shape preserving rational cubic fractal interpolation function abstract a new type of c 1 fractal interpolation function fif is developed using the iterated function system ifs which contains the rational spline the numerator of this rational spline contains cubic polynomial and the denominator of the rational spline contains quadratic polynomial we find uniform error bound between the original function which belongs to the class c 2 and the fif we described suitable conditions on scaling factors and shape parameters such that they preserve the shape properties which are inherited in the data

exponential p convergence analysis for stochastic bam neural networks with time varying and infinite distributed delays we discuss exponential p convergence for stochastic bam neural networks the delays here are multiple time varying and infinite distributed delays we establish a new l operator delay differential integral inequality delay dependent criteria ensuring exponential p convergence are obtained giving the detail estimations of the exponential p convergence ball this paper is concerned with the problem of global exponential p convergence for stochastic bam neural networks with time varying and infinite distributed delays by constructing a new delay differential integral inequality and a novel l operator differential integral inequality and coupling with stochastic analysis techniques some delay dependent sufficient conditions are derived to guarantee exponential p convergence and the state variables of the discussed stochastic bam neural networks are globally exponentially convergent to a ball in the state space with a pre specified convergence rate meanwhile the exponential p convergent balls are also estimated here the existence and the uniqueness of the equilibrium point needs not to be considered finally two examples with numerical simulations are given to illustrate the effectiveness of the theoretical results

on monotone and convex spline interpolation this paper is concerned with the problem of existence of monotone and or convex splines having degree n and order of continuity k which interpolate to a set of data at the knots the interpolating splines are obtained by using bernstein polynomials of suitable continuous piecewise linear functions they satisfy the inequality k n k the theorems presented here are useful in developing algorithms for the construction of shape preserving splines interpolating arbitrary sets of data points earlier results of mcallister passow and roulier can be deduced from those given in this paper

cubic hermite interpolation with minimal derivative oscillation in this paper a new optimal cubic hermite interpolation method is presented the method is to optimize the derivative of the interpolant the diagonally dominant property of the obtained system of normal equations and the error bound are better than some of the existing cubic interpolants for parametric curve design the vector valued interpolation method is given some numerical examples are provided to illustrate the satisfactory shape of the interpolation curves

stochastic stability of neutral type markovian jumping bam neural networks with time varying delays abstract in this paper stochastic stability of neutral type markovian jumping bidirectional associative memory bam neural networks is investigated the jumping parameters are modeled as a continuous time discrete state markov chain the activation functions are supposed to be bounded and globally lipschitz continuous furthermore based on the lyapunov krasovskii functional a linear matrix inequality lmi approach is developed to establish sufficient conditions and novel delay dependent conditions are established for the stochastic asymptotic stability of markovian jumping bam neural networks the condition is presented in terms of linear matrix inequalities lmis which can be easily checked by using matlab lmi toolbox finally numerical examples are provided to show the effectiveness of the main results

a fractal procedure for monotonicity preserving interpolation interpolation subject to strip condition on first derivative is considered with a fif shape parameters involved in the fif controls shape of the curve near left and right end points some traditional rational splines emerge as special cases of the fif derivative of the monotonic rational fif may be nondifferentiable in a finite or dense subset of interval this paper is concerned with interpolation subject to a strip condition on the first order derivative using a class of rational cubic fractal interpolation functions fifs this facilitates the fif to generate monotonic curves for a given set of monotonic data the proposed monotonicity preserving rational fif subsumes and supplements a classical monotonic rational cubic spline in models leading to the monotonicity preserving interpolation problem wherein the first order derivative of the constructed interpolant is to be nondifferentiable in a finite or dense subset of the interpolation interval the developed fractal scheme is well suited in contrast to its classical nonrecursive counterpart it is shown that the present fractal interpolation scheme has o h 4 accuracy provided the original function belongs to c 4 i and the parameters involved in the fif are appropriately chosen

hyperchaos in the generalized rossler system introduced as a model for hyperchaos the generalized r ossler system of dimension n is obtained by linearly coupling n ensuremath 3 additional degrees of freedom to the original r ossler equation under variation of a single control parameter it is able to exhibit the chaotic hierarchy ranging from fixed points via limit cycles and tori to chaotic and finally hyperchaotic attractors through the help of a mode transformation we reveal a structural symmetry of the generalized r ossler system the latter will allow us to interpret the number shape and location in phase space of the observed coexisting attractors within a common scheme for arbitrary odd dimension n the appearance of hyperchaos is explained in terms of interacting coexisting attractors in a second part we investigate the lyapunov spectra and related properties of the generalized r ossler system as a function of the dimension n we find scaling properties which are not similar to those found in homogeneous spatially extended systems indicating that the high dimensional chaotic dynamics of the generalized r ossler system fundamentally differs from spatiotemporal chaos if the time scale is chosen properly though a universal scaling function of the lyapunov exponents is found which is related to the real part of the eigenvalues of an unstable fixed point

