the dynamics of an impulsive delay predator prey model with variable coefficients abstract in this paper we formulate a new robust two species nonautonomous predator prey model with multi delays and impulsive effects and perform a systematic mathematical and ecological study our results in this paper indicate that under the appropriate linear periodic impulsive perturbations the system is permanent and has a unique positive globally attractive semi trivial periodic solution by using the brouwer fixed point theorem we prove that if the periodic system is permanent then there is at least one positive periodic solution of the system we show that the conditions for global attractivity of the positive semi trivial periodic solution and permanence of the population of the model depend on time delay so we call it profitless in this paper the main feature is that we introduce multi delays and impulses into the predator prey model exhibit a new modeling method which is applied to investigate multi species impulsive multi delays differential equations

solution of toeplitz normal equations by sine transform based preconditioning abstract the normal equations constructed by a toeplitz matrix are studied in order to find a suitable preconditioner related to the discrete sine transform new results are given about the structure of the product of two toeplitz matrices which allow the cgn method to achieve a superlinear rate of convergence this preconditioner outperforms the circulant one for the iterative solution of toeplitz least squares problems such strategy can also be applied to nonsymmetric linear systems a block generalization is discussed

permanence and global attractivity of a delayed periodic logistic equation in this paper we consider the delayed periodic logistic equation n t n t a t b t np t t c t nq t t which describes the evolution of a single species sufficient conditions which guarantee the permanence and the globally attractivity of the system are obtained

global attractivity of positive periodic solution to periodic lotka volterra competition systems with pure delay abstract we consider a periodic lotka volterra competition system without instantaneous negative feedbacks i e pure delay systems x i t x i t r i t j 1 n a i j t x j t i j t i 1 2 n we establish some 3 2 type criteria for global attractivity of a positive periodic solution of the system which generalize the well known wright s 3 2 criteria for the autonomous delay logistic equation and thereby address the open problem proposed by both kuang y kuang global stability in delayed nonautonomous lotka volterra type systems without saturated equilibria differential integral equations 9 1996 557 567 and teng z teng nonautonomous lotka volterra systems with delays j differential equations 179 2002 538 561

existence and global stability of periodic solutions of a discrete predator prey system with delays with the help of continuation theorem in coincidence degree theory and lyapunov functions we derive sufficient and realistic conditions that guarantee the existence of a positive periodic solution for a delayed discrete predator prey system and also obtain sufficient conditions for the global stability of positive periodic solutions

global attractivity in delayed differential equations with applications to food limited population model abstract a new criterion is built which guarantees the global attractivity of zero solution for equation having the form x t 1 x t f t x t the behavior of global solution on r is also addressed as an application we study the existence of globally attractive positive almost periodic solution for the food limited single population model our results improve those in literature

multiplicity of periodic solutions for a delayed ratio dependent predator prey model with monotonic functional response and harvesting terms abstract the existence of four positive periodic solutions for a delayed ratio dependent predator prey model with monotonic functional response x t x t a t b t x t c t g x t y t y t h 1 t y t y t f t g x t t y t t d t h 2 t is established by using the generalized continuation theorem where a t b t c t d t f t t h 1 t and h 2 t are all nonnegative periodic continuous functions with period 0 when h 1 t h 2 t 0 the conditions that guarantee the existence of four positive periodic solutions reduces exactly to that in fan et al 2004 1 and our main result also improves the corresponding results in zhang and hou 2010 2 and fan and wang 2001 3

scaling and memory in the return intervals of realized volatility abstract we perform return interval analysis of 1 min realized volatility defined by the sum of absolute high frequency intraday returns for the shanghai stock exchange composite index ssec and 22 constituent stocks of ssec the scaling behavior and memory effect of the return intervals between successive realized volatilities above a certain threshold q are carefully investigated in comparison with the volatility defined by the closest tick prices to the minute marks the return interval distribution for the realized volatility shows a better scaling behavior since 20 stocks out of 22 stocks and the ssec pass the kolmogorov smirnov ks test and exhibit scaling behaviors among which the scaling function for 8 stocks could be approximated well by a stretched exponential distribution revealed by the ks goodness of fit test under the significance level of 5 the improved scaling behavior is further confirmed by the relation between the fitted exponent and the threshold q in addition the similarity of the return interval distributions for different stocks is also observed for the realized volatility the investigation of the conditional probability distribution and the detrended fluctuation analysis dfa show that both short term and long term memory exists in the return intervals of realized volatility

