analytical methods for solving the time fractional swift hohenberg s h equation in this paper the most effective methods the homotopy perturbation method hpm and the differential transform method dtm are applied to obtain the approximate solutions of the nonlinear time fractional swift hohenberg s h equation the basic philosophy of these methods does not involve linearization weak nonlinearity assumptions or perturbation theory numerical solutions for various combinations of the parameters a eigenvalue parameter l length and a fractional index are obtained the solutions of the s h equation are useful for studies of shear thinning effects in non newtonian fluid flows at the end the solutions obtained are also presented graphically

testing time reversibility without moment restrictions in this paper we propose a class of new tests for time reversibility it is shown that this test has an asymptotic normal distribution under the null hypothesis and non trivial power under local alternatives a novel feature of this test is that it does not have any moment restriction in contrast with other time reversibility and linearity tests our simulations also confirm that the proposed test is very robust when data do not possess proper moments an empirical study of stock market indices is also included to illustrate the usefulness of the new test

numerical method for non linear wave and diffusion equations by the variational iteration method this paper applies he s variational iteration to the wave equations in an infinite one dimensional medium and some non linear diffusion equations a suitable choice of an initial solution can lead to the needed exact solution by a few iterations copyright 2007 john wiley sons ltd

entropy production and kullback leibler divergence between stationary trajectories of discrete systems the irreversibility of a stationary time series can be quantified using the kullback leibler divergence kld between the probability of observing the series and the probability of observing the time reversed series moreover this kld is a tool to estimate entropy production from stationary trajectories since it gives a lower bound to the entropy production of the physical process generating the series in this paper we introduce analytical and numerical techniques to estimate the kld between time series generated by several stochastic dynamics with a finite number of states we examine the accuracy of our estimators for a specific example a discrete flashing ratchet and investigate how close the kld is to the entropy production depending on the number of degrees of freedom of the system that are sampled in the trajectories

variational iteration method for autonomous ordinary differential systems in this paper a new iteration technique is proposed to solve autonomous ordinary differential systems in this method general lagrange multipliers are introduced to construct correction functionals for the systems the multipliers in the functionals can be identified by the variational theory the initial approximations can be freely chosen with possible unknown constants which can be determined by imposing the boundary initial conditions some examples are given the results reveal that the method is very effective and convenient

variational iteration method and homotopy perturbation method for nonlinear evolution equations he s variational iteration and homotopy perturbation methods are applied to various evolution equations to assess the accuracy of the solutions we compare the results with the exact solutions revealing that both methods are capable of solving effectively a large number of nonlinear differential equations with high accuracy

invariant subset and set stability of boolean networks under arbitrary switching signals this study investigates the set stability of switched boolean networks bns with arbitrary switching signals based on invariant subsets set stability determines whether a bn converges to a given subset while arbitrary switching signals can be used to characterize uncertainties and disturbances an algorithm is proposed to calculate the largest invariant subset contained in any given set as this is the key step in establishing the set stability criterion based on this algorithm a necessary and sufficient condition for set stability is obtained the result is then used to solve the robust output synchronization problem and the robust node synchronization problem for bns in the presence of uncertainties and disturbances examples are presented to demonstrate the use of the proposed approach

improvement of he s variational iteration method for solving systems of differential equations in recent years a lot of attention from researchers has been attracted to the various aspects of the well known he s variational iteration method this method is a very powerful method for solving a large amount of problems it provides a sequence which converges to the solution of the problem without discretization of the variables in this work an idea is proposed that accelerates the convergence of the sequences which result from the variational iteration method for solving systems of differential equations illustrative examples are presented to show the validity of the new method

numerical simulation of equal width wave equation by means of the variational iteration method the solution of the equal width wave equation is numerically obtained and compared with that obtained by the adomian decomposition method numerical results show that the variational iteration method can readily be implemented with excellent accuracy to nonlinear equations

synchronization design of boolean networks via the semi tensor product method we provide a general approach for the design of a response boolean network bn to achieve complete synchronization with a given drive bn the approach is based on the algebraic representation of bns in terms of the semi tensor product of matrices instead of designing the logical dynamic equations of a response bn directly we first construct its algebraic representation and then convert the algebraic representation back to the logical form the results are applied to a three neuron network in order to illustrate the effectiveness of the proposed approach