an always successful method in univariate convex c 2 interpolation we consider convex interpolation with cubic c 2 splines on grids built by adding two knots in each subinterval of neighbouring data sites the additional knots have to be variable in order to get a chance to always retain convexity by means of the staircase algorithm we provide computable intervals for the added knots such that all knots from these intervals allow convexity preserving spline interpolation of c 2 continuity

information cascade with marginal stability in a network of chaotic elements abstract a newly discovered cascade process of clusters is studied in a network of chaotic elements it is shown that the splitting of clusters and the synchronization of elements are balanced in a class of partially ordered states where marginal stability is sustained over an interval of the bifurcation parameters the partition information creation in bit space shows an avalanche process of information which leads to the anomalous behavior of power spectra roughly fitted by a power law form of the wavenumber lyapunov spectra have accumulation at null exponents analogous with those studied in fluid turbulence models

the g2 and c2 rational quadratic trigonometric bezier curve with two shape parameters with applications the rational quadratic trigonometric bezier curve with two shape parameters is presented in this paper which is new in literature the purposed curve inherits all the geometric properties of the traditional rational quadratic bezier curve the presence of shape parameters provides a control on the shape of the curve more than that of traditional bezier curve moreover the weight offers an additional control on the curve simple constraints for shape parameters are derived using the end points curvature so that their values always fall within the defined range the composition of two segments of curve using g 2 and c 2 continuity is given the new curves can accurately represent some conics and best approximates the traditional rational quadratic bezier curve

intrinsic stochasticity with many degrees of freedom we study a simple model equation describing a system with an infinity of degrees of freedom which displays an intrinsically chaotic behavior some concepts of fully developed turbulence are discussed in relation to this model we also develop an approach based on lyapunov exponent measurements numerical results on the distribution of lyapunov numbers and the power spectrum of the associated lyapunov vectors are presented and briefly discussed

on shape preserving quadratic spline interpolation in this paper we discuss the design of algorithms for interpolating discrete data using c 1 quadratic splines in such a way that the monotonicity and or convexity of the data is preserved the analysis culminates in an interactive algorithm which takes full advantage of the flexibility which quadratic splines permit

delay differential equation versus 1d map application to chaos control abstract theoretical and experimental results on the control of chaotic motion in an electronic circuit modeled by a delay differential equation are presented the model is derived from a nonlinear optical system with time delay feedback our control method is based on pyragas approach and applied to the infinite dimensional system generalized mean floquet multipliers and mean lyapunov exponents related to delay differential equations are introduced in order to compare a discrete time approximation with the continuous time equation this control method is also used to find the so called isomers related to harmonic periodic solutions predicted by ikeda and matsumoto

global asymptotic stability of markovian jumping stochastic cohen grossberg bam neural networks with discrete and distributed time varying delays this paper considers the problem of global asymptotic stability analysis for markovian jumping stochastic cohen grossberg bam mjscgbam neural networks the systems have discrete and distributed time varying delays based on the stochastic stability theory the assumption is proposed to obtain the global asymptotic stability criteria by using linear matrix inequalities for the first time finally an example is provided to illustrate the effectiveness of the theoretical results

staircase algorithm and construction of convex spline interpolants up to the continuity c3 abstract this paper is concerned with the convex interpolation of data sets based on the staircase algorithm several methods are presented which allow the construction of convex spline interpolants up to the continuity c 3