spectral and computational properties of band symmetric toeplitz matrices abstract we are investigating spectral properties of band symmetric toeplitz matrices bst matrices by giving a suitable representation of a bst matrix we achieve separation results and multiplicity conditions for the eigenvalues of a 7 r 5 diagonal bst matrix and also structural properties of the eigenvectors we give eigenvalue bounds for a 2k 1 diagonal bst matrix and also necessary and sufficient conditions for positive definiteness which are easy to check the same conditions apply in the case of block bst matrices either with full blocks or with bst blocks we exhibit fast computational methods for the evaluation of the determinant and the characteristic polynomial of a bst matrix either for sequential or for parallel computations two algorithms based on the bisection technique and newton s method are shown to be very fast for computing the eigenvalues of a 7 or 5 diagonal bst matrix

stability and bifurcation analysis in hematopoietic stem cell dynamics with multiple delays abstract this paper is devoted to the analysis of a maturity structured system of hematopoietic stem cell hsc populations in the bone marrow the model is a system of differential equations with several time delays we discuss the stability of equilibria and perform the analysis of hopf bifurcation more precisely we first obtain a set of improved sufficient conditions ensuring the global asymptotical stability of the zero solution using the lyapunov method and the embedding technique of asymptotically autonomous semiflows then we prove that there exists at least one positive periodic solution for the n dimensional system as a time delay varies in some region this result is established by combining hopf bifurcation theory the global hopf bifurcation theorem due to wu j wu symmetric functional differential equations and neural networks with memory trans amer math soc 350 1998 4799 4838 and a continuation theorem of coincidence degree theory some numerical simulations are also presented to illustrate the analytic results

persistence and global stability of positive periodic solutions of three species food chains with omnivory in this paper we investigate the existence and global stability of the positive periodic solutions of delayed discrete food chains with omnivory with the help of continuation theorem in coincidence degree theory and lyapunov functions some sufficient conditions are obtained the results show that for such a system with omnivory more conditions are required for the persistence of the positive periodic solutions than that of a linear food chain on the other hand omnivory makes no differences on the stability of the solutions

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

existence and global stability of periodic solutions of a discrete ratio dependent food chain model with delay by using the continuation theorem base on gaines and mawhin s coincidence degree sufficient and realistic conditions are obtained for the global existence of positive periodic solutions for a discrete time nonautonomous food chain model and sufficient conditions for the global stability of positive periodic solutions are also obtained some known results are extended

existence of positive periodic solutions of a neutral delay lotka volterra system with impulses sufficient conditions are obtained for the existence of periodic positive solutions of a class of neutral impulsive delay lotka volterra systems n i t n i t a i t j 1n b i j t n j t t i j t j 1nc i j t n j t c i j t n i t k n i t k b i kn i t k i 1 2 n k 1 2 by using some techniques of mawhin coincidence degree theory my results generalize some known results it is shown that under the appropriate linear periodic impulsive perturbations the neutral impulsive delay lotka volterra system preserves the original periodicity of the neutral nonimpulsive delay lotka volterra system

multiplicity of positive periodic solutions to a generalized delayed predator prey system with stocking abstract in this paper by using the continuation theorem of coincidence degree theory the existence of multiple positive periodic solutions for a generalized delayed predator prey system with stocking is established when our result is applied to a delayed predator prey system with nonmonotonic functional response and stocking we establish the sufficient condition for the existence of multiple positive periodic solutions for the system

c g preconditioning for toeplitz matrices abstract we consider the problem of solving a toeplitz system of equations by conjugate gradient method when a sequence of nested toeplitz matrices is associated to a function the spectral behaviour of the matrices involved is closely related to the analytical properties of the generating function thus it is possible to devise efficient preconditioning techniques by using various functional approximation strategies this approach leads to attractive results in the case of ill conditioned matrices for which a wide class of preconditioners are proposed

existence and global attractivity of a positive periodic solution of a delayed periodic respiration model in this paper we consider the following delayed periodic differential equation x t v t x t x n t t t q t x n t t t t t which describes a dynamic disease involving respiratory disorders using the method of coincidence degree we first show the existence of a positive periodic solution this result greatly extends the existing ones then several sufficient conditions for the global attractivity of this periodic solution are established these results are independent of each other and in general are much better than the existing ones

global attractivity and oscillations in a periodic delay logistic equation abstract sufficient conditions are obtained for the global attractivity of a positive periodic solution of the delay logistic equation dx t dt r t x t 1 x t n k t where r and k are positive periodic functions of period and n is a positive integer sufficient conditions are also obtained for all solutions to be oscillatory about k

permanence of a delayed non autonomous gilpin ayala competition model abstract in this paper we consider a delayed non autonomous n species gilpin ayala competitive system which is more general and more realistic then classical lotka volterra competition model by means of ahmad and lazer s definitions of lower and upper averages of a function we give the average conditions for the permanence of the system it is shown that our result is the generalization of those of zhao et al j d zhao j f jiang a c lazer the permanence and global attractivity in a nonautonomous lotka volterra system nonlinear analysis real world applications 5 4 2004 265 276 our results also supplement the results of fan and wang m fan k wang global periodic solutions of a generalized n species gilpin ayala competition model computer and mathematics with applications 40 2000 1141 1151

positive periodic solutions of higher dimensional functional difference equations with a parameter by using krasnoselskii s fixed point theorem and upper and lower solutions method we find some sets of positive values determining that there exist positive t periodic solutions to the higher dimensional functional difference equations of the form x n 1 a n x n h n fxn n n z where a n diag a1 n a2 n am n h n diag h1 n h2 n hm n aj hj z r z z are t periodic j 1 2 m t 1 0 x z rm f r m r m where r m x1 xm t rm xj 0 j 1 2 m r x r x 0

new results on positive periodic solutions of a periodic integro differential competition system considered is the periodic integro differential competition system with infinite delays recently studied by fan and wang z angew math mech 81 2001 197 using the method of coincidence degree we present another set of sufficient conditions for the existence of positive componentwise periodic solutions of the system our results improve and supplement those obtained by fan and wang z angew math mech 81 2001 197

the properties and mechanism of long term memory in nonparametric volatility abstract recent empirical literature documents the presence of long term memory in return volatility but the mechanism of the existence of long term memory is still unclear in this paper we investigate the origin and properties of long term memory with nonparametric volatility using high frequency time series data of the chinese shanghai composite stock price index we perform detrended fluctuation analysis dfa on three different nonparametric volatility estimators with different sampling frequencies for the same volatility series the hurst exponents reduce as the sampling time interval increases but they are still larger than 1 2 which means that no matter how the interval changes it still cannot change the existence of long memory rrv presents a relatively stable property on long term memory and is less influenced by sampling frequency rv and rbv have some evolutionary trends depending on time intervals which indicating that the jump component has no significant impact on the long term memory property this suggests that the presence of long term memory in nonparametric volatility can be contributed to the integrated variance component considering the impact of microstructure noise rbv and rrv still present long term memory under various time intervals we can infer that the presence of long term memory in realized volatility is not affected by market microstructure noise our findings imply that the long term memory phenomenon is an inherent characteristic of the data generating process not a result of microstructure noise or volatility clustering

on the distribution of the singular values of toeplitz matrices in 1920 g szego proved a basic result concerning the distribution of the eigenvalues n j of the toeplitz sections tn f where f l is a real valued function simple examples show that this result cannot hold in the case where f is not real valued in this note we give an extension of this theorem for the singular values of tn f when f f0 r0 with f0 real valued and r0 continuous periodic with period 2 and such that r0 1 in addition we apply the basic theorem of szego to resolve a question of c moler

global existence of periodic solutions in a class of delayed gause type predator prey systems where x t y t denote the population density of prey and predator at time t respectively g e p e and z s are assumed to satisfy appropriate conditions v a positive constant stands for the death rate of predator y in the absence of prey x we may think of this system as herbivores y grazing upon vegetation x which take time r to recover in view of the fact that many predator prey systems display sustained fluctuations for examples see freedman l it is thus desirable to construct predator prey models capable of producing nonconstant periodic solutions when r 0 1 1 reduces to the well known undelayed gause type or kolmogorov predator prey systems again see freedman l and the references cited theorein under some assumptions the resulting systems can have a unique limit cycle in the positive cone see kuang and freedman 2 and the references cited therein to the best of our knowledge about delayed population interaction models the existing literature establishes the existence of a periodic solution by hopf bifurcation argument or reduces the delayed systems to undelayed systems of higher dimensions therefore these existence results are generally local most of the existing results on the global existence of nonconstant periodic solutions in delayed equations deal with scalar equations with single discrete delay such as 13 101

persistence and periodicity of a delayed ratio dependent predator prey model with stage structure and prey dispersal a delayed periodic ratio dependent predator prey model with prey dispersal and stage structure for predator is investigated it is assumed that immature individuals and mature individuals of the predator species are divided by a fixed age and that immature predators don t have the ability to attack prey and that predator species is confined to one of the patches while the prey species can disperse between two patches we first discuss the uniform persistence and impermanence of the model by using gaines and mawhin s continuation theorem of coincidence degree theory a set of easily verifiable sufficient conditions are derived for the existence of positive periodic solutions of the proposed model numerical simulations are presented to illustrate the feasibility of our main results

existence of periodic solutions in neutral state dependent delays equations and models sufficient conditions are obtained for the existence of positive periodic solutions of neutral equations with state dependent delays the proof is based on the theory of coincidence degree the existence results are applied to equations of population dynamics

a unifying approach to abstract matrix algebra preconditioning in earlier papers tyrtyshnikov 42 and the first author 14 considered the analysis of clustering properties of the spectra of specific toeplitz preconditioned matrices obtained by means of the best known matrix algebras here we generalize this technique to a generic banach algebra of matrices by devising general preconditioners related to convergent approximation processes 36 finally as case study we focus our attention on the tau preconditioning by showing how and why the best matrix algebra preconditioners for symmetric toeplitz systems can be constructed in this class

long term memory in stock market prices a test for long term memory that is robust to short range dependence is developed it is a modification of the r s statistic and the relevant asymptotic sampling theory is derived via functional central limit theory contrary to previous findings when applied to daily and monthly stock returns indexes over several time periods this test yields no evidence of long range dependence once short range dependence is accounted for monte carlo experiments show that the modified r s test has power against at least two specific models of long term memory suggesting that models with short range dependence may adequately capture the behavior of historical stock returns copyright 1991 by the econometric society

how fast do stock prices adjust to market efficiency evidence from a detrended fluctuation analysis abstract in this paper we analyse price fluctuations with the aim of measuring how long the market takes to adjust prices to weak form efficiency i e how long it takes for prices to adjust to a fractional brownian motion with a hurst exponent of 0 5 the hurst exponent is estimated for different time horizons using detrended fluctuation analysis a method suitable for non stationary series with trends in order to identify at which time scale the hurst exponent is consistent with the efficient market hypothesis using high frequency share price exchange rate and stock data we show how price dynamics exhibited important deviations from efficiency for time periods of up to 15 min thereafter price dynamics was consistent with a geometric brownian motion the intraday behaviour of the series also indicated that price dynamics at trade opening and close was hardly consistent with efficiency which would enable investors to exploit price deviations from fundamental values this result is consistent with intraday volume volatility and transaction time duration patterns

positive periodic solutions of nonautonomous functional differential systems abstract considered is the periodic functional differential system with a parameter x t a t x t x t f t x t using the eigenvalue problems of completely continuous operators we establish some criteria on the existence of positive periodic solutions moreover we apply the results to a couple of population models and obtain sufficient conditions for the existence of positive periodic solutions which are compared with existing ones

positive solutions to a type of multi point boundary value problem with delay and one dimensional p laplacian abstract this paper deals with a type of multi point boundary value problem with delay and one dimensional p laplacian by using guo krasnosel skii fixed point theorem and generalization of the leggett williams fixed point theorem due to avery and peterson we obtain that bvp 1 1 has at least one positive solution or three positive solutions

time varying hurst exponent for us stock markets abstract in this work the dynamical behavior of the us stock markets is characterized on the basis of the temporal variations of the hurst exponent estimated with detrended fluctuation analysis dfa over moving windows for the historical dow jones 1928 2007 and the s p 500 1950 2007 daily indices according to the results drawn i the hurst exponent displays an erratic dynamics with some episodes alternating low and high persistent behavior ii the major breakthrough of the long term trend of the scaling behavior occurred in 1972 at the end of the bretton woods system when the hurst exponent shifted form a positive to a negative long term trend other effects such as the 1987 crisis and the emergence of anti correlated behavior in the recent two years are also discussed

explicit estimates and limit formulae for the solutions of linear delay functional differential systems with nonnegative volterra type operators abstract in this paper we discuss the asymptotic properties of solutions of special inhomogeneous linear delay functional differential systems generated by nonnegative volterra type operators in a recent paper of us a variation of constants formula has been given for such systems and this is particularly suited to handling the studied problems first we investigate the boundedness of the solutions then some estimates are given for the upper and lower limits of the solutions by using this we study the existence of the limit of the solutions and obtain a formula for the limit the applicability of our results is illustrated by studying the dependence of limits of the solutions on the choice of inhomogeneities synchronisation and lotka volterra type delay functional differential systems

influence of matrix operations on the distribution of eigenvalues and singular values of toeplitz matrices abstract suppose some toeplitz matrix families a n are given generated by the fourier expansions for and a new family a n is constructed from a n via basic matrix operations theorems are proved that describe the singular value distribution for a n in the terms of as well as the eigenvalue distribution for h a n a n a n 2 and k a n a n a n 2i in particular if l and only multiplication is used then we show the singular values of a n are distributed as x where x x at the same time the eigenvalues of h a n are distributed as re x while those of k a n are distributed as im x the extension to multilevel toeplitz matrices is also suggested finally an application to circulant preconditioning is discussed

environmental periodicity and time delays in a food limited population model abstract sufficient conditions are obtained for the existence of a globally attracting positive periodic solution of the food limited population system modelled by the equation n t r t k t n t m k t c t r t n t m where m is a nonnegative integer and k r c are continuous positive periodic functions of period

periodic solution of a delayed predator prey system without dominating instantaneous negative feedback by using the continuation theorem base on gaines and mawhin s coincidence degree sufficient and realistic conditions are obtained for the global existence of positive periodic solution for a delayed predator prey system without dominating instantaneous negative feedback indeed our result are applicable to statedependent delays

periodic solutions of delayed leslie gower predator prey models with the help of continuation theorem base on gaines and mawhin s coincidence degree sufficient and realistic conditions are obtained for the global existence of positive periodic solutions for both the first and the second leslie gower predator prey models with distributed or state dependent delays

four periodic solutions of a generalized delayed predator prey system by using the continuation theorem of coincidence degree theory the existence conditions of four periodic solutions for the delayed predator prey system is established

fft based preconditioners for toeplitz block least squares problems discretized two dimensional deconvolution problems arising e g in image restoration and seismic tomography can be formulated as least squares computations min b tx 2 where t is often a large scale rectangular toeplitz block matrix the authors consider solving such block least squares problems by the preconditioned conjugate gradient algorithm using square nonsingular circulant block and related preconditioners constructed from the blocks of the rectangular matrix t preconditioning with such matrices allows efficient implementation using the one dimensional or two dimensional fast fourier transform fft two block preconditioners related to those proposed by t chan and j olkin for square nonsingular toeplitz block systems are derived and analyzed it is shown that for important classes of t the singular values of the preconditioned matrix are clustered around one this extends the authors earlier work on preconditioners for toeplitz least squares iterations for one dimensiona

auto correlated behavior of wti crude oil volatilities a multiscale perspective abstract in this paper we investigate the long range auto correlated behavior of wti crude oil volatility series employing multifractal detrended fluctuation analysis our findings show that the for small time scales the auto correlations of volatilities were multifractal while for large time scales the auto correlations were nearly monofractal based on multiscale analysis we also investigate the dynamics of auto correlations for different intervals of time scales and find that several shocks could make significant effects on the auto correlated behaviors for small time scales analyzing the dynamics of multifractality degrees of auto correlations for small time scales we find that the stronger auto correlations were always related to the lower degrees of multifractality at last we have discussions on the determination factors of price behavior the predictive implications of scaling behavior in volatilities for oil markets and the reasons why long range auto correlations of volatility were always strong for both small time scales and large time scales our results are very important theoretically and practically

positive periodic solutions of a class of delay differential system with feedback control with the help of continuation theorem based on gaines and mawhin s coincidence degree sufficient and realistic conditions are obtained for the global existence of positive periodic solutions for the delay differential system with feedback control when these results are applied to some special delay population models some new results are obtained and some known results are generalized

almost periodic solutions of single population model with hereditary effects the main purpose of this paper is to show how the coincidence degree theory can be used to obtain almost periodic solutions for single population model with almost periodic coefficients some sufficient conditions are obtained for checking the existence uniqueness and stability of almost periodic solution the analysis generalizes the results corresponding to the periodic case of the single population model

superlinear pcg methods for symmetric toeplitz systems in this paper we deal with the solution by means of preconditioned conjugate gradient pcg methods of n x n symmetric toeplitz systems a n f x b with nonnegative generating function f here the function f is assumed to be continuous and strictly positive or is assumed to have isolated zeros of even order in the first case we use as preconditioner the natural and the optimal approximation of a n f proposed by bini and di benedetto and we prove that the related pcg method has a superlinear rate of convergence and a total arithmetic cost of o n log n ops under the second hypothesis we cannot guarantee that the natural matrix is positive definite while for the optimal we show that in the ill conditioned case this can be really a bad choice consequently we define a new matrix for preconditioning the given system then by applying the sherman morrison woodbury inversion formula to the preconditioned system we introduce a small constant number of subsidiary systems which can be solved again by means of the previous pcg method finally we perform some numerical experiments that show the effectiveness of the devised technique and the adherence with the theoretical analysis

analysis of preconditioning techniques for ill conditioned toeplitz matrices several preconditioning techniques for solving toeplitz systems are known in literature but their convergence features are completely understood only in the well conditioned case we study the application of tau circulant and hartley preconditioners to ill conditioned toeplitz matrices by proving that only the first class realizes a rate of convergence not depending on the dimension of the system

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

efficiency and multifractality analysis of csi 300 based on multifractal detrending moving average algorithm abstract we apply the multifractal detrending moving average mfdma to investigate and compare the efficiency and multifractality of 5 min high frequency china securities index 300 csi 300 the results show that the csi 300 market becomes closer to weak form efficiency after the introduction of csi 300 future we find that the csi 300 is featured by multifractality and there are less complexity and risk after the csi 300 index future was introduced with the shuffling surrogating and removing extreme values procedures we unveil that extreme events and fat distribution are the main origin of multifractality besides we discuss the knotting phenomena in multifractality and find that the scaling range and the irregular fluctuations for large scales in the f q s vs s plot can cause a knot

positive periodic solution for a two species ratio dependent predator prey system with time delay and impulse abstract a two species ratio dependent predator prey model with time delay and impulse is investigated by using the continuation theorem of coincidence degree theory the existence of a positive periodic solution for this system is established

periodic solutions and permanence for a delayed nonautonomous ratio dependent predator prey model with holling type functional response by using the continuation theorem of coincidence degree theory the existence of positive periodic solutions for a delayed ratio dependent predator prey model with holling type iii functional response x t x t a t b t t k t s x s ds c t x2 t y t m2y2 t x2 t y t y t e t x2 t m2y2 t x2 t d t is established where a t b t c t e t and d t are all positive periodic continuous functions with period 0 m 0 and k s is a measurable function with period is a nonnegative constant the permanence of the system is also considered in particular if k s 0 s where 0 s is the dirac delta function at s 0 our results show that the permanence of the above system is equivalent to the existence of positive periodic solution

existence and stability of periodic solution for bam neural networks with distributed delays we use the continuation theorem of coincidence degree theory and liapunov functions to study the existence and stability of positive periodic solutions for a class of two layer heteroassociative networks called bidirectional associative memory networksdx idt a i t x i t j 1 mp j i t f j y j t t j i t y j t i i t i 1 2 n dy jdt b j t y j t i 1 nq i j t f i x i t s i j t x i t j j t j 1 2 manddx idt a i t x i t j 1 mp j i t f j 0 h j i s y j t s ds i i t i 1 2 n dy jdt b j t y j t i 1 nq i j t f i 0 k i j s x i t s ds j j t j 1 2 m

positive periodic solutions of neutral lotka volterra system with feedback control with the help of a continuation theorem based on gaines and mawhin s coincidence degree easily verifiable criteria are established for the global existence of positive periodic solutions of neutral lotka volterra system with periodic delays and feedback control our results extend and improve existing results and have further applications in population dynamics

positive periodic solutions in delayed gause type predator prey systems abstract by using a continuation theorem based on coincidence degree theory we establish easily verifiable criteria for the existence of positive periodic solutions in delayed gause type predator prey systems some known results are shown to be special cases of the presented paper

arch garch approaches to modeling high frequency financial data we model the power law stability in distribution of returns for s p500 index by the garch process which we use to account for the long memory in the variance correlations precisely we analyze the distributions corresponding to temporal aggregation of the garch process i e the sum of n garch variables the stability in the power law tails is controlled by the garch parameters we model the crossover behavior in magnitude correlations of returns by the so called two fiarch process besides detrended fluctuation analysis we employ the method proposed by geweke and porter hudak to estimate the fractional parameter in magnitude correlations

sufficient conditions for the existence positive periodic solutions of a class of neutral delay models with feedback control with the help of a continuation theorem based on gaines and mawhin s coincidence degree easily verifiable criteria are established for the global existence of positive periodic solutions of a neutral model with periodic delays and feedback controldndt n t a t email protected t n t email protected i 1nb i t n email protected i t email protected i 1nc i t n email protected i t email protected t u t email protected i 1nd i t u email protected i t dudt e t u t f t n t email protected i 1ng i t n email protected i t our results extend and improve existing results and have further applications in population dynamics

analysis of the efficiency of the shanghai stock market a volatility perspective abstract by applying the rolling window method we investigate the efficiency of the shanghai stock market through the dynamic changes of local hurst exponents based on multifractal detrended fluctuation analysis we decompose the realized volatility into continuous sample paths and jump components and analyze their long range correlations of decomposing components our results reveal that the efficiency of the shanghai stock market improved greatly based on the time varying hurst exponents

dynamic behaviors of a delay differential equation model of plankton allelopathy in this paper we consider a modified delay differential equation model of the growth of n species of plankton having competitive and allelopathic effects on each other we first obtain the sufficient conditions which guarantee the permanence of the system as a corollary for periodic case we obtain a set of delay dependent condition which ensures the existence of at least one positive periodic solution of the system after that by means of a suitable lyapunov functional sufficient conditions are derived for the global attractivity of the system for the two dimensional case under some suitable assumptions we prove that one of the components will be driven to extinction while the other will stabilize at a certain solution of a logistic equation examples show the feasibility of the main results