new iterative method application to partial differential equations abstract in the present article we implement the new iterative method nim proposed by daftardar gejji and jafari v daftardar gejji h jafari an iterative method for solving non linear functional equations j math anal appl 316 2006 753 763 to solve linear nonlinear partial differential equations of integer and fractional order the results obtained are compared with those obtained by other iterative methods such as adomian decomposition homotopy perturbation and variational iteration methods

application of the variational iteration method to the whitham broer kaup equations explicit traveling wave solutions including blow up and periodic solutions of the whitham broer kaup equations are obtained by the variational iteration method moreover the results are compared with those obtained by the adomian decomposition method revealing that the variational iteration method is superior to the adomian decomposition method

a review of the decomposition method in applied mathematics abstract the decomposition method can be an effective procedure for analytical solution of a wide class of dynamical systems without linearization or weak nonlinearity assumptions closure approximations perturbation theory or restrictive assumptions on stochasticitiy

numerical method for solving fractional coupled burgers equations in this paper we use the fractional variational iteration method fvim to solve a time and space fractional coupled burgers equations some numerical examples are presented to show the efficiency of considered method a comparison of the proposed method is made with the exact solution adomain decomposition method adm generalized differential transformation method gdtm and homotopy perturbation method hpm

decomposition method for solving fractional riccati differential equations in this article we implement a relatively new analytical technique the adomian decomposition method for solving fractional riccati differential equations the fractional derivatives are described in the caputo sense in this scheme the solution takes the form of a convergent series with easily computable components the diagonal pade approximants are effectively used in the analysis to capture the essential behavior of the solution the corresponding solutions of the integer order equations are found to follow as special cases of those of fractional order equations some numerical examples are presented to illustrate the efficiency and reliability of the method

the variational iteration method an efficient scheme for handling fractional partial differential equations in fluid mechanics variational iteration method has been used to handle linear and nonlinear differential equations the main property of the method lies in its flexibility and ability to solve nonlinear equations accurately and conveniently in this work a general framework of the variational iteration method is presented for analytical treatment of fractional partial differential equations in fluid mechanics the fractional derivatives are described in the caputo sense numerical illustrations that include the fractional wave equation fractional burgers equation fractional kdv equation fractional klein gordon equation and fractional boussinesq like equation are investigated to show the pertinent features of the technique comparison of the results obtained by the variational iteration method with those obtained by adomian decomposition method reveals that the first method is very effective and convenient the basic idea described in this paper is expected to be further employed to solve other similar linear and nonlinear problems in fractional calculus

a variety of exact travelling wave solutions for the 2 1 dimensional boiti leon pempinelli equation abstract in this paper the 2 1 dimensional boiti leon pempinelli blp equation will be studied the tanh coth method will be used to obtain exact travelling wave solutions for this equation the exp function method will also be applied to the blp equation to derive a new variety of travelling wave solutions with distinct physical structures

a collocation method for fractional diffusion equation in a long time with chebyshev functions abstract in this paper our aim is to find a new numerical method for diffusion equation with fractional derivative on time and space the employed fractional derivative is in the caputo sense also by employing a class of shifted chebyshev polynomials for the space area and a collection of rational chebyshev functions for the time domain and then using collocation method we obtain an algebraic system of equations the convergence estimate of the new scheme have been concluded finally we evaluate results of this method with other numerical methods

approximate analytical solution of the nonlinear fractional kdv burgers equation in this paper explicit and approximate solutions of the nonlinear fractional kdv burgers equation with time space fractional derivatives are presented and discussed the solutions of our equation are calculated in the form of rabidly convergent series with easily computable components the utilized method is a numerical technique based on the generalized taylor series formula which constructs an analytical solution in the form of a convergent series five illustrative applications are given to demonstrate the effectiveness and the leverage of the present method graphical results and series formulas are utilized and discussed quantitatively to illustrate the solution the results reveal that the method is very effective and simple in determination of solution of the fractional kdv burgers equation