parametric representation of fuzzy numbers and application to fuzzy calculus we present several models to obtain simple parametric representations of the fuzzy numbers or intervals based on the use of piecewise monotonic functions of different forms the representations have the advantage of allowing flexible and easy to control shapes of the fuzzy numbers we use the standard cuts setting but also the membership functions are obtained immediately and can be used directly to obtain error controlled approximations of the fuzzy calculus in terms of a finite set of parameters the general setting is the hermite type interpolation where the values and the slopes of the monotonic interpolators are given by appropriate parameters and the overall errors of the fuzzy computations can be controlled within a prefixed tolerance by eventually augmenting the total number of pieces and of the parameters by which the results are obtained the representations are designed to model the lower and the upper extremal values of each cut compact intervals of the fuzzy numbers and are able to produce almost any possible configuration differentiable continuous or with a finite number of discontinuity points by using parametric monotonic functions of different types we show applications in the standard fuzzy calculus and we stress the generality and the applicability of the proposed representation to a large class of problems including the numerical solution of fuzzy differential equations the fuzzy linear regression and the stochastic extensions of the fuzzy mathematics the proposed model is called the lower upper representation and we denote the associated fuzzy numbers or intervals as lu fuzzy

the theoretical analysis and algorithm on a class of optimal curve fitting problems in this paper the theory and algorithm on a class of optimal curve fitting problems which can be extensively applied to the engineering are established and completed with regard to the curve fitting problems the available theories and methods are largely concerned with the spline interpolation and linear or nonlinear least squares methods and there are lots of ripe results to my best knowledge however in view of the complexity the third method that is to resort to solve functional extremal problems remains completed both in theories and algorithms regarding the class of this problems that is here called as the optimal curve fitting problems under relaxation constraints the analytic expression of solution and solving algorithms were discussed in p cheng k c zhang on a class of constrained functional minimization problems and their numerical solution journal of optimization theory and applications 78 2 1993 p267 p287 p cheng kc zhang unified method for a kind of constrained functional minimization computing technology and automation 10 2 1991 13 25 k c zhang a numerical method for solving a class of variation problems with constraint and its application to engineering numerical mathematics a journal of chinese universities 11 2 1989 1 9 k c zhang the algorithm and analysis of numerical computation beijing science press 2003 pp 172 184 but the existence of optimal solution has not been solved so far in the paper with help of variational principle and convexity analysis we give the proof of existence in details and a different proof about the analytic expression of optimal solution moreover we prove that for every smoothing parameter m this class of optimal curve fitting problems is equivalent to solve a quadratic programming with a spherical constraint which usually appears in the trust region and sqp subproblems and its algorithms have been quite ripe therefore a novel algorithm different from zhang 2003 for this class problems is established finally we give an example of m 2 to validate our theory and method numerical test shows that the method is effective and practical

convex interval interpolation using a three term staircase algorithm motivated by earlier considerations of interval interpolation problems as well as a particular application to the reconstruction of railway bridges we deal with the problem of univariate convexity preserving interval interpolation to allow convex interpolation the given data intervals have to be in strictly convex position this property is checked by applying an abstract three term staircase algorithm which is presented in this paper additionally the algorithm provides strictly convex ordinates belonging to the data intervals therefore the known methods in convex lagrange interpolation can be used to obtain interval interpolants in particular we refer to methods based on polynomial splines defined on grids with additional knots

power spectra and dynamical invariants for delay differential and difference equations abstract the mackey glass and ikeda delay differential equations ddes are models of feedback systems in which attractor dimension is proportional to the delay power spectra from these models are investigated analytically and numerically as the delay increases much beyond the system response time an exponentially decaying spectrum with a near periodic superimposed modulation appears it is shown that each peak in this modulation is associated with a mode of oscillation predicted by linear stability analysis around the fixed point the number of such modes within a characteristic autocorrelation time of the solution agrees with the lyapunov dimension of the attractor the disappearance of this modulation at higher delay values is also explained the decay rate of the spectrum in the mid to high frequency range is found to agree with the sum of the positive lyapunov exponents i e with the metric entropy realistic models with a distribution of delays display similar spectra as their memory kernel narrows into a delta function for very large delay the dde approaches an infinite dimensional continuous time difference equation ctde with each point on a delay interval evolving independently and according to a chaotic discrete time map ctde spectra which have many features of finite delay dde spectra can be computed analytically if the spectrum of this map is known for constant initial functions they have a 1 f 2 form at low frequencies our analysis suggests that the spectrum of the chaotic map is at the origin of the peak shapes in dde spectra at low frequency our findings highlight the relevance of the linear prrperties of ddes to the characterization of their nonlinear properties

a necessary and sufficient criteria for the existence of the least squares estimate for a 3 parametric exponential function given the data p i t i y i i 1 m m 3 we give necessary and sufficient conditions which guarantee the existence of the least squares estimate for a 3 parametric exponential function to this end we suggest a choice of the initial approximation and give some numerical examples

