamical systems thus we propose that the returns are modeled by the first poincare return time of a low dimensional chaotic trajectory this modeling which captures the recurrent properties of the return fluctuations is able to predict well the evolution of the observed statistical quantities in addition it explains the reason for which stocks present simultaneously dynamical properties and high uncertainties in our analysis we use data from the s p 500 index and the brazilian stock telebras

transition from anticipatory to lag synchronization via complete synchronization in time delay systems the existence of anticipatory complete and lag synchronization in a single system having two different time delays that is feedback delay tau1 and coupling delay tau2 is identified the transition from anticipatory to complete synchronization and from complete to lag synchronization as a function of coupling delay tau2 with a suitable stability condition is discussed in particular it is shown that the stability condition is independent of the delay times tau1 and tau2 consequently for a fixed set of parameters all the three types of synchronizations can be realized further the emergence of exact anticipatory complete or lag synchronization from the desynchronized state via approximate synchronization when one of the system parameters b2 is varied is characterized by a minimum of the similarity function and the transition from on off intermittency via periodic structure in the laminar phase distribution

measuring multifractality of stock price fluctuation using multifractal detrended fluctuation analysis abstract analyzing the shanghai stock price index daily returns using mf dfa method it is found that there are two different types of sources for multifractality in time series namely fat tailed probability distributions and non linear temporal correlations based on that a sliding window of 240 frequency data in 5 trading days was used to study stock price index fluctuation it is found that when the stock price index fluctuates sharply a strong variability is clearly characterized by the generalized hurst exponents h q therefore two measures h and based on generalized hurst exponents were proposed to compare financial risks before and after price limits and reform of non tradable shares the empirical results verify the validity of the measures and this has led to a better understanding of complex stock markets

assessing market uncertainty by means of a time varying intermittency parameter for asset price fluctuations abstract maximum likelihood estimation techniques for multifractal processes are applied to high frequency data in order to quantify intermittency in the fluctuations of asset prices from time records as short as one month these methods permit extraction of a meaningful intermittency parameter characterising the degree of volatility clustering we can therefore study the time evolution of volatility clustering and test the statistical significance of this variability by analysing data from the oslo stock exchange and comparing the results with the investment grade spread we find that the estimates of are lower at times of high market uncertainty

synchronization of hyperchaotic systems with delayed bidirectional coupling synchronization of three bidirectionally coupled hyperchaotic systems is studied using the ikeda model as the hyperchaotic unit the whole system is given by three delay differential equations with two distinct time lags sufficient condition for the global stability of the manifold of exact synchronization is found analytically local stability of the synchronization manifold is studied by numerical computation of the transverse lyapunov exponent and statistical properties of the orbits

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

scale invariant distribution and multifractality of volatility multipliers in stock markets abstract the statistical properties of the multipliers of the absolute returns are investigated using 1 min high frequency data of financial time series the multiplier distribution is found to be independent of the box size s when s is larger than some crossover scale providing direct evidence of the existence of scale invariance in financial data the multipliers with base a 2 are well approximated by a normal distribution and the most probable multiplier scales as a power law with respect to the base a we unravel that the volatility multipliers possess multifractal nature which is independent of construction of the multipliers that is the values of s and a

mu stability of nonlinear positive systems with unbounded time varying delays the stability of the zero solution plays an important role in the investigation of positive systems in this brief we discuss the mu stability of positive nonlinear systems with unbounded time varying delays the system is modeled by the continuous time ordinary differential equation under some assumptions on the nonlinear functions such as homogeneous cooperative and nondecreasing we propose a novel transform by which the nonlinear system reduces to a new system thus we analyze its dynamics which can simplify the nonlinear homogenous functions with respect to the arbitrary dilation map to those with respect to the standard dilation map we finally get some new criteria for the global mu stability taking the degree into consideration a numerical example is given to demonstrate the validity of obtained results