on the solutions of nonlinear fractional klein gordon equation with modified riemann liouville derivative abstract in this paper fractional variational iteration method fvim is applied for finding approximate analytical solutions of nonlinear fractional klein gordon equation time fractional derivative is described in the riemann liouville sense a new application of fractional variational iteration method fvim is extended to derive analytical solutions in the form of a series for this equation the behavior of the solutions and the effects of different values of fractional order are indicated graphically it is shown that the solutions obtained by the fvim are reliable convenient and effective for strongly nonlinear partial equations with modified riemann liouville derivative

the variational iteration method a highly promising method for solving the system of integro differential equations this paper applies he s variational iteration method for solving two systems of volterra integro differential equations the solution process is illustrated and various physically relevant results are obtained comparison of the obtained results with exact solutions shows that the used method is an effective and highly promising method for various classes of both linear and nonlinear integro differential equations

a characterization of horizontal visibility graphs and combinatorics on words abstract a horizontal visibility graph hvg is defined in association with an ordered set of non negative reals hvgs realize a methodology in the analysis of time series their degree distribution being a good discriminator between randomness and chaos luque et al b luque l lacasa f ballesteros j luque horizontal visibility graphs exact results for random time series phys rev e 80 2009 046103 we prove that a graph is an hvg if and only if it is outerplanar and has a hamilton path therefore an hvg is a noncrossing graph as defined in algebraic combinatorics flajolet and noy p flajolet m noy analytic combinatorics of noncrossing configurations discrete math 204 1999 203 229 our characterization of hvgs implies a linear time recognition algorithm treating ordered sets as words we characterize subfamilies of hvgs highlighting various connections with combinatorial statistics and introducing the notion of a visible pair with this technique we determine asymptotically the average number of edges of hvgs

solution of the complex modified korteweg de vries equation by the projected differential transform method in this paper we first transform the complex modified korteweg de vries cmkdv equation into a real valued system of partial differential equations then the projected differential transformation method is used to compute an approximate solution of the cmkdv equation three illustrative examples are given to show the effectiveness of the method and comparing with the differential transformation method and the variational iteration method

state space analysis of boolean networks this paper provides a comprehensive framework for the state space approach to boolean networks first it surveys the authors recent work on the topic using semitensor product of matrices and the matrix expression of logic the logical dynamic equations of boolean control networks can be converted into standard discrete time dynamics to use the state space approach the state space and its subspaces of a boolean network have been carefully defined the basis of a subspace has been constructed particularly the regular subspace y friendly subspace and invariant subspace are precisely defined and the verifying algorithms are presented as an application the indistinct rolling gear structure of a boolean network is revealed

an improvement of the measurement of time series irreversibility with visibility graph approach abstract we propose a method to improve the measure of real valued time series irreversibility which contains two tools the directed horizontal visibility graph and the kullback leibler divergence the degree of time irreversibility is estimated by the kullback leibler divergence between the i n and o u t degree distributions presented in the associated visibility graph in our work we reframe the i n and o u t degree distributions by encoding them with different embedded dimensions used in calculating permutation entropy pe with this improved method we can not only estimate time series irreversibility efficiently but also detect time series irreversibility from multiple dimensions we verify the validity of our method and then estimate the amount of time irreversibility of series generated by chaotic maps as well as global stock markets over the period 2005 2015 the result shows that the amount of time irreversibility reaches the peak with embedded dimension d 3 under circumstances of experiment and financial markets

variational iteration method for solving burger s and coupled burger s equations by means of variational iteration method the solutions of burger s equation and coupled burger s equations are exactly obtained comparison with the adomian decomposition method is made showing that the former is more effective than the later in this paper he s variational iteration method is introduced to overcome the difficulty arising in calculating adomian polynomials

policy iteration algorithm for optimal control of stochastic logical dynamical systems this brief investigates the infinite horizon optimal control problem for stochastic multivalued logical dynamical systems with discounted cost applying the equivalent descriptions of stochastic logical dynamics in term of markov decision process the discounted infinite horizon optimal control problem is presented in an algebraic form then employing the method of semitensor product of matrices and the increasing dimension technique a succinct algebraic form of the policy iteration algorithm is derived to solve the optimal control problem to show the effectiveness of the proposed policy iteration algorithm an optimization problem of p53 mdm2 gene network is investigated