high dimensional chaos in delayed dynamical systems abstract we introduce a general class of iterative delay maps to model high dimensional chaos in dynamical systems with delayed feedback the class includes as particular cases systems with a linear local dynamics we report analytic and numerical results on the scaling laws of lyapunov spectra with a number of degrees of freedom invariant measure is computed through a self consistent frobenius perron formalism which allows also a recalculation of the maximum lyapunov exponent in good agreement with the one measured directly

monotonicity preserving c2 rational cubic spline for monotone data abstract designers in industries need to generate splines which can interpolate the data points in such a way that they preserve the inherited shape characteristics positivity monotonicity convexity of data among the properties that the spline for curves and surfaces need to satisfy smoothness and shape preservation of given data are mostly needed by all the designers in this paper a rational cubic function with three shape parameters has been developed data dependent sufficient constraints are derived for one of these shape parameters to preserve the inherited shape feature like monotonicity of data remaining two shape parameters are left free for designer to refine the shape of the monotone curve as desired numerical examples and interpolation error analysis show that the interpolant is not only c 2 local computationally economical and visually pleasant but also smooth the error of rational cubic function is also calculated when the arbitrary function being interpolated is c 3 in an interpolating interval the order of approximation of interpolant is o h i 3

existence of optimal solution for exponential model by least squares in this paper we prove the existence theorem for the best least squares approximation of the optimal parameters for the exponential model function we give sufficient conditions which guarantee the existence of such optimal parameters using these results and methods we are able to localize a sufficiently narrow area where one can choose a good initial approximation

localized behavior in the lyapunov vectors for quasi one dimensional many hard disk systems we introduce a definition of a localization width whose logarithm is given by the entropy of the distribution of particle component amplitudes in the lyapunov vector different types of localization widths are observed for example a minimum localization width where the components of only two particles are dominant we can distinguish a delocalization associated with a random distribution of particle contributions a delocalization associated with a uniform distribution and a delocalization associated with a wavelike structure in the lyapunov vector using the localization width we show that in quasi one dimensional systems of many hard disks there are two kinds of dependence of the localization width on the lyapunov exponent index for the larger exponents one is exponential and the other is linear differences due to these kinds of localizations also appear in the shapes of the localized peaks of the lyapunov vectors the lyapunov spectra and the angle between the spatial and momentum parts of the lyapunov vectors we show that the krylov relation for the largest lyapunov exponent ensuremath lambda ensuremath sim ensuremath ensuremath rho mathrm ln ensuremath rho as a function of the density ensuremath rho is satisfied apart from a factor in the same density region as the linear dependence of the localization widths is observed it is also shown that there are asymmetries in the spatial and momentum parts of the lyapunov vectors as well as in their x and y components

delay induced instabilities in nonlinear feedback systems extending general methods developed in synergetics to construct order parameter equations we work out a systematic elimination procedure for the stable modes in nonlinear delay systems it will be shown that in the vicinity of an instability the dynamical behavior of the infinite dimensional delay system is approximately governed by a low dimensional set of order parameter equations which turn out to be of the form of ordinary differential equations i e they no longer contain memory terms the general formalism will then be compared with experimental data obtained from the nonlinear operation of a phase locked loop where the finite propagation time of the signal in the feedback loop is taken into account

asymptotic theory of multidimensional chaos a delay differential equation u t u t f u t 1 0 t and its generalization are investigated in the limit 0 when the attractor s dimension increases infinitely it is shown that a number of statistical characteristics are asymptotically independent of as for the attractor it can be regarded as a direct product ofo 1 equivalent subattractors their statistical characteristics being asymptotically independent of the results enable one to predict some characteristics of the attractor with fractal dimensiond 1 for the case 1 when they are inaccessible numerically the approach developed seems to be applicable for a wide class of spatiotemporal systems

convexity preserving piecewise rational cubic interpolation a twice continuously differentiable piecewise rational cubic interpolant f to data s x j y j j 1 cdots n delta j 2 ne 0 x j 1 x j is defined in terms of turn parameters tau j j 1 cdots n 1 and end conditions f x 1 f x n 0 the necessary and sufficient condition f x j delta j 2 geqq 0 j 2 cdots n 1 is derived which ensures that the interpolant f preserves the local convexity concavity properties of s a fast simple and robust procedure for generating f is described and the results obtained for a specific data set s are compared with some standard cubic spline interpolants