from turbulence to financial time series abstract we develop a framework especially suited to the autocorrelation properties observed in financial times series by borrowing from the physical picture of turbulence the success of our approach as applied to high frequency foreign exchange data is demonstrated by the overlap of the curves in a figure fig 1 since we are able to provide an analytical derivation of the relative sizes of the quantities depicted these quantities include departures from gaussian probability density functions and various two and three point autocorrelation functions

autonomous and non autonomous attractors for differential equations with delays abstract the asymptotic behaviour of some types of retarded differential equations with both variable and distributed delays is analysed in fact the existence of global attractors is established for different situations with and without uniqueness and for both autonomous and non autonomous cases using the classical notion of attractor and the recently new concept of pullback one respectively

liouville type and uniqueness results for a class of elliptic equations abstract liouville type results are obtained for fourth order elliptic equations of the form 2 u q x g u p x f u 0 and q x g u u p x f u 0 by means of two subharmonic functionals defined appropriately on their respective solutions and a green inequality

synchronization in complex delayed dynamical networks with nonsymmetric coupling abstract a new general complex delayed dynamical network model with nonsymmetric coupling is introduced and then we investigate its synchronization phenomena several synchronization criteria for delay independent and delay dependent synchronization are provided which generalize some previous results the matrix jordan canonical formalization method is used instead of the matrix diagonalization method so in our synchronization criteria the coupling configuration matrix of the network does not required to be diagonalizable and may have complex eigenvalues especially we show clearly that the synchronizability of a delayed dynamical network is not always characterized by the second largest eigenvalue even though all the eigenvalues of the coupling configuration matrix are real furthermore the effects of time delay on synchronizability of networks with unidirectional coupling are studied under some typical network structures the results are illustrated by delayed networks in which each node is a two dimensional limit cycle oscillator system consisting of a two cell cellular neural network numerical simulations show that these networks can realize synchronization with smaller time delay and will lose synchronization when the time delay increase larger than a threshold

characteristic distributions of finite time lyapunov exponents we study the probability densities of finite time or local lyapunov exponents in low dimensional chaotic systems while the multifractal formalism describes how these densities behave in the asymptotic or long time limit there are significant finite size corrections which are coordinate dependent depending on the nature of the dynamical state the distribution of local lyapunov exponents has a characteristic shape for intermittent dynamics and at crises dynamical correlations lead to distributions with stretched exponential tails while for fully developed chaos the probability density has a cusp exact results are presented for the logistic map stackrel ensuremath rightarrow x 4x 1 ensuremath x at intermittency the density is markedly asymmetric while for typical chaos it is known that the central limit theorem obtains and a gaussian density results local analysis provides information on the variation of predictability on dynamical attractors these densities which are used to characterize the nonuniform spatial organization on chaotic attractors are robust to noise and can therefore be measured from experimental data

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

generalized halanay inequalities and their applications to neural networks with unbounded time varying delays in this brief we discuss some variants of generalized halanay inequalities that are useful in the discussion of dissipativity and stability of delayed neural networks integro differential systems and volterra functional differential equations we provide some generalizations of the halanay inequality which is more accurate than the existing results as applications we discuss invariant set dissipative synchronization and global asymptotic stability for the hopfield neural networks with infinite delays we also prove that the dynamical systems with unbounded time varying delays are globally asymptotically stable

characteristic exponents and invariant manifolds in hilbert space the multiplicative ergodic theorem and the construction almost everywhere of stable and unstable manifolds pesin theory are extended to differentiable dynamical systems on hilbert manifolds under some compactness assumptions the results apply to partial differential equations of evolution and also to non invertible maps of compact manifolds

