non conservative perturbations of homoclinic snaking scenarios abstract homoclinic snaking refers to the continuation of homoclinic orbits to an equilibrium e near a heteroclinic cycle connecting e and a periodic orbit p typically homoclinic snaking appears in one parameter families of reversible conservative systems here we discuss perturbations of this scenario which are both non reversible and non conservative we treat this problem analytically in the spirit of the work 3 the continuation of homoclinic orbits happens with respect to both the original continuation parameter and the perturbation parameter the continuation curves are parametrised by the dwelling time l of the homoclinic orbit near p it turns out that l tends to zero while the vs l diagram displays isolas or criss cross snaking curves in a neighbourhood of the original snakes and ladder structure in the course of our studies we adapt both fenichel coordinates near p and the analysis of shilnikov problems near p to the present situation

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

nonlinear structural response of laminated composite plates subjected to blast loading we are concerned with the theoretical analysis of the laminated composite plates exposed to normal blast shock waves as well as presenting correlation between the theoretical analysis and the experimental results of the strain time histories the laminated composite plate is clamped at all edges on the theoretical side of the study dynamic equations of the plates are derived by the use of the virtual work principle within the framework of the love theory of plates the geometric nonlinearity effects are taken into account with von karman assumptions then the governing equations of the laminated plate are solved by the runge kutta verner method a new displacement function is considered for the theoretical solution of the blast loaded clamped plate furthermore finite element modeling and analysis for the blast loaded composite plates are presented on the experimental side of the study tests have been carried out on the laminated composite plates with clamped edges for two different blast loads the results of theoretical and finite element methods are compared with the experimental results theoretical and finite element analyses results are in a good agreement there is a qualitative agreement between the analyses and experimental results in the first load case the predicted peak strains and response frequency are in an agreement with the experimental results for first load case thus the theoretical solution may be used for providing material in the preliminary design stage there is a difference between the analysis and experimental results in the second load case because of the extremely large deflections in this study the effects of loading conditions geometrical properties and material properties are separately examined on the dynamic behavior as well

tracking invariant manifolds with differential forms in singularly perturbed systems abstract a technique is developed for finding homoclinic orbits in singularly perturbed systems the desired orbit lies near a singular solution that has both fast and slow time scales the orbit is to be constructed as the transverse intersection of a center stable and center unstable manifold which requires tracking the invariant manifolds near the singular solution the main technical advance is the exchange lemma which allows one to convert information about transversality of manifolds associated with the singular limit equations to information about behavior of the invariant manifold as it leaves a neighborhood of a slow segment of the singular solution the computations for this lemma are done with the use of differential forms and the lemma is applied to prove the existence of a homoclinic orbit in a class of singularly perturbed equations

time dependent hurst exponent in financial time series abstract we calculate the hurst exponent h t of several time series by dynamical implementation of a recently proposed scaling technique the detrending moving average dma in order to assess the accuracy of the technique we calculate the exponent h t for artificial series simulating monofractal brownian paths with assigned hurst exponents h we next calculate the exponent h t for the return of high frequency tick by tick sampled every minute series of the german market we find a much more pronounced time variability in the local scaling exponent of financial series compared to the artificial ones the dma algorithm allows the calculation of the exponent h t without any a priori assumption on the stochastic process and on the probability distribution function of the random variables as happens for example in the case of the kitagawa grid and the extended kalmann filtering methods the present technique examines the local scaling exponent h t around a given instant of time this is a significant advance with respect to the standard wavelet transform or to the higher order power spectrum technique which instead operate on the global properties of the series by legendre or fourier transform of qth order moments

on hurst exponent estimation under heavy tailed distributions abstract in this paper we show how the sampling properties of the hurst exponent methods of estimation change with the presence of heavy tails we run extensive monte carlo simulations to find out how rescaled range analysis r s multifractal detrended fluctuation analysis m f d f a detrending moving average d m a and generalized hurst exponent approach g h e estimate hurst exponent on independent series with different heavy tails for this purpose we generate independent random series from stable distribution with stability exponent changing from 1 1 heaviest tails to 2 gaussian normal distribution and we estimate the hurst exponent using the different methods r s and g h e prove to be robust to heavy tails in the underlying process g h e provides the lowest variance and bias in comparison to the other methods regardless the presence of heavy tails in data and sample size utilizing this result we apply a novel approach of the intraday time dependent hurst exponent and we estimate the hurst exponent on high frequency data for each trading day separately we obtain hurst exponents for s p500 index for the period beginning with year 1983 and ending by november 2009 and we discuss the surprising result which uncovers how the market s behavior changed over this long period