shape preserving piecewise rational interpolation with higher order continuity abstract a united form of the classical hermite interpolation and shape preserving interpolation is presented in this paper the presented interpolation method provides higher order continuous shape preserving interpolation splines the given interpolants are explicit piecewise rational expressions without solving a linear or nonlinear system of consistency equations by setting parameter values the interpolation curve can be generated by choosing the classical piecewise hermite interpolation polynomials or the presented piecewise rational expressions for monotonicity preserving and convexity preserving interpolation the appropriate values of a parameter are given on each subinterval numerical examples indicate that the given method produces visually pleasing curves

c 2 positivity preserving rational interpolation splines in one and two dimensions abstract a class of rational quartic cubic interpolation spline with two local control parameters is presented which can be c 2 continuous without solving a linear system of consistency equations for the derivative values at the knots the effects of the local control parameters on generating interpolation curves are illustrated for c 2 interpolation the given interpolant can locally reproduce quadratic polynomials and has o h 2 or o h 3 convergence simple schemes for the c 2 interpolant to preserve the shape of 2d positive data are developed moreover based on the boolean sum of quintic interpolating operators a class of bi quintic partially blended rational quartic cubic interpolation surfaces is also constructed the given interpolation surface provides four local control parameters and can be c 2 continuous without using the second or higher mixed partial derivatives on a rectangular grid simple sufficient data dependent constraints are also derived on the local control parameters to preserve the shape of a 3d positive data set arranged over a rectangular grid

convexity preserving piecewise rational quartic interpolation a family of piecewise rational quartic interpolants is given identified uniquely by the value of a tension parameter lambda i each interpolant of the family can be c 2 spline without solving a linear or nonlinear system of consistency equations for the derivative values at the knots the interpolant can preserve the local convexity concavity properties of the given data a proper choice of lambda i to guarantee shape preservation is given a convergence analysis establishes an error bound in terms of lambda i and shows that o h 3 accuracy is obtained for c 2 continuity several examples are supplied to support the practical value of the method

convexity preserving approximation by univariate cubic splines a convexity preserving approximation method is presented similar to the cubic spline interpolation the given approximation function is univariate cubic spline with c 2 continuity a very simple computing method is described the approximation order and polynomial reproducing property of this convexity preserving approximant are discussed the computing method for interpolating a small quantity of data is given some numerical examples are given to show the effectivity

dynamical behavior of delayed reaction diffusion hopfield neural networks driven by infinite dimensional wiener processes in this paper we focus on the long time behavior of the mild solution to delayed reaction diffusion hopfield neural networks drdhnns driven by infinite dimensional wiener processes we analyze the existence uniqueness and stability of this system under the local lipschitz function by constructing an appropriate lyapunov krasovskii function and utilizing the semigroup theory some easy to test criteria affecting the well posedness and stability of the networks such as infinite dimensional noise and diffusion effect are obtained the criteria can be used as theoretic guidance to stabilize drdhnns in practical applications when infinite dimensional noise is taken into consideration meanwhile considering the fact that the standard brownian motion is a special case of infinite dimensional wiener process we undertake an analysis of the local lipschitz condition which has a wider range than the global lipschitz condition two samples are given to examine the availability of the results in this paper simulations are also given using the matlab

almost sure exponential stability of stochastic reaction diffusion systems abstract the lyapunov direct method as the most effective measure of studying stability theory for ordinary differential systems and stochastic ordinary differential systems has not been generalized to research concerning stochastic partial differential systems owing to the emptiness of the corresponding ito differential formula the goal of this paper is just employing the lyapunov direct method to investigate the stability of ito stochastic reaction diffusion systems including asymptotical stability in probability and almost sure exponential stability the obtained results extend the conclusions of x x liao x r mao exponential stability and instability of stochastic neural networks stochastic analysis and applications 14 2 1996 165 185 x x liao s z yang s j cheng y l fu stability of general neural networks with reaction diffusion science in china f 44 5 2001 389 395

preserving convexity through rational cubic spline fractal interpolation function we propose a new type of c 1 rational cubic spline fractal interpolation function fif for convexity preserving univariate interpolation the associated iterated function system ifs involves rational functions of the form p n x q n x where p n x are cubic polynomials determined through the hermite interpolation conditions of the fif and q n x are preassigned quadratic polynomials with two shape parameters the rational cubic spline fif converges to the original function f as rapidly as the rth power of the mesh norm approaches to zero provided f r is continuous for r 1 or 2 and certain mild conditions on the scaling factors are imposed furthermore suitable values for the rational ifs parameters are identified so that the property of convexity carries from the data set to the rational cubic fifs in contrast to the classical non recursive convexity preserving interpolation schemes the present fractal scheme is well suited for the approximation of a convex function f whose derivative is continuous but has varying irregularity