exponential synchronization of hybrid coupled networks with delayed coupling this paper investigates exponential synchronization of coupled networks with hybrid coupling which is composed of constant coupling and discrete delay coupling there is only one transmittal delay in the delayed coupling the fact is that in the signal transmission process the time delay affects only the variable that is being transmitted from one system to another then it makes sense to assume that there is only one single delay contributing to the dynamics some sufficient conditions for synchronization are derived based on lyapunov functional and linear matrix inequality lmi in particular the coupling matrix may be asymmetric or nondiagonal moreover the transmittal delay can be different from the one in the isolated system a distinctive feature of this work is that the synchronized state will vary in comparison with the conventional synchronized solution especially the degree of the nodes and the inner delayed coupling matrix heavily influence the synchronized state finally a chaotic neural network is used as the node in two regular networks to show the effectiveness of the proposed criteria

an intriguing hybrid synchronization phenomenon of two coupled complex networks this paper investigates the hybrid synchronization problem of two coupled complex networks employing the linear feedback and the adaptive feedback control methods which are simple efficient and easy to implement in practical applications we obtain some useful criteria of the hybrid synchronization of two coupled networks based on the lyapunov stability theory and lasalle s invariance principle it shows that under suitable conditions two coupled complex networks can realize an intriguing hybrid synchronization the outer anti synchronization between the driving network and the response network and the inner complete synchronization in the driving network and the response network respectively numerical simulations demonstrate the effectiveness of the proposed hybrid synchronization scheme

global synchronization criteria of linearly coupled neural network systems with time varying coupling in this paper global synchronization of linearly coupled neural network nn systems with time varying coupling is investigated the dynamical behavior of the uncoupled system at each node is general which can be chaotic or others the coupling configuration is time varying i e the coupling matrix is not a constant matrix based on lyapunov function method and the specific property of householder transform some criteria for the global synchronization are obtained by these criteria one can verify whether the coupled system with time varying coupling is globally synchronized which is important and useful for both understanding and interpreting synchronization phenomena and designing coupling configuration finally two simulations are given to demonstrate the effectiveness of the theoretical results

fractal and multifractal properties of exit times and poincarerecurrences systems with chaotic dynamics possess anomalous statistical properties and their trajectories do not correspond to the gaussian process this property imposes description of such time characteristics as the distribution of exit times or poincar acute e recurrences by introducing a multi fractal time scale in order to satisfy the observed powerlike tails of the distributions we introduce a corresponding phase space time partitioning and spectral function for dimensions and make a connection between dimensions and transport exponent that defines the anomalous open quotes strange close quotes kinetics copyright ital 1997 ital the american physical society

multifractal analysis of hang seng index in hong kong stock market abstract in this paper the daily hang seng index in hong kong stock market is analyzed by multifractal the correlation of the parameters of the multifractal spectra with the variation of close return z is studied statistically it is found that the amount of the variation of return is correlated with the amount of of that day the increase or decrease of the return is related to the positive or negative value of f the gain probability and the increasing day s probability can be higher than 70 at the larger f region and be lower than 20 at the more negative region

neural network for quadratic optimization with bound constraints a recurrent neural network is presented which performs quadratic optimization subject to bound constraints on each of the optimization variables the network is shown to be globally convergent and conditions on the quadratic problem and the network parameters are established under which exponential asymptotic stability is achieved through suitable choice of the network parameters the system of differential equations governing the network activations is preconditioned in order to reduce its sensitivity to noise and to roundoff errors the optimization method employed by the neural network is shown to fall into the general class of gradient methods for constrained nonlinear optimization and in contrast with penalty function methods is guaranteed to yield only feasible solutions

on the stock market recurrence abstract we analyze the return of the s p 500 index and characterize its evolution as being typical of a low dimensional recurrent deterministic system the first poincare return time of the chaotic logistic mapping trajectories is used to model the return evolution the efficiency of the model is demonstrated by daily predictions over an interval of time since january 1950 of this index and long term prediction for a period of 150 days