on the geometry of an atmospheric slow manifold abstract we examine the hyperbolic structure and the invariant manifolds of a model proposed by lorenz to introduce the concept of an atmospheric slow manifold within the framework of dynamical system theory we address the question of the long time asymptotic behaviour of the system using the global geometric point of view it is shown that the model can be reduced to the classical example of a pendulum coupled to a harmonic oscillator the dynamical regimes of interest for the slow manifold hypothesis correspond to regions of phase space near the saddle center fixed point of this model which were not previously explored these phase space regions are analysed using a combination of melnikov type methods and ideas from singular perturbation theory by using the reversible symmetries of the model an extension of the melnikov theory is derived this extension allows us to find homoclinic orbits and determine their approximation by simply computing the zeros of a certain function which is constructed in terms of the usual melnikov function countable infinities of global homoclinic bifurcations and existence of chaotic dynamics can be shown to exist by using the new tool

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

sad and stock returns revisited nonlinear analysis based on mf dcca and granger test abstract using both multifractal detrended fluctuation analysis mf dfa and multifractal detrended cross correlation analysis mf dcca methods this paper examines the effects of seasonal affective disorder sad on stock returns in the chinese stock market we first separate stocks into small and large cap stocks according to market value and find that sad and these two stock return series are multifractal based on mf dfa moreover we employ mf dcca and show that the cross correlation between sad and stock returns is anti persistent and the cross correlation between sad and return of small cap stock is stronger than that between sad and return of large cap stock furthermore we find that long range correlation is the main source of multifractality in the cross correlations between sad and small cap stock while both long range correlation and fat tails contribute to the multifractality between sad and large cap stock finally utilizing nonlinear granger causality test we find that sad is the granger cause of stock returns not vice versa

extreme values and fat tails of multifractal fluctuations in this paper we discuss the problem of the estimation of extreme event occurrence probability for data drawn from some multifractal process we also study the heavy power law tail behavior of probability density function associated with such data we show that because of strong correlations the standard extreme value approach is not valid and classical tail exponent estimators should be interpreted cautiously extreme statistics associated with multifractal random processes turn out to be characterized by non self averaging properties our considerations rely upon some analogy between random multiplicative cascades and the physics of disordered systems and also on recent mathematical results about the so called multifractal formalism applied to financial time series our findings allow us to propose an unified framework that accounts for the observed multiscaling properties of return fluctuations the volatility clustering phenomenon and the observed inverse cubic law of the return pdf tails

regime switching for dynamic correlations we propose a new model for the variance between multiple time series the regime switching dynamic correlation we decompose the covariances into correlations and standard deviations and the correlation matrix follows a regime switching model it is constant within a regime but different across regimes the transitions between the regimes are governed by a markov chain this model does not suffer from a curse of dimensionality and it allows analytic computation of multi step ahead conditional expectations of the variance matrix when combined with the armach model taylor modelling financial time series wiley new york and schwert j finance 44 5 1989 1115 for the standard deviations we also present an empirical application which illustrates that our model can have a better fit of the data than the dynamic conditional correlation model proposed by engle j business econ statist 20 3 2002 339

analysis of time series subject to changes in regime abstract this paper introduces an em algorithm for obtaining maximum likelihood estimates of parameters for processes subject to discrete shifts in autoregressive parameters with the shifts themselves modeled as the outcome of a discrete valued markov process the simplicity of the em algorithm permits potential application of the approach to large vector systems

the free vibrations of inhomogeneous elastic cylinders and spheres abstract the variational statement governing equations and corresponding ritz approximations are derived in cartesian cylindrical and spherical coordinates for the evaluation of the natural frequencies of free vibrations of elastic cylinders and spheres the formulation can account for orthotropic material symmetry and can be applied to either solid or hollow geometries the approximating functions selected for the displacement components depend on the geometry and coordinate system used to describe the problem and are a combination of power series fourier series and spherical harmonics representative examples are given in the various coordinate systems for both the cylinder and the sphere in general excellent agreement is found with results obtained by other methods

free vibration of a conical shell with variable thickness abstract an analysis is presented for the free vibration of a truncated conical shell with variable thickness by use of the transfer matrix approach the applicability of the classical thin shell theory is assumed and the governing equations of vibration of a conical shell are written as a coupled set of first order differential equations by using the transfer matrix of the shell once the matrix has been determined by quadrature of the equations the natural frequencies and the mode shapes of vibration are calculated numerically in terms of the elements of the matrix under any combination of boundary conditions at the edges the method is applied to truncated conical shells with linearly parabolically or exponentially varying thickness and the effects of the semi vertex angle truncated length and varying thickness on the vibration are studied

structural response of laminated composite shells subjected to blast loading comparison of experimental and theoretical methods abstract the results from a theoretical and experimental investigation of the dynamic response of cylindrically curved laminated composite shells subjected to normal blast loading are presented the dynamic equations of motion for cylindrical laminated shells are derived using the assumptions of love s theory of thin elastic shells kinematically admissible displacement functions are chosen to represent the motion of the clamped cylindrical shell and the governing equations are obtained in the time domain using the galerkin method the time dependent equations of the cylindrically curved laminated shell are then solved by the runge kutta verner method finite element modelling and analysis for the blast loaded cylindrical shell are also presented experimental results for cylindrically curved laminated composite shells with clamped edges and subjected to blast loading are presented the blast pressure and strain measurements are performed on the shell panels the strain response frequencies of the clamped cylindrical shells subjected to blast load are obtained using the fast fourier transformation technique in addition the effects of material properties on the dynamic behaviour are examined the strain time history curves show agreement between the experimental and analysis results in the longitudinal direction of the cylindrical panels however there is a discrepancy between the experimental and analysis results in the circumferential direction of the cylindrical panels a good prediction is obtained for the response frequency of the cylindrical shell panels

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

governing equations of a stiffened laminated inhomogeneous conical shell this study presents the dynamic equations of a stiffened composite laminated conical thin shell under the influence of initial stresses the governing equations of a truncated conical shell are based on the donnell mushtari theory of thin shells including the transverse shear deformation and rotary inertia the extension bending coupling is considered in the derivation the composite laminated conical shell is also reinforced at uniform intervals by elastic rings and or stringers the stiffening elements are relatively closely spaced and therefore the stiffeners are smeared out along the conical shell the inhomogeneity of material properties because of temperature moisture or manufacturing processes is taken into account in the constitutive equations a generalized variational theorem is derived so as to describe the complete set of the fundamental equations of the conical shell next the uniqueness is examined in solutions of the dynamic equations of the conical shell and the boundary and initial conditions are shown to be sufficient for the uniqueness in solutions the equations of the laminated composite conical shell are solved by the use of the finite difference method as an illustrative example the accuracy of results is tested by certain earlier results and a good agreement is found

true and apparent scaling the proximity of the markov switching multifractal model to long range dependence in this paper we consider daily financial data of a collection of different stock market indices exchange rates and interest rates and we analyze their multi scaling properties by estimating a simple specification of the markov switching multifractal msm model in order to see how well the estimated model captures the temporal dependence of the data we estimate and compare the scaling exponents h q for q 1 2 for both empirical data and simulated data of the msm model in most cases the multifractal model appears to generate apparent long memory in agreement with the empirical scaling laws

one dimensional steady state poisson nernst planck systems for ion channels with multiple ion species abstract the one dimensional poisson nernst planck pnp system is a basic model for ion flow through membrane channels if the debye length is much smaller than the characteristic radius of the channel the pnp system can be treated as a singularly perturbed system we provide a geometric framework for the study of the steady state pnp system involving multiple types of ion species with multiple regions of piecewise constant permanent charge special structures of this particular problem are revealed which together with the general framework allows one to reduce the existence and multiplicity of singular orbits to a system of nonlinear algebraic equations near each singular orbit an application of the exchange lemma from the geometric singular perturbation theory gives rise to the existence and local uniqueness of a solution of the singular boundary value problem a new phenomenon on multiplicity and spatial behavior of steady states involving three or more types of ion species is discovered in an example the phenomenon cannot occur when only two types of ion species are involved

nonlinear damped vibrations of a laminated composite plate subjected to blast load this research deals with the derivation and solution of nonlinear dynamic equations of a clamped laminated plate exposed to blast load including structural damping effects dynamic equations of the plate are derived by the use of the virtual work principle the geometric nonlinearity effects are taken into account with the von karman large deflection theory of thin plates an appropriate approximate solution is assumed for the space domain considering the finite element analysis results for the large deformation static analysis of the laminated plate the galerkin method is used to obtain the nonlinear differential equations in the time domain these nonlinear differential equations include structural damping effects the finite difference method is applied to solve the system of coupled nonlinear equations the results of the theoretical analysis are compared with the experimental results good agreement is found for the peak values and frequencies effects of aspect ratio and damping on the dynamic response of the plate are examined the damping coefficient greatly affects the nonlinear dynamic response

singular heteroclinic orbits for degenerate modulation equations the problem of finding heteroclinic orbits for the quintic ginzburg landau equation in the case that the imaginary parts of the coefficients are o with 0 1 is considered when c where is a distinguished parameter in the equation and 0 there exists a singular heteroclinic orbit connecting a stable finite amplitude state to the stable zero state it is shown that for a certain region of parameter space this orbit persists for small with a wave speed c which is o furthermore using an approach reminiscent of the melnikov method the sign of c 0 is calculated this calculation is crucial in settling the persistence question finally it is shown that for this wave speed it is possible for additional heteroclinic orbits to exist these additional orbits connect two finite amplitude states