stability and hopf bifurcation of controlled complex networks model with two delays abstract this paper considers hopf bifurcation of complex network with two independent delays by analyzing the eigenvalue equations the local stability of the system is studied taking delay as parameter the change of system stability with time is studied and the emergence of inherent bifurcation is given by changing the value of the delay the bifurcation of a given system can be controlled numerical simulation results confirm the validity of the results found

an improved emd method with modified envelope algorithm based on c2 piecewise rational cubic spline interpolation for emi signal decomposition abstract in this paper we propose an improved empirical mode decomposition emd method termed iemd with modified envelope algorithm based on c2 piecewise rational and c2 monotone piecewise rational cubic spline interpolations for the decomposition of nonlinear and non stationary emi signals in the sifting procedure we first construct the upper and lower envelopes employing c2 piecewise rational cubic spline interpolation prcsi technique considering the existence of undershoots we further modify the original envelopes iteratively with c2 monotone piecewise rational cubic spline interpolation mprcsi technique for the elimination of undershoots as accurate as possible experiments on synthetic and real signals compared with three improved versions of emd three for ensemble emd eemd and tl svd demonstrate that the proposed method is more valid and flexible when applied to the decomposition of synthesis harmonic signals and real eeg signals signifying it also can be applied to the decomposition of emi signals which are known to be extremely nonlinear and non stationary

high dimensional chaotic behavior in systems with time delayed feedback abstract the nature of high dimensional chaos exhibited by a class of delay differential equation is investigated by various methods this delay differential equation models systems with time delayed feedback such as nonlinear optical resonators we first describe briefly the bifurcation phenomena exhibited by the system with an increase in a control parameter representing the energy flow rate periodic states bi multi furcate themselves successively forming a hierarchy of multistable periodic states with increasing complexities finally each branch of multistable periodic states makes transition to chaos the possibility of applying such a multistability as a memory device for complicated information is discussed in the chaotic regime each of the bifurcated states in turn merge successively into fewer sets of states with larger attractor dimensions and finally a single developed chaos with a very large attractor dimension is formed lyapunov analysis is introduced to study the high dimensional chaotic states the lyapunov vectors as well as lyapunov spectrum are shown to be very useful to understand the underlying mechanism of the successive merging process mentioned above characteristics of developed chaos are investigated by high pass filtered time series hfts the intermittency characteristics of the hfts changes markedly at a certain frequency the lyapunov analysis reveals that this frequency corresponds to a characteristic lyapunov mode number this characteristic number can be looked upon as the dimension of subspace in which active chaotic information is generated and is different from the attractor dimension in the customary sense

global asymptotic stability of bam neural networks with mixed delays and impulses in this paper bam neural networks with mixed delays and impulses are considered a new set of sufficient conditions are derived by constructing suitable lyapunov functional with matrix theory for the global asymptotic stability of bam neural networks with mixed delays and impulses moreover an example is also provided to illustrate the effectiveness of the results

synchronization of noisy delayed feedback systems with delayed coupling synchronization of delayed coupled and stochastically perturbed systems with delayed nonlinear feedback is studied using as an example circular chains of three and four delayed coupled ikeda oscillators it is proved that in the case of multiplicative noise the exact synchronization in the mean occurs for sufficiently large coupling and an analytic estimate of the sufficient coupling is given the sufficiency condition is compared with numerical computations and typical effects of noise on the exact and some generalized types of synchronization are illustrated

robust exponential stability of markovian jump impulsive stochastic cohen grossberg neural networks with mixed time delays this paper is concerned with the problem of exponential stability for a class of markovian jump impulsive stochastic cohen grossberg neural networks with mixed time delays and known or unknown parameters the jumping parameters are determined by a continuous time discrete state markov chain and the mixed time delays under consideration comprise both time varying delays and continuously distributed delays to the best of the authors knowledge till now the exponential stability problem for this class of generalized neural networks has not yet been solved since continuously distributed delays are considered in this paper the main objective of this paper is to fill this gap by constructing a novel lyapunov krasovskii functional and using some new approaches and techniques several novel sufficient conditions are obtained to ensure the exponential stability of the trivial solution in the mean square the results presented in this paper generalize and improve many known results finally two numerical examples and their simulations are given to show the effectiveness of the theoretical results