generalized synchronization in time delayed systems we investigate the generalized synchronization between two unidirectionally linearly and nonlinearly coupled chaotic nonidentical ikeda models and find existence conditions of the generalized synchronization also we study the chaos synchronization between nonidentical ikeda models with variable feedback delay times and find the existence and sufficient stability conditions for the retarded synchronization manifold with the coupling delay lag time generalization of the approach to the wide class of nonlinear chaotic systems is also presented

power law and multiscaling properties of the chinese stock market abstract we investigate the cumulative probability density function pdf and the multiscaling properties of the returns in the chinese stock market by using returns data adjusted for thin trading we find that the distribution has power law tails at shorter microscopic timescales or lags however the distribution follows an exponential law for longer timescales furthermore we investigate the long range correlation and multifractality of the returns in the chinese stock market by the dfa and mfdfa methods we find that all the scaling exponents are between 0 5 and 1 by dfa method which exhibits the long range power law correlations in the chinese stock market moreover we find by mfdfa method that the generalized hurst exponents h q are not constants which shows the multifractality in the chinese stock market we also find that the correlation of shenzhen stock market is stronger than that of shanghai stock market

forecasting volatility in shanghai and shenzhen markets based on multifractal analysis abstract this paper analyzes the multifractality in shanghai and shenzhen stock markets using multifractal spectrum analysis and multifractal detrended fluctuation analysis we find that the main source of multifractality is long range correlations of large and small fluctuations then we introduce a multifractal volatility measure mv and find that by taking mv as daily conditional volatility the simulated series displayed similar stylized facts to the original daily return series by capturing the dynamics of mv using the arfima model we find that the out of sample forecasting performance of the arfima mv model is better than some garch class models and the arfima rv model under some criteria of loss function

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

measuring daily value at risk of ssec index a new approach based on multifractal analysis and extreme value theory abstract recent studies in the econophysics literature reveal that price variability has fractal and multifractal characteristics not only in developed financial markets but also in emerging markets taking high frequency intraday quotes of the shanghai stock exchange component ssec index as example this paper proposes a new method to measure daily value at risk var by combining the newly introduced multifractal volatility mfv model and the extreme value theory evt method two var backtesting techniques are then employed to compare the performance of the model with that of a group of linear and nonlinear generalized autoregressive conditional heteroskedasticity garch models the empirical results show the multifractal nature of price volatility in chinese stock market var measures based on the multifractal volatility model and evt method outperform many garch type models at high risk levels

observer based synchronization in complex dynamical networks with nonsymmetric coupling abstract based on a general complex dynamical network model with nonsymmetric coupling some criteria for synchronization are proposed based on the approach of state observer design unlike the nonobserver based dynamical networks where the coupling between two connected nodes is defined by an inner coupling matrix and full state coupling is typically needed in this paper smaller amount of coupling variables or even only a scalar output signal of each node is needed to synchronize the network unlike the commonly researched complex network model where the coupling between nodes is symmetric here in our network model the coupling configuration matrix is not assumed to be symmetric and may have complex eigenvalues the matrix jordan canonical formalization method is used instead of the matrix diagonalization method so in our synchronization criteria the coupling configuration matrix is not required to be diagonalizable especially the proposed step by step approach is simpler in computation than the existent ones which usually rely heavily on numerical toolbox and may be done by hand completely an example is given to illustrate the step by step approach in which each node is a two dimensional dynamical limit cycle oscillator system consisting of a two cell cellular neural network and numerical simulations are also done to verify the results of design