irreversibility and fluctuation theorem in stationary time series the relative entropy between the joint probability distribution of backward and forward sequences is used to quantify time asymmetry or irreversibility for stationary time series the parallel with the thermodynamic theory of nonequilibrium steady states allows us to link the degree of asymmetry in the time signal with the distance from equilibrium and the lack of detailed balance among its states we study the statistics of time asymmetry in terms of the fluctuation theorem showing that this type of relationship derives from simple general symmetries valid for any stationary time series

variational iteration method new development and applications variational iteration method has been favourably applied to various kinds of nonlinear problems the main property of the method is in its flexibility and ability to solve nonlinear equations accurately and conveniently in this paper recent trends and developments in the use of the method are reviewed major applications to nonlinear wave equation nonlinear fractional differential equations nonlinear oscillations and nonlinear problems arising in various engineering applications are surveyed the confluence of modern mathematics and symbol computation has posed a challenge to developing technologies capable of handling strongly nonlinear equations which cannot be successfully dealt with by classical methods variational iteration method is uniquely qualified to address this challenge the flexibility and adaptation provided by the method have made the method a strong candidate for approximate analytical solutions this paper outlines the basic conceptual framework of variational iteration technique with application to nonlinear problems both achievements and limitations are discussed with direct reference to approximate solutions for nonlinear equations a new iteration formulation is suggested to overcome the shortcoming a very useful formulation for determining approximately the period of a nonlinear oscillator is suggested examples are given to illustrate the solution procedure

correspondence between neural threshold networks and kauffman boolean cellular automata for an asymmetric version of the mcculloch pitts neural network 1943 and for kauffman s infinite range boolean network model 1984 the time evolution of the hamming distances between two different initial configurations are compared in the thermodynamic limit it is shown that in both models phase transitions occur for corresponding values of the transition parameters and that their hamming distances can have the same time evolution leading to quantitatively the same dynamics as known from time dependent landau theory for phase transitions

on the solution of nonlinear fractional order differential equation abstract this paper investigates the uniqueness and dependence of the solution of nonlinear differential equation with fractional order by the fixed points theorem the obtained results include naturally those in open literature for some special cases and a numerical approach to the discussed problem is suggested

numerical methods for fourth order fractional integro differential equations this paper outlines a reliable strategy for solving linear and nonlinear boundary value problems for fourth order fractional integro differential equations the fractional derivative is considered in the caputo sense the adomian decomposition method is found to be fast and accurate numerical examples are presented to illustrate the efficiency and reliability of the method

numerical solution of a biological population model using he s variational iteration method this paper presents numerical solution of a degenerate parabolic equation arising in the spatial diffusion of biological populations the variational iteration method and adomian decomposition method are used for solving this equation and then numerical results are compared with each other showing that the variational iteration method leads to more accurate results furthermore variational iteration method overcomes the difficulty arising in calculating the adomian s polynomials which is an important advantage over the adomian decomposition method

application of the variational iteration method to the regularized long wave equation this paper applies the variational iteration method to the regularized long wave equation in this method a generalized lagrange multiplier is introduced to construct a correction functional for the discussed problem the multiplier can be identified optimally via variational theory three invariants of the motion are evaluated to determine the conservation properties of the system

he s variational iteration method for fourth order parabolic equations he s variational iteration method is applied to fourth order parabolic partial differential equations with variable coefficients to illustrate the ability and reliability of the method some examples are given revealing its effectiveness and simplicity

application of a variational iteration method to linear and nonlinear viscoelastic models with fractional derivatives two nonlinear anelastic models with fractional derivatives describing the properties of a series of materials as polymers and polycrystalline materials are presented in this paper these models are studied analytically using a variational iteration method the paper clarifies the different ways in which the fractional differentiation operator can be defined a volterra series method of model parameters identification from the experimental data is also presented

solving systems of fractional differential equations using differential transform method this paper presents approximate analytical solutions for systems of fractional differential equations using the differential transform method the fractional derivatives are described in the caputo sense the application of differential transform method developed for differential equations of integer order is extended to derive approximate analytical solutions of systems of fractional differential equations the solutions of our model equations are calculated in the form of convergent series with easily computable components some examples are solved as illustrations using symbolic computation the numerical results show that the approach is easy to implement and accurate when applied to systems of fractional differential equations the method introduces a promising tool for solving many linear and nonlinear fractional differential equations

variational iteration method for solving the epidemic model and the prey and predator problem in this article two problems are considered the first one is the problem of the spread of a non fatal disease in a population which is assumed to have constant size over the period of the epidemic and the other one is the problem of prey and predator the variational iteration method is employed to compute an approximation to the solutions of the systems of nonlinear ordinary differential equations governing on these problems the results are compared with the results obtained by adomian decomposition and power series methods some plots are presented to show the reliability and simplicity of the method

application of he s variational iteration method to nonlinear jaulent miodek equations and comparing it with adm instead of finding a small parameter for solving nonlinear problems through perturbation method a new analytical method called he s variational iteration method vim is introduced to be applied to solve nonlinear jaulent miodek coupled kdv and coupled mkdv equations in this article in this method general lagrange multipliers are introduced to construct correction functionals for the problems the multipliers can be identified optimally via the variational theory the results are compared with exact solutions

divergence estimation of continuous distributions based on data dependent partitions we present a universal estimator of the divergence d p spl par q for two arbitrary continuous distributions p and q satisfying certain regularity conditions this algorithm which observes independent and identically distributed i i d samples from both p and q is based on the estimation of the radon nikodym derivative dp dq via a data dependent partition of the observation space strong convergence of this estimator is proved with an empirically equivalent segmentation of the space this basic estimator is further improved by adaptive partitioning schemes and by bias correction the application of the algorithms to data with memory is also investigated in the simulations we compare our estimators with the direct plug in estimator and estimators based on other partitioning approaches experimental results show that our methods achieve the best convergence performance in most of the tested cases

the variational iteration method for cauchy problems in this paper the variational iteration method is used to solve the cauchy problem some examples are given to elucidate the solution procedure and reliability of the obtained results the variational iteration algorithm leads to exact solutions in the present study

the variational iteration method for solving riesz fractional partial differential equations in this paper the variational iteration method is applied to obtain the solution for space fractional partial differential equations where the space fractional derivative is in the riesz sense on the basis of the properties and definition of the fractional derivative the iterative technique is carried out in a straightforward manner without the need for transforms or numerical approximations examples demonstrate that the series solution obtained shows agreement with the exact solutions of the problems solved

symbolic computation and new families of exact travelling solutions for the kawahara and modified kawahara equations in this paper we consider the nonlinear evolution equations such as kawahara equation and modified kawahara equation by using the tanh method and an exp function method the travelling wave solutions for the these equations are presented new exact travelling solutions are explicitly obtained with the aid of symbolic computation the obtained solutions include compactons solitons solitary patterns and periodic solutions

complete synchronization of boolean networks we examine complete synchronization of two deterministic boolean networks bns coupled unidirectionally in the drive response configuration a necessary and sufficient criterion is presented in terms of algebraic representations of bns as a consequence we show that complete synchronization can occur only between two conditionally identical bns when the transition matrix of the drive network is nonsingular two examples are worked out to illustrate the obtained results

variational iteration method for solving nonlinear boundary value problems abstract in this paper he s variational iteration method is implemented to give approximate and analytical solutions for a class of boundary value problems the variational iteration method which produces the solutions in terms of convergent series requiring no linearization or small perturbation numerical examples are given and comparisons are made with the adomian decomposition method the fact that this method solves nonlinear equations without using adomian polynomials can be considered as an advantage of this method over adomian decomposition method

variational approach to solitary wave solution of the generalized zakharov equation he s semi inverse method is applied to search for the solitary wave solution of the generalized zakharov equation gze the solution process reveals that the method is easy and straightforward

homotopy perturbation method for fractional fornberg whitham equation this article presents the approximate analytical solutions to solve the nonlinear fornberg whitham equation with fractional time derivative by using initial values the explicit solutions of the equations are solved by using a reliable algorithm like homotopy perturbation method the fractional derivatives are taken in the caputo sense numerical results show that the hpm is easy to implement and accurate when applied to time fractional pdes