shape preserving approximations by polynomials and splines a review of shape preserving approximation methods and algorithms for approxi mating univariate functions or discrete data is given the notion of shape refers to the geometrical behavior of a function s or approximant s graph and usually includes positivity monotonicity and or convexity but in the recent literature the broader concept of shape also includes symmetry gen eralized convexity unimodality lipschitz property possessing peaks or discontinuities etc special stress is put on shape preserving interpolation methods by polynomials and splines of course this text has no pretensions to be complete geywords shape preserving approximation approximation of univariate functions approxima tion of discrete data shape preserving interpolation polynomial spline positivity monotonicity convexity generalized convexity unimodality lipschitz property

exponential passivity of bam neural networks with time varying delays the problem of delay dependent exponential passivity analysis is investigated for bam neural networks with time varying delays by establishing a suitable augmented lyapunov krasovskii function and a novel sufficient condition is obtained to guarantee the exponential stability of the considered system the several exponential stability criterion proposed in this paper is simpler and effective a numerical example is provided to demonstrate the feasibility and effectiveness of our results

a bivariate rational cubic interpolating spline with biquadratic denominator a bivariate rational bicubic interpolating spline bris with biquadratic denominator and six shape parameters is constructed in a rectangle domain the c1 continuous condition of bris discussed bris is proved to be bounded and its error is estimated in the case of the equally spaced knots the matrix expression and symmetry of bris are presented some properties of the basis of bris are given in the end a numerical example is given to illustrat the effect of the shape parameters on the shape of bris surface

optimal curve fitting and smoothing using normalized uniform b splines a tool for studying complex systems the basic problem considered in this paper is how to reduce measures of complex systems to easily understood measures we show that optimal smoothing splines are an ideal means to solve the problem in some cases of course no single method will work for all complex systems and all measures the problem of constructing optimal curves for given set of data at discrete data points is considered both equally spaced and non equally spaced data points are treated the curves are constructed by using b splines as basis functions namely as weighted sum of shifted b splines of degree k it is then shown that an optimal approximation can be solved without any boundary conditions wherein explicit solution formulas are presented a problem of optimal interpolation is also considered in parallel we apply this technique to the dow jones industrial index for both long and short time periods we see that long term trends can be easily identified

global asymptotic stability of stochastic bam neural networks with distributed delays and reaction diffusion terms this paper is concerned with global asymptotic stability of a class of reaction diffusion stochastic bi directional associative memory bam neural networks with discrete and distributed delays based on suitable assumptions we apply the linear matrix inequality lmi method to propose some new sufficient stability conditions for reaction diffusion stochastic bam neural networks with discrete and distributed delays the obtained results are easy to check and improve upon the existing stability results an example is also given to demonstrate the effectiveness of the obtained results

multiple scale analysis of delayed dynamical systems abstract the model equations of a semiconductor laser with delayed feeback are studied as a prototype of general delayed systems in the case of long delay thermodynamic limit it is shown that its behaviour in the vicinity of the hopf bifurcation can be described by suitable amplitude equations the derivation of the final model follows naturally from the space time representation of the evolution and by the corresponding re formulation of the linear stability problem regions characterized by both direct and inverse hopf bifurcations are found and in particular parameter values are identified for which a chaotic evolution is expected

fluctuations of lyapunov vectors in large volume limit and the information flow configuration in space time dynamics abstract the fluctuation of lyapunov vectors in r n for large n and in the infinite dimensional limit are studied in the context of entropy balance from dynamical system theory the density of the fluctuation yields the information flow configuration ifc which captures the interaction of degrees of freedom dof in information flow terms generally the ifc can be extended or localized the study of these cases leads to the local formulation of entropy balance for a dof two examples of coupled map lattice are given to demonstrate the approach based on the numerical data we conjecture that a locally balance imbalance configuration of the extended localized ifc implies absence presence of pattern in the spatially extended system moreover for dissipative dynamics the localization for the largest and smallest exponents can take place in a fixed spatial domain which describes a stronger version fluctuation dissipation principle derived by ruelle 1982 in viscous turbulence flow some of its implications are discussed