non stationary multifractality in stock returns abstract we perform an extensive empirical analysis of scaling properties of equity returns suggesting that financial data show time varying multifractal properties this is obtained by comparing empirical observations of the weighted generalised hurst exponent wghe with time series simulated via multifractal random walk mrw by bacry et al e bacry j delour j f muzy multifractal random walk physical review e 64 2 2001 026103 while dynamical wghe computed on synthetic mrw series is consistent with a scenario where multifractality is constant over time fluctuations in the dynamical wghe observed in empirical data are not in agreement with a mrw with constant intermittency parameter we test these hypotheses of constant multifractality considering different specifications of mrw model with fatter tails in all cases considered although the thickness of the tails accounts for most of the anomalous fluctuations of multifractality it still cannot fully explain the observed fluctuations

scaling behaviors in differently developed markets scaling properties of four di erent stock market indices are studied in terms of a generalized hurst exponent approach we nd that the deviations from pure brownian motion behavior are associated with the degrees of development of the markets and we observe strong di erentiations in the scaling properties of markets at di erent development stage c

measuring the self similarity exponent in levy stable processes of financial time series abstract geometric method based procedures which will be called gm algorithms herein were introduced in m a sanchez granero j e trinidad segovia j garcia perez some comments on hurst exponent and the long memory processes on capital markets phys a 387 2008 5543 5551 to efficiently calculate the self similarity exponent of a time series in that paper the authors showed empirically that these algorithms based on a geometrical approach are more accurate than the classical algorithms especially with short length time series the authors checked that gm algorithms are good when working with fractional brownian motions moreover in j e trinidad segovia m fernandez martinez m a sanchez granero a note on geometric method based procedures to calculate the hurst exponent phys a 391 2012 2209 2214 a mathematical background for the validity of such procedures to estimate the self similarity index of any random process with stationary and self affine increments was provided in particular they proved theoretically that gm algorithms are also valid to explore long memory in fractional levy stable motions in this paper we prove empirically by monte carlo simulation that gm algorithms are able to calculate accurately the self similarity index in levy stable motions and find empirical evidence that they are more precise than the absolute value exponent denoted by ave onwards and the multifractal detrended fluctuation analysis mf dfa algorithms especially with a short length time series we also compare them with the generalized hurst exponent ghe algorithm and conclude that both gm2 and ghe algorithms are the most accurate to study financial series in addition to that we provide empirical evidence based on the accuracy of gm algorithms to estimate the self similarity index in levy motions that the evolution of the stocks of some international market indices such as u s small cap and nasdaq100 cannot be modelized by means of a brownian motion

the use of the hurst exponent to investigate the global maximum of the warsaw stock exchange wig20 index abstract the wig20 index the index of the 20 biggest companies traded on the warsaw stock exchange reached the global maximum on 29th october 2007 i have used the local dfa detrended functional analysis to obtain the hurst exponent diffusion exponent and investigate the signature of anti correlation of share price evolution around the maximum the analysis was applied to the share price evolution for variable dfa parameters for many values of parameters the evidence of anti correlation near the wig20 maximum was pointed out

multifractal random walk we introduce a class of multifractal processes referred to as multifractal random walks mrws to our knowledge it is the first multifractal process with continuous dilation invariance properties and stationary increments mrws are very attractive alternative processes to classical cascadelike multifractal models since they do not involve any particular scale ratio the mrws are indexed by four parameters that are shown to control in a very direct way the multifractal spectrum and the correlation structure of the increments we briefly explain how in the same way one can build stationary multifractal processes or positive random measures

dynamical generalized hurst exponent as a tool to monitor unstable periods in financial time series we investigate the use of the hurst exponent dynamically computed over a weighted moving time window to evaluate the level of stability instability of financial firms financial firms bailed out as a consequence of the 2007 2008 credit crisis show a neat increase with time of the generalized hurst exponent in the period preceding the unfolding of the crisis conversely firms belonging to other market sectors which suffered the least throughout the crisis show opposite behaviors we find that the multifractality of the bailed out firms increase at the crisis suggesting that the multi fractal properties of the time series are changing these findings suggest the possibility of using the scaling behavior as a tool to track the level of stability of a firm in this paper we introduce a method to compute the generalized hurst exponent which assigns larger weights to more recent events with respect to older ones in this way large fluctuations in the remote past are less likely to influence the recent past we also investigate the scaling associated with the tails of the log returns distributions and compare this scaling with the scaling associated with the hurst exponent observing that the processes underlying the price dynamics of these firms are truly multi scaling