generalized continuous time random walks master equations and fractional fokker planck equations continuous time random walks which generalize random walks by adding a stochastic time between jumps provide a useful description of stochastic transport at mesoscopic scales the continuous time random walk model can accommodate certain features such as trapping which are not manifest in the standard macroscopic diffusion equation the trapping is incorporated through a waiting time density and a fractional diffusion equation results from a power law waiting time a generalized continuous time random walk model with biased jumps has been used to consider transport that is also subject to an external force here we have derived the master equations for continuous time random walks with space and time dependent forcing for two cases when the force is evaluated at the start of the waiting time and at the end of the waiting time the differences persist in low order spatial continuum approximations however the two processes are shown to be governed by the same fokker planck equations in the diffusi

coupling technique of variational iteration and homotopy perturbation methods for nonlinear matrix differential equations the variational iteration method proposed by ji huan he is a new analytical method to solve nonlinear equations this paper applies the method to search for exact analytical solutions of linear differential equations with constant coefficients furthermore based on the precise integration method a coupling technique of the variational iteration method and homotopy perturbation method is proposed to solve nonlinear matrix differential equations a dynamic system and burgers equation are taken as examples to illustrate its effectiveness and convenience

numerical treatment for solving the perturbed fractional pdes using hybrid techniques in this article an accurate numerical approach is introduced in this approach we mixed between the fractional finite difference method and the restrictive taylor approximation rta the proposed method is implemented to solve numerically the perturbed fractional partial differential equations fpdes special attention is given to study the stability and consistency of the method by means of gerschgorin theorem and using the stability matrix analysis two numerical examples are given and compared with the exact solution

choice of an optimal initial solution for a wave equation in the variational iteration method this paper suggests a new approach to the choice of an initial guess in the variational iteration method by solving an ordinary differential equation by rewriting the approximate solution u n of the variational iteration method as u n v 0 v 1 v n we transform the problems of solving partial differential equations into problems of solving ordinary differential equations which satisfy the boundary conditions the solutions obtained show that the modification is effective and easy

a fractional variational iteration method for solving fractional nonlinear differential equations recently fractional differential equations have been investigated by employing the famous variational iteration method however all the previous works avoid the fractional order term and only handle it as a restricted variation a fractional variational iteration method was first proposed in g c wu e w m lee fractional variational iteration method and its application phys lett a 374 2010 2506 2509 and gave a generalized lagrange multiplier in this paper two fractional differential equations are approximately solved with the fractional variational iteration method

econophysics financial time series from a statistical physics point of view in recent years physicists have started applying concepts and methods of statistical physics to study economic problems the word econophysics is sometimes used to refer to this work much recent work is focused on understanding the statistical properties of nancial time series one reason for this interest is that nancial markets are examples of complex interacting systems for which a huge amount of data exist and it is possible that nancial time series viewed from a dierent perspective might yield new results this article reviews the results of three recent phenomenological studies i the probability distribution of stock price uctuations stock price uctuations occur in all magnitudes in analogy to earthquakes from tiny uctuations to drastic events such as market crashes the distribution of price uctuations decays with a power law tail well outside the levy stable regime and describes uctuations that dier by as much as eight orders of magnitude in addition this distribution preserves its functional form for uctuations on time scales that dier by three orders of magnitude from 1 min up to approximately 10 d ii correlations in nancial time series while price uctuations themselves have rapidly decaying correlations the magnitude of uctuations measured by either the absolute value or the square of the price uctuations has correlations that decay as a power law and persist for several months iii correlations among dierent companies the third result bears on the application of random matrix theory to understand the correlations among price uctuations of any two dierent stocks from a study of the eigenvalue statistics of the cross correlation matrix constructed from price uctuations of the leading 1000 stocks we nd that the largest 1 of the eigenvalues and the corresponding eigenvectors show systematic deviations from the predictions for a random matrix whereas the rest of the eigenvalues conform to random matrix behavior suggesting that these 1 of the eigenvalues contain system specic information about correlated time evolution of dierent companies c 2000 published by elsevier science b v all rights reserved

model construction of boolean network via observed data in this paper a set of data is assumed to be obtained from an experiment that satisfies a boolean dynamic process for instance the dataset can be obtained from the diagnosis of describing the diffusion process of cancer cells with the observed datasets several methods to construct the dynamic models for such boolean networks are proposed instead of building the logical dynamics of a boolean network directly its algebraic form is constructed first and then is converted back to the logical form firstly a general construction technique is proposed to reduce the size of required data the model with the known network graph is considered motivated by this the least in degree model is constructed that can reduce the size of required data set tremendously next the uniform network is investigated the number of required data points for identification of such networks is independent of the size of the network finally some principles are proposed for dealing with data with errors

he s variational iteration method for solving nonlinear mixed volterra fredholm integral equations in this paper he s variational iteration method is used to give the approximate solution of nonlinear mixed volterra fredholm integral equations the method constructs a convergent sequence of functions which approximates the exact solution with few iterations numerical results and a comparison with the exact solution are given which reveal its efficiency

the numerical simulation for stiff systems of ordinary differential equations in this paper the variational iteration method is applied to solve systems of ordinary differential equations in both linear and nonlinear cases focusing interest on stiff problems some examples are given to illustrate the accuracy and effectiveness of the method we compare our results with results obtained by the adomian decomposition method this comparison reveals that the variational iteration method is easier to be implemented in fact the variational iteration method is a promising method to various systems of linear and nonlinear equations

the variational iteration method for solving a neutral functional differential equation with proportional delays in this paper the variational iteration method is applied to neutral functional differential equations with proportional delays illustrative examples are given to show the efficiency of the method we also compare the performance of the method with that of a particular runge kutta method and a one leg q method

a linear representation of dynamics of boolean networks a new matrix product called semi tensor product of matrices is reviewed using it a matrix expression of logic is proposed where a logical variable is expressed as a vector a logical function is expressed as a multiple linear mapping under this framework a boolean network equation is converted into an equivalent algebraic form as a conventional discrete time linear system analyzing the transition matrix of the linear system formulas are obtained to show a the number of fixed points b the numbers of cycles of different lengths c transient period for all points to enter the set of attractors and d basin of each attractor the corresponding algorithms are developed and used to some examples

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

relative controllability of fractional dynamical systems with distributed delays in control this paper is concerned with the global relative controllability of fractional dynamical systems with multiple delays in control for finite dimensional spaces sufficient conditions for controllability results are obtained using schauder s fixed point theorem and the controllability grammian matrix which is defined by the mittag leffler matrix function an example is provided to illustrate the theory

symbolic approach for measuring temporal irreversibility we describe a symbolic approach for measuring temporal irreversibility in time series measurements temporal irreversibility is important because it excludes gaussian linear dynamics and static transformations of such dynamics from the set of possible generating processes a symbolic method for measuring temporal irreversibility is attractive because it is computationally efficient robust to noise and simplifies statistical analysis of confidence limits we propose a specific algorithm called false flipped symbols for establishing the presence of temporal irreversibility without the need for generating surrogate data besides characterizing experimental data our results are relevant to the question of selecting alternative models we illustrate our points with numerical model output and experimental measurements

semilinear fractional integro differential equations with compact semigroup abstract in this paper we study the local and global existence of mild solutions to a class of fractional integro differential equations in an arbitrary banach space associated with operators generating compact semigroup on the banach space

analytical solution of a fractional diffusion equation by variational iteration method in the present paper the analytical approximate solution of a fractional diffusion equation is deduced with the help of powerful variational iteration method by using an initial value the explicit solutions of the equation for different cases have been derived which accelerate the rapid convergence of the series solution the present method performs extremely well in terms of efficiency and simplicity numerical results for different particular cases of the problem are presented graphically

a mathematical model for simulation of a water table profile between two parallel subsurface drains using fractional derivatives by considering the initial and boundary conditions corresponding to parallel subsurface drains the linear form of a one dimensional fractional boussinesq equation was solved and an analytical mathematical model was developed to predict the water table profile between two parallel subsurface drains the developed model is a generalization of the glover dumm s mathematical model as a result the new model is applicable for both homogeneous and heterogeneous soils it considers the degree of heterogeneity of soil as a determinable parameter this parameter was called the heterogeneity index the laboratory and field tests were conducted to study the performance of the proposed mathematical model in a homogenous soil and in an agricultural soil the optimal values of parameters of the fractional model developed in this study and glover dumm s model were estimated using the inverse problem method in the proposed inverse model a bees algorithm ba was used the results showed that in the homogenous soil the heterogeneity index was nearly equal to 2 and therefore the developed mathematical model reduced to the glover dumm s mathematical model the heterogeneity index of the experimental field soil considered was equal to 1 04 hence this soil was classified as a very heterogeneous soil in the experimental field soil the proposed mathematical model better represented the water table profile between two parallel subsurface drains than the glover dumm s mathematical model therefore it appears that the proposed fractional model presented is a highly general and effective method to estimate the water table profile between two parallel subsurface drains and the scale effects are robustly reflected by the introduced heterogeneity index

variational iteration method for solving cubic nonlinear schrodinger equation the variational iteration method is applied to solve the cubic nonlinear schrodinger cnls equation in one and two space variables in both cases we will reduce the cnls equation to a coupled system of nonlinear equations numerical experiments are made to verify the efficiency of the method comparison with the theoretical solution shows that the variational iteration method is of high accuracy

comparison between the homotopy perturbation method and the variational iteration method for linear fractional partial differential equations in this article the homotopy perturbation method proposed by j h he is adopted for solving linear fractional partial differential equations the fractional derivatives are described in the caputo sense comparison of the results obtained by the homotopy perturbation method with those obtained by the variational iteration method reveals that the present methods are very effective and convenient

approximate analytical solution for seepage flow with fractional derivatives in porous media abstract in this paper a new and more exact model for seepage flow in porous media with fractional derivatives has been proposed which has modified the well known darcy law and overcome the continuity assumption of seepage flow a new kind of analytical method of nonlinear problem called the variational iteration method is described and used to give approximate solutions of the problem the results show that the proposed iteration method requiring no linearization or small perturbation is very effective and convenient

application of he s methods to nonlinear chemistry problems in this paper he s variational iteration method vim and homotopy perturbation method hpm are implemented for solving analytically two systems of ordinary differential equations that often appear in chemical applications in both methods the initial approximations can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions the solution procedure is of utter simplicity and the obtained solution is of high accuracy

numerical solutions of nonlinear evolution equations using variational iteration method the variational iteration method is used to solve three kinds of nonlinear partial differential equations coupled nonlinear reaction diffusion equations hirota satsuma coupled kdv system and drinefel d sokolov wilson equations numerical solutions obtained by the variational iteration method are compared with the exact solutions revealing that the obtained solutions are of high accuracy he s variational iteration method is introduced to overcome the difficulty arising in calculating adomian polynomial in adomian method the method is straightforward and concise and it can also be applied to other nonlinear evolution equations in mathematical physics

variational iteration method for solving wave equation by the variational iteration method the solution of the wave equation in different forms is exactly obtained the obtained solutions show that the variational iteration method is effective simple and easy compared with many of the other methods so it has a wide range of applications in physical and mathematical problems linear and nonlinear as well

fourth order integro differential equations using variational iteration method in this paper the variational iteration method proposed by ji huan he is applied to solve both linear and nonlinear boundary value problems for fourth order integro differential equations the numerical results obtained with minimum amount of computation are compared with the exact solutions to show the efficiency of the method the results show that the variational iteration method is of high accuracy more convenient and efficient for solving integro differential equations

approximate solution of nonlinear differential equations with convolution product nonlinearities in this paper a new iteration method is proposed to solve nonlinear problems special attention is paid to nonlinear differential equations with convolution product nonlinearities the results reveal the approximations obtained by the proposed method are uniformly valid for both small and large parameters in nonlinear problems furthermore the first order of approximations are more accurate than perturbation solutions at high order of approximation

synchronization of kauffman networks we analyze the synchronization transition for a pair of coupled identical kauffman networks in the chaotic phase the annealed model for kauffman networks shows that synchronization appears through a transcritical bifurcation and provides an approximate description for the whole dynamics of the coupled networks we show that these analytical predictions are in good agreement with numerical results for sufficiently large networks and study finite size effects in detail preliminary analytical and numerical results for partially disordered networks are also presented