global robust asymptotic stability analysis of bam neural networks with time delay and impulse an lmi approach the global robust asymptotic stability of bi directional associative memory bam neural networks with constant or time varying delays and impulse is studied an approach combining the lyapunov krasovskii functional with the linear matrix inequality lmi is taken to study the problem some a criteria for the global robust asymptotic stability which gives information on the delay dependent property are derived some illustrative examples are given to demonstrate the effectiveness of the obtained results

exponential stability for stochastic reaction diffusion bam neural networks with time varying and distributed delays abstract in this paper we study the stability for a class of stochastic bidirectional associative memory bam neural networks with reaction diffusion and mixed delays the mixed delays considered in this paper are time varying and distributed delays based on a new lyapunov krasovskii functional and the poincare inequality as well as stochastic analysis theory a set of novel sufficient conditions are obtained to guarantee the stochastically exponential stability of the trivial solution or zero solution the obtained results show that the reaction diffusion term does contribute to the exponentially stabilization of the considered system moreover two numerical examples are given to show the effectiveness of the theoretical results

global stochastic stability analysis for stochastic neural networks with infinite delay and markovian switching we consider a novel stochastic nns model the method is the lyapunov method stochastic analysis technique and m matrix theory we derive sufficient criteria for three kinds of stochastic stability numerical examples demonstrate the applicability and effectiveness of the theoretical theorems this paper focuses on the stochastic stability for a novel kind of stochastic neural networks with infinite delay and markovian switching by using the lyapunov method stochastic analysis technique and m matrix theory some simple and easily testable sufficient conditions are presented to ensure the trivial solution is stochastically stable stochastically asymptotically stable and globally stochastically asymptotically stable respectively as a subsequent result we develop the conditions that guarantee global stochastic asymptotic stability for stochastic neural networks with infinite delay as well as global asymptotic stability for neural networks with infinite delay from the perspective of theory the derived stability criteria include some existing ones as its special cases and are thus less conservative finally two examples are given to demonstrate the applicability and effectiveness of the theoretical theorems

finite time boundary control for delay reaction diffusion systems abstract this paper considers finite time stabilization and h performance for delay reaction diffusion systems by boundary control first a full domain controller is designed and sufficient conditions are obtained to achieve finite time stability using finite time stability lemma and wirtinger s inequality method then a boundary controller furnished with sufficient conditions to achieve finite time stability is presented when taking into consideration external noise on a delay reaction diffusion system finite horizon h boundary control with a criterion that guarantees the h performance of delay reaction diffusion systems is proposed how to handle neumann boundary conditions and mixed boundary conditions are discussed numerical simulations are carried out to verify the effectiveness of our theoretical results

c1 positive scattered data interpolation a local c 1 surface construction scheme is presented to preserve the shape of positive scattered data arranged over a triangular grid each boundary curve of the triangle is constructed by a rational cubic function with two free parameters and this rational function is also used for the side vertex interpolation the final surface patch is constructed by taking the convex combination of three side vertex interpolants for each triangular patch there are three boundary curves and three side vertex interpolants simple sufficient data dependent constraints are derived on these free parameters to preserve the shape of the positive scattered data the developed scheme is not only local and computationally economical but visually pleasing as well

direction consistent tangent vectors for generating interpolation curves abstract in this paper monotonicity preserving interpolation is generalized to direction consistent interpolation the conditions for constructing direction consistent tangent vectors are given the conditions on the tangent vectors are also obtained such that the piecewise cubic hermite interpolation curves are tangent direction consistent with the direction of data polygon based on geometric insights the balanced tangent vectors are presented and proved to be direction consistent tangent vectors with the balanced tangent vectors the generated cubic hermite interpolation curves are tangent direction consistent and the generated quintic hermite interpolation curves are also tangent direction consistent provided that we use the accumulative chord length parametrization some graphic examples are given to show that the generated interpolation curves preserve satisfactorily the shape of the given data control polygon

a new c2 rational interpolation based on function values and constrained control of the interpolant curves in this paper a new method is developed to create a high order smoothness interpolation using values of the function being interpolated this is a kind of rational cubic interpolation with quadratic denominator this rational spline not only belongs to c 2 in the interpolating interval but could also be used to constrain the shape of the interpolant curve such as to force it to be in the given region all because of the selectable parameters in the rational spline itself the more important achievement mathematically of this method is that the uniqueness of the interpolating function for the given data would be replaced by the uniqueness of the interpolating curve for the given data and the selected parameters

shape preserving piecewise rational interpolant with quartