improved global exponential stability for delay difference equations with impulses abstract in this paper by means of constructing an impulsive delay difference inequality we study the global exponential stability for a class of delay difference equations with impulses a new criterion ensuring the global exponential stability of the equilibrium point is obtained which is less restrictive and conservative than that given in the earlier reference an illustrative example is given to demonstrate the effectiveness and advantage of the obtained result

fractional governing equations for coupled random walks in a continuous time random walk ctrw a random waiting time precedes each random jump the ctrw is coupled if the waiting time and the subsequent jump are dependent random variables the ctrw is used in physics to model diffusing particles its scaling limit is governed by an anomalous diffusion equation some applications require an overshoot continuous time random walk octrw where the waiting time is coupled to the previous jump this paper develops stochastic limit theory and governing equations for ctrw and octrw the governing equations involve coupled space time fractional derivatives in the case of infinite mean waiting times the solutions to the ctrw and octrw governing equations can be quite different

projection methods for nonlinear boundary value problems where l d l c x y is a linear map n x y is nonlinear and x and y are banach spaces recently cesari and mckenna s proved that if the underlying spaces possess a schauder basis or more generally they have what the authors call property l it is theoretically possible to establish a finite dimensional alternative problem for 1 3 their paper unities previous results 12 131 that established conditions under which 1 3 could be reduced to finite 282 0022 0396 85 3 00

pinning impulsive synchronization of reaction diffusion neural networks with time varying delays this paper investigates the exponential synchronization of reaction diffusion neural networks with time varying delays subject to dirichlet boundary conditions a novel type of pinning impulsive controllers is proposed to synchronize the reaction diffusion neural networks with time varying delays by applying the lyapunov functional method sufficient verifiable conditions are constructed for the exponential synchronization of delayed reaction diffusion neural networks with large and small delay sizes it is shown that synchronization can be realized by pinning impulsive control of a small portion of neurons of the network the technique used in this paper is also applicable to reaction diffusion networks with neumann boundary conditions numerical examples are presented to demonstrate the effectiveness of the theoretical results

impulsive stabilization and impulsive synchronization of discrete time delayed neural networks this paper investigates the problems of impulsive stabilization and impulsive synchronization of discrete time delayed neural networks ddnns two types of ddnns with stabilizing impulses are studied by introducing the time varying lyapunov functional to capture the dynamical characteristics of discrete time impulsive delayed neural networks didnns and by using a convex combination technique new exponential stability criteria are derived in terms of linear matrix inequalities the stability criteria for didnns are independent of the size of time delay but rely on the lengths of impulsive intervals with the newly obtained stability results sufficient conditions on the existence of linear state feedback impulsive controllers are derived moreover a novel impulsive synchronization scheme for two identical ddnns is proposed the novel impulsive synchronization scheme allows synchronizing two identical ddnns with unknown delays simulation results are given to validate the effectiveness of the proposed criteria of impulsive stabilization and impulsive synchronization of ddnns finally an application of the obtained impulsive synchronization result for two identical chaotic ddnns to a secure communication scheme is presented

superstatistical fluctuations in time series applications to share price dynamics and turbulence we report a general technique to study a given experimental time series with superstatistics crucial for the applicability of the superstatistics concept is the existence of a parameter beta that fluctuates on a large time scale as compared to the other time scales of the complex system under consideration the proposed method extracts the main superstatistical parameters out of a given data set and examines the validity of the superstatistical model assumptions we test the method thoroughly with surrogate data sets then the applicability of the superstatistical approach is illustrated using real experimental data we study two examples velocity time series measured in turbulent taylor couette flows and time series of log returns of the closing prices of some stock market indices

globally asymptotical stability of discrete time analog neural networks some globally asymptotical stability criteria for the equilibrium states of a general class of discrete time dynamic neural networks with continuous states are presented using a diagonal lyapunov function approach the neural networks are assumed to have the asymmetrical weight matrices throughout the paper the resulting criteria are described by the diagonal stability of some matrices associated with the network parameters some novel stability conditions represented by either the existence of the positive diagonal solutions of the lyapunov equations or some inequalities are given using the equivalence between the diagonal stability and the schur stability for a nonnegative matrix some simplified global stability conditions are also presented finally some examples are provided for demonstrating the effectiveness of the global stability conditions presented

governing equations and solutions of anomalous random walk limits fachbereich mathematik university of dortmund 44221 dortmund germany received 5 june 2002 published 30 december 2002 continuous time random walks model anomalous diffusion coupling allows the magnitude of particlejumps to depend on the waiting time between jumps governing equations for the long time scaling limits ofthese models are found to have fractional powers of coupled space and time differential operators explicitsolutions and scaling properties are presented for these equations which can be used to model ow in porousmedia and other physical systems doi 10 1103 physreve 66 060102 pacs number s 05 40 2a 02 50 cw 05 60 2k 47 55 mhi introduction

global exponential stability of impulsive discrete time neural networks with time varying delays this paper studies the problem of global exponential stability and exponential convergence rate for a class of impulsive discrete time neural networks with time varying delays firstly by means of the lyapunov stability theory some inequality analysis techniques and a discrete time halanay type inequality technique sufficient conditions for ensuring global exponential stability of discrete time neural networks are derived and the estimated exponential convergence rate is provided as well the obtained results are then applied to derive global exponential stability criteria and exponential convergence rate of impulsive discrete time neural networks with time varying delays finally numerical examples are provided to illustrate the effectiveness and usefulness of the obtained criteria

coupled continuous time random walk approach to the rachev ruschendorf model for financial data abstract in this paper we expand the rachev ruschendorf asset pricing model introducing a coupled continuous time random walk ctrw like form of the random number of price changes such a form results from the concept of the random clustering procedure that resembles the coarse graining methods of statistical physics and on the other hand indicates applicability of the ctrw idea widely used in physics to model anomalous diffusion for describing financial markets in the framework of the proposed model we derive the limiting distributions of log returns and the corresponding pricing formulas for european call option in order to illustrate the obtained theoretical results we present their fitting with several sets of financial data

reprint of boundary conditions for fractional diffusion abstract this paper derives physically meaningful boundary conditions for fractional diffusion equations using a mass balance approach numerical solutions are presented and theoretical properties are reviewed including well posedness and steady state solutions absorbing and reflecting boundary conditions are considered and illustrated through several examples reflecting boundary conditions involve fractional derivatives the caputo fractional derivative is shown to be unsuitable for modeling fractional diffusion since the resulting boundary value problem is not positivity preserving

anomalous diffusion schemes underlying the cole cole relaxation the role of the inverse time α stable subordinator abstract the paper presents the random variable formalism of the anomalous diffusion processes the emphasis is on a rigorous presentation of asymptotic behaviour of random walk processes with infinite mean random time intervals between jumps we elucidate the role of the so called inverse time stochastic process the main mathematical tool that allows us to modify the dynamics of standard relaxation processes and give rise to the nonexponential decay of modes in particular we show that the brownian motion in combination with an appropriate inverse time process may lead not only to exponential but also to the nonexponential relaxation responses

space time fractional diffusion equations and asymptotic behaviors of a coupled continuous time random walk model abstract in this paper we consider a type of continuous time random walk model where the jump length is correlated with the waiting time the asymptotic behaviors of the coupled jump probability density function in the fourier laplace domain are discussed the corresponding fractional diffusion equations are derived from the given asymptotic behaviors corresponding to the asymptotic behaviors of the joint probability density function in the fourier laplace space the asymptotic behaviors of the waiting time probability density and the conditional probability density for jump length are also discussed

pricing on electricity market based on coupled continuous time random walk concept abstract in this paper we propose a model of electricity market based on the forward rate dynamics described by a diffusion with jumps as a generalization of the classical diffusion approach we consider jump components resulting from a coupled continuous time random walk ctrw with jump lengths proportional to the corresponding inter jump time intervals in the framework of the model we derive a formula for the euro price of a standard european call option showing applicability of ctrw processes for pricing of financial instruments the result obtained by an advance theory of semimartingales is an essential extension of the pricing formula derived in the classical diffusion model of the forward rate dynamics it indicates an influence of both the continuous and the jump parts of the forward rate process on the option price

configurations of steady states for hopfield type neural networks the dependence of the steady states on the external input vector i for the continuous time and discrete time hopfield type neural networks of n neurons is discussed conditions for the existence of one or several paths of steady states are derived it is shown that in some conditions for an external input i there may exist at least 2 n exponentially stable steady states called configuration of steady states and their regions of attraction are estimated this means that there exist 2 n paths of exponentially stable steady states defined on a certain set of input values conditions assuring the transfer of a configuration of exponentially stable steady states to another configuration of exponentially stable steady states by successive changes of the external input are obtained these results may be important for the design and maneuvering of hopfield type neural networks used to analyze associative memories

boundary conditions for fractional diffusion abstract this paper derives physically meaningful boundary conditions for fractional diffusion equations using a mass balance approach numerical solutions are presented and theoretical properties are reviewed including well posedness and steady state solutions absorbing and reflecting boundary conditions are considered and illustrated through several examples reflecting boundary conditions involve fractional derivatives the caputo fractional derivative is shown to be unsuitable for modeling fractional diffusion since the resulting boundary value problem is not positivity preserving

hopping models of charge transfer in a complex environment coupled memory continuous time random walk approach charge transport processes in disordered complex media are accompanied by anomalously slow relaxation for which usually a broad distribution of relaxation times is adopted to account for those properties of the environment a standard kinetic approach in description of the system is addressed either in the framework of continuous time random walks ctrws or fractional diffusion in this paper the power of the ctrw approach is illustrated by use of the probabilistic formalism and limit theorems that allow one to rigorously predict the limiting distributions of the paths traversed by charges and to derive effective relaxation properties of the entire system of interest in particular the standard ctrw scenario is generalized to a new class of coupled memory ctrws that effectivly can lead to the well known havriliak negami response application of the method is discussed for nonexponential electron transfer processes controlled by dynamics of the surrounding medium

exponential stability of discrete time hopfield neural networks in this paper some sufficient conditions for the local and global exponential stability of the discrete time hopfield neural networks with general activation functions are derived which gen eralize those existing results by means of m matrix theory and some inequality analysis techniques the exponential convergence rate of the neural networks to the equilibrium is estimated and for the local exponential stability the basin of attraction of the stable equilibrium is also characterized 2004 elsevier ltd all rights reserved

coupled continuous time random walks in finance continuous time random walks ctrws are used in physics to model anomalous diffusion by incorporating a random waiting time between particle jumps in finance the particle jumps are log returns and the waiting times measure delay between transactions these two random variables log return and waiting time are typically not independent for these coupled ctrw models we can now compute the limiting stochastic process just like brownian motion is the limit of a simple random walk even in the case of heavy tailed power law price jumps and or waiting times the probability density functions for this limit process solve fractional partial differential equations in some cases these equations can be explicitly solved to yield descriptions of long term price changes based on a high resolution model of individual trades that includes the statistical dependence between waiting times and the subsequent log returns in the heavy tailed case this involves operator stable space time random vectors that generalize the familiar stable models in this paper we will review the fundamental theory and present two applications with tick by tick stock and futures data

semi markov approach to continuous time random walk limit processes continuous time random walks ctrws are versatile models for anomalous diffusion processes that have found widespread application in the quantitative sciences their scaling limits are typically non markovian and the computation of their finite dimensional distributions is an important open problem this paper develops a general semi markov theory for ctrw limit processes in mathbb r d with infinitely many particle jumps renewals in finite time intervals the particle jumps and waiting times can be coupled and vary with space and time by augmenting the state space to include the scaling limits of renewal times a ctrw limit process can be embedded in a markov process explicit analytic expressions for the transition kernels of these markov processes are then derived which allow the computation of all finite dimensional distributions for ctrw limits two examples illustrate the proposed method

generalized mittag leffler relaxation clustering jump continuous time random walk approach a stochastic generalization of renormalization group transformation for continuous time random walk processes is proposed the renormalization consists in replacing the jump events from a randomly sized cluster by a single renormalized i e overall jump the clustering of the jumps followed by the corresponding transformation of the interjump time intervals yields a new class of coupled continuous time random walks which applied to modeling of relaxation lead to the general power law properties usually fitted with the empirical havriliak negami function

on the cole cole relaxation function and related mittag leffler distribution abstract in the framework of the one dimensional fractal time random walk ftrw relaxation model we rigorously show that the frequency domain response takes in both nonbiased and biased walks the only possible cole cole form the underlying reason for this is the specific form of the relaxation function the survival probability of a relaxing system determined in this model by the mittag leffler distribution we provide also analytical formulas for the propagators of the nonbiased and biased ftrws

tempered fractional calculus fractional derivatives and integrals are convolutions with a power law multiplying by an exponential factor leads to tempered fractional derivatives and integrals tempered fractional diffusion equations where the usual second derivative in space is replaced by a tempered fractional derivative govern the limits of random walk models with an exponentially tempered power law jump distribution the limiting tempered stable probability densities exhibit semi heavy tails which are commonly observed in finance tempered power law waiting times lead to tempered fractional time derivatives which have proven useful in geophysics the tempered fractional derivative or integral of a brownian motion called a tempered fractional brownian motion can exhibit semi long range dependence the increments of this process called tempered fractional gaussian noise provide a useful new stochastic model for wind speed data a tempered fractional difference forms the basis for numerical methods to solve tempered fractional diffusion equations and it also provides a useful new correlation model in time series

a note on stability of analog neural networks with time delays this note presents a generalized sufficient condition which guarantees stability of analog neural networks with time delays the condition is derived using a lyapunov functional and the stability criterion is stated as the equilibrium of analog neural networks with delays is globally asymptotically stable if the product of the norm of connection matrix and the maximum neuronal gain is less than one

global attractivity of a synchronized periodic orbit in a delayed network abstract we consider an artificial neural network where the signal transmission is of a digital mcculloch pitts nature and is delayed due to the finite switching speed of neurons amplifiers for a particular connection topology we show that all solutions starting from nonoscillatory initial states will be eventually synchronized and stabilized at a unique limit cycle and hence such a network can be used as a synchronized oscillator

models of anomalous diffusion the subdiffusive case abstract the paper discusses a model for anomalous diffusion processes their one point probability density functions p d f are exact solutions of fractional diffusion equations the model reflects the asymptotic behavior of a jump anomalous random walk process with random jump sizes and random inter jump time intervals with infinite means and variances which do not satisfy the law of large numbers in the case when these intervals have a fractional exponential p d f the fractional komogorov feller equation for the corresponding anomalous diffusion is provided and methods of finding its solutions are discussed finally some statistical properties of solutions of the related langevin equation are studied the subdiffusive case is explored in detail the emphasis is on a rigorous presentation which however would be accessible to the physical sciences audience

an alternative method for boundary value problems with large nonlinearities where g r r is continuously differentiable and b and d are nonsingular 12 x n matrices historically lyapunov schmidt and the alternative method are able to reduce the problem to a finite dimensional one provided the norm of the nonlinear term is sufficiently small in the region of interest that is the weakly nonlinear case recently the finite dimensional reduction for ordinary differential equations with periodic boundary conditions was accomplished 161 in this paper a constructive technique is developed that allows us to reduce 1 1 to a finite dimensional problem

global exponential stability of impulsive delay difference equation abstract in this paper an impulsive delay difference equation is considered by establishing an impulsive delay difference inequality and using the properties of cone and eigenspace of the spectral radius of nonnegative matrices some new sufficient conditions for global exponential stability of the impulsive delay difference equation are obtained the results extend and improve the earlier publications an example is given to demonstrate the effectiveness of the theory

levy flights from a continuous time process l evy flight dynamics can stem from simple random walks in a system whose operational time number of steps n typically grows superlinearly with physical time t thus this process is a kind of continuous time random walk ctrw dual to the typical scher montroll model in which n grows sublinearly with t models in which l evy flights emerge due to a temporal subordination allow one easily to discuss the response of a random walker to a weak outer force which is shown to be nonlinear on the other hand the relaxation of an ensemble of such walkers in a harmonic potential follows a simple exponential pattern and leads to a normal boltzmann distribution mixed models describing normal ctrw s in superlinear operational time and l evy flights under the operational time of subdiffusive ctrw s lead to a paradoxical diffusive behavior similar to the one found in transport on polymer chains the relaxation to the boltzmann distribution in such models is slow and asymptotically follows a power law

hopf bifurcating periodic orbits in a ring of neurons with delays in this paper we consider a ring of neurons with self feedback and delays the linear stability of the model is investigated by analyzing the associated characteristic transcendental equation based on the normal form approach and the center manifold theory we derive the formula for determining the properties of hopf bifurcating slowly oscillating periodic orbits for a ring of neurons with delays including the direction of hopf bifurcation stability of the hopf bifurcating slowly oscillating periodic orbits and so on moreover by means of the symmetric bifurcation theory of delay differential equations coupled with representation theory of standard dihedral groups we not only investigate the effect of synaptic delay of signal transmission on the pattern formation but also obtain some important results about the spontaneous bifurcation of multiple branches of periodic solutions and their spatio temporal patterns

stability analysis of a delayed hopfield neural network in this paper we study a class of neural networks which includes bidirectional associative memory networks and cellular neural networks as its special cases by brouwer s fixed point theorem a continuation theorem based on gains and mawhin s coincidence degree matrix theory and inequality analysis we not only obtain some different sufficient conditions ensuring the existence uniqueness and global exponential stability of the equilibrium but also estimate the exponentially convergent rate our results are less restrictive than previously known criteria and can be applied to neural networks with a broad range of activation functions assuming neither differentiability nor strict monotonicity