measuring volatility with the realized range realized variance being the summation of squared intra day returns has quickly gained popularity as a measure of daily volatility following parkinson 1980 the extreme value method for estimating the variance of the rate of return journal of business 53 61 65 we replace each squared intra day return by the high low range for that period to create a novel and more efficient estimator called the realized range in addition we suggest a bias correction procedure to account for the effects of microstructure frictions based upon scaling the realized range with the average level of the daily range simulation experiments demonstrate that for plausible levels of non trading and bid ask bounce the realized range has a lower mean squared error than the realized variance including variants thereof that are robust to microstructure noise empirical analysis of the s p500 index futures and the s p100 constituents confirms the potential of the realized range

existence of multiple positive periodic solutions of delayed predator prey models with functional responses in this paper by applying the continuation theorem of coincidence degree theory we establish some new criteria for the existence of multiple positive periodic solutions for the delayed predator prey model x t x t r t a t x t b t f x t y t y t y t c t f x email protected d t when functional response function f is monotonic or nonmonotonic

realized range based estimation of integrated variance abstract we provide a set of probabilistic laws for estimating the quadratic variation of continuous semimartingales with the realized range based variance a statistic that replaces every squared return of the realized variance with a normalized squared range if the entire sample path of the process is available and under a set of weak conditions our statistic is consistent and has a mixed gaussian limit whose precision is five times greater than that of the realized variance in practice of course inference is drawn from discrete data and true ranges are unobserved leading to downward bias we solve this problem to get a consistent mixed normal estimator irrespective of non trading effects this estimator has varying degrees of efficiency over realized variance depending on how many observations that are used to construct the high low the methodology is applied to taq data and compared with realized variance our findings suggest that the empirical path of quadratic variation is also estimated better with the realized range based variance

existence and global stability of positive periodic solutions of a predator prey system with delays this paper studies the existence global stability and uniform persistence of positive periodic solutions of a periodic predator prey system with holling type iii functional response by using the continuation theorem of coincidence degree theory and liapunov functional some sufficient conditions are obtained

positive periodic solutions of a class of functional differential systems with feedback controls abstract in this paper by using the upper and lower solutions method we investigate the existence and nonexistence of positive periodic solutions of infinite delay functional differential system with a parameter and feedback controls x t a t x t f t x t x g t x t u t x t u t b t u t e t x t x h t x t

periodic solution of a delayed predator prey system with michaelis menten type functional response by using the continuation theorem base on gaines and mawhin s coincidence degree sufficient and realistic conditions are obtained for the global existence of positive periodic solution for a delayed predator prey system with michaelis menten type functional response indeed our results are applicable to state dependent delays

periodic solutions of periodic delay lotka volterra equations and systems abstract by using the continuation theorem of coincidence degree theory sufficient and realistic conditions are obtained for the existence of positive periodic solutions for both periodic lotka volterra equations and systems with distributed or state dependent delays our results substantially extend and improve existing results

existence uniqueness and stability of positive periodic solution for a nonlinear prey competition model with delays a nonlinear periodic predator prey model with m preys and n m predators and delays is proposed in this paper which can be seen as the modification of the traditional lotka volterra prey competition model sufficient conditions which guarantee the existence of a unique globally attractive positive periodic solution of the system are obtained

multiple periodic solutions for a non autonomous delayed predator prey model with harvesting terms abstract by using the generalized continuation theorem the existence of at least two positive periodic solutions for a non autonomous delayed periodic predator prey model with harvesting x t x t r t a t x t b t x t m x t y t h 1 t y t y t c t x t t m x t t d t h 2 t is established the method used here is more convenient than mawhin s continuation theorem and the main results show that the harvesting terms consult in the additional periodic solution

positive periodic solutions of higher dimensional nonlinear functional difference equations abstract by using a well known fixed point index theorem we study the existence multiplicity and nonexistence of positive t periodic solution s to the higher dimensional nonlinear functional difference equations of the form x n 1 a n x n h n f x n n n z where a n diag a 1 n a 2 n a m n h n diag h 1 n h 2 n h m n a j h j z r z z are t periodic j 1 2 m t 1 0 x z r m f r m r where r m x 1 x m t r m x j 0 j 1 2 m r x r x 0