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

effect of linear and nonlinear filters on multifractal analysis in this paper we investigate how various linear and nonlinear transformations affect the multifractal properties of both artificial and traffic signals using the multifractal analysis based on partition function with comparison with the multifractal detrended fluctuation analysis specifically we study the effect of three types of transforms which are often encountered in physical and biological processes linear nonlinear polynomial and logarithmic filters we compare the multifractal scaling properties of signals before and after the transform it is shown that linear filters do not change the multifractal properties while the effect of nonlinear polynomial depends on the power of the polynomial filter in addition the maximum value of the multifractal spectrum remains almost unchanged after the logarithmic filter however we find that the width of the multifractal spectrum changes significantly even for much smaller value of the offset parameter

price volume multifractal analysis and its application in chinese stock markets abstract an empirical research on chinese stock markets is conducted using statistical tools first the multifractality of stock price return series r i r i ln p t 1 ln p t and trading volume variation series v i v i ln v t 1 ln v t is confirmed using multifractal detrended fluctuation analysis furthermore a multifractal detrended cross correlation analysis between stock price return and trading volume variation in chinese stock markets is also conducted it is shown that the cross relationship between them is also found to be multifractal second the cross correlation between stock price p i and trading volume v i is empirically studied using cross correlation function and detrended cross correlation analysis it is found that both shanghai stock market and shenzhen stock market show pronounced long range cross correlations between stock price and trading volume third a composite index r based on price and trading volume is introduced compared with stock price return series r i and trading volume variation series v i r variation series not only remain the characteristics of original series but also demonstrate the relative correlation between stock price and trading volume finally we analyze the multifractal characteristics of r variation series before and after three financial events in china namely price limits reform of non tradable shares and financial crisis in 2008 in the whole period of sample to study the changes of stock market fluctuation and financial risk it is found that the empirical results verified the validity of r

enlightenment from various conditional probabilities about hang seng index in hong kong stock market abstract the daily hang seng index in the hong kong stock market has been analyzed in this paper two kinds of sign sequences as given conditions have been used to predict the future price movements one is the parameter of multifractal spectrum f based on the indexes recorded in every minute and the other is the variation of the close index i results show that correlation between large fluctuations of the close price and the condition in these two methods is strong and some sign sequences of the parameter f can be used to predict the probability of the near future price movements

recurrence time analysis long term correlations and extreme events the recurrence times between extreme events have been the central point of statistical analyses in many different areas of science simultaneously the poincar e recurrence time has been extensively used to characterize nonlinear dynamical systems we compare the main properties of these statistical methods pointing out their consequences for the recurrence analysis performed in time series in particular we analyze the dependence of the mean recurrence time and of the recurrence time statistics on the probability density function on the interval whereto the recurrences are observed and on the temporal correlations of time series in the case of long term correlations we verify the validity of the stretched exponential distribution which is uniquely defined by the exponent ensuremath gamma at the same time showing that it is restricted to the class of linear long term correlated processes simple transformations are able to modify the correlations of time series leading to stretched exponentials recurrence time statistics with different ensuremath gamma which shows a lack of invariance under the change of observables

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

ordinary differential equations in the oscillation theory of partial half linear differential equation abstract in the paper we study the damped half linear partial differential equation div a x u p 2 u b x u p 2 u c x u p 2 u 0 using radialization method we derive general oscillation results which allow to deduce new oscillation criteria for this equation from oscillation criteria for ordinary differential equations using careful radialization we improve several known oscillation criteria

does the singular value decomposition entropy have predictive power for stock market evidence from the shenzhen stock market abstract this paper analyzes the predictive ability of the singular value decomposition entropy for the shenzhen component index based on different scales it is found that the predictive ability of the entropy for the index is affected by the width of moving time windows and the structural break in stock market by moving time windows with one year the predictive power of singular value decomposition entropy of shenzhen stock market for its component index is found after the reform of non tradable shares

forecasting volatility of ssec in chinese stock market using multifractal analysis abstract in this paper taking about 7 years high frequency data of the shanghai stock exchange composite index ssec as an example we propose a daily volatility measure based on the multifractal spectrum of the high frequency price variability within a trading day an arfima model is used to depict the dynamics of this multifractal volatility mfv measures the one day ahead volatility forecasting performances of the mfv model and some other existing volatility models such as the realized volatility model stochastic volatility model and garch are evaluated by the superior prediction ability spa test the empirical results show that under several loss functions the mfv model obtains the best forecasting accuracy

multifractal analysis of spot rates in tanker markets and their comparisons with crude oil markets abstract this paper investigates the dynamic features of the spot rates for vlcc ulcc suezmax aframax panamax and handysize tanker markets by means of multifractal detrended fluctuation analysis mf dfa the hurst exponents especially the time dependent hurst exponents of the daily rate returns are calculated to capture the fractal properties of these different tanker markets the origins of multifractility in these markets are identified by comparing their multifractal scaling exponents based on the original data the shuffled data and the surrogate data furthermore the non periodic cycles for these markets are detected by the v statistic finally the comparisons of the fractal properties between the tanker markets and the crude oil commodity markets suggest that the tanker markets are more fractal than their upstream counterparts

a novel approach to synchronization of nonlinearly coupled network systems with delays in this investigation a novel approach to establishing the global synchronization of coupled network systems is presented under this approach individual subsystems can be non autonomous and the coupling configuration is rather general the coupling terms can be non diffusive nonlinear time dependent asymmetric and with time delays with an iteration scheme the problem of synchronization is transformed into solving a corresponding linear system of algebraic equations subsequently delay dependent and delay independent criteria for global synchronization can be established we implement the present approach to analyze synchronization of the fitzhugh nagumo systems under delayed and nonlinear sigmoidal coupling two examples are presented to demonstrate new dynamical scenarios where oscillatory behavior and multistability emerge or are suppressed as the coupled neurons synchronize under the synchronization criterion in addition asynchrony induced by the coupling strength or coupling delay occurs while the synchronization criterion is violated

which is the better forecasting model a comparison between har rv and multifractality volatility abstract in this paper by taking the 5 min high frequency data of the shanghai composite index as example we compare the forecasting performance of har rv and multifractal volatility realized volatility realized bipower variation and their corresponding short memory model with rolling windows forecasting method and the model confidence set which is proved superior to spa test the empirical results show that for six loss functions har rv outperforms other models moreover to make the conclusions more precise and robust we use the mcs test to compare the performance of their logarithms form models and find that the har log rv has a better performance in predicting future volatility furthermore by comparing the two models of har rv and har log rv we conclude that in terms of performance forecasting the har log rv model is the best model among models we have discussed in this paper

liouville type and uniqueness results for a class of sixth order elliptic equations on considere des equations de la forme 3 u p 2 u q u ru 0 ou p q et r sont des fonctions positives et c 2 dans e n et on demontre des resultats de type liouville a l aide des fonctions sous harmoniques definies sur les solutions et des inegalites de type green

scaling of the distribution of fluctuations of financial market indices up to more than one month we find that the distributions for dt 4d 1560 min are consistent with a power law asymptotic behavior characterized by an exponent a 3 well outside the stable levy regime 0 a 2 to test the robustness of the s p result we perform a parallel analysis on two other financial market indices database iv contains 3560 daily records of the nikkei index for the 14 year period 1984 1997 and database v contains 4649 daily records of the hang seng index for the 18 year period 1980 1997 we find estimates ofa consistent with those describing the distribution of s p 500 daily returns one possible reason for the scaling of these distributions is the long persistence of the autocorrelation function of the volatility for time scales longer than dt 3 4 d our results are consistent with a slow convergence to gaussian behavior s1063 651x 99 11211 x pacs number s 05 40 fb 05 45 tp 89 90 1n

inertial and slow manifolds for delay equations with small delays abstract yu a ryabov and r d driver proved that delay equations with small delays have lipschitz inertial manifolds we prove that these manifolds are smooth in addition we show that expansion in the small delay can be used to obtain the dynamical system on the inertial manifold this justifies post newtonian approximation for delay equations

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

multifractal description of stock price index fluctuation using a quadratic function fitting abstract in order to obtain a quantitative multifractal characterization of the stock price index the multifractal spectrum of shanghai stock price index time series in 2005 was investigated and the multifractal spectrum was fitted using a quadratic function a sliding window of 240 frequency data in 5 trading days was used to investigate the stock price index fluctuation the multifractal parameters and coefficients in each window were obtained by fitting the local multifractal spectrum using a quadratic function it is found that when the stock price index fluctuates sharply a strong variability is clearly characterized by the multifractal parameters and the quadratic function coefficients this has led to a better understanding of complex stock markets

consensus of multi agent systems with unbounded time varying delays in this note the consensus problem with infinite time varying delays for linearly coupled static network is investigated the delay affects only the off diagonal terms in continuous time equations at first we define an effective consensus ability index then by using the graph theory and a new concept of consensus we prove that under some mild conditions the network can realize consensus an example is given to show the validity of obtained results

multipeaked probability distributions of recurrence times we determine probabilities of recurrence time into finite sized physically meaningful subsets of phase space we consider three different autonomous chaotic systems i scattering in a three peaked potential ii connected billiards and iii lorenz equations we find multipeaked probability distributions similar to the distributions found in driven stochastically resonant systems in nondriven systems such as ours only monotonic decaying distributions exponentials stretched exponentials power laws and slight variations or combinations of these have hitherto been reported discrete peaks in autonomous systems have as yet escaped attention in autonomous systems and correspond to specific trajectory subsets involving an integer number of loops

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

multifractal properties of chinese stock market in shanghai abstract in this article we apply three methods of multifractal analysis partition function method singular spectrum method and multifractal detrended fluctuation analysis method to analyze the closing index fluctuations of shanghai stock market during the past seven years we have found that shanghai stock market has weak multifractal features and there are long range power law correlations between index series the shapes of singular spectrums do not change with time scales and their strengths weaken when the scales shorten but when the orders of partition function increase the strengths of multifractal increase the singular spectrums become rougher and the general hurst exponents decrease these results provide solid and important values for further study on the dynamic mechanism of stock market price fluctuation

synchronization in dynamic networks with nonsymmetrical time delay coupling based on linear feedback controllers based on a general complex dynamic network model with nonsymmetrical time delay coupling and without assuming irreducibility a strategy for global exponential synchronization is proposed based on the approach of linear state feedback controllers especially the criteria for controller design can be expressed by inequalities instead of matrix inequalities thus the proposed controllers can be easily constructed without relying on any numerical toolbox the efficiency of the control scheme is revealed by simulations on a network consisting of the unified chaotic systems with nearest neighbour unidirectional time delay coupling

exponential synchronization of coupled stochastic memristor based neural networks with time varying probabilistic delay coupling and impulsive delay this paper deals with the exponential synchronization of coupled stochastic memristor based neural networks with probabilistic time varying delay coupling and time varying impulsive delay there is one probabilistic transmittal delay in the delayed coupling that is translated by a bernoulli stochastic variable satisfying a conditional probability distribution the disturbance is described by a wiener process based on lyapunov functions halanay inequality and linear matrix inequalities sufficient conditions that depend on the probability distribution of the delay coupling and the impulsive delay were obtained numerical simulations are used to show the effectiveness of the theoretical results

largest lyapunov exponent estimation and selective prediction by means of simplex forecast algorithms limited predictability is one of the remarkable features of deterministic chaos and this feature may be quantized in terms of lyapunov exponents accordingly lyapunov exponent estimates may be expected to follow in a natural way from forecast algorithms exploring this idea we propose a method estimating the largest lyapunov exponent from a time series which uses the behavior of so called simplex forecasts the method considers the estimation of properties of the distribution of local simplex expansion coefficients these are also used for the definition of error bars for the lyapunov exponent estimates and allows for selective forecasts with improved prediction accuracy we demonstrate these concepts on standard test examples and three realistic applications to time series concerning largest lyapunov exponent estimation of an experimentally obtained hyperchaotic nmr signal brain state differentiation and stock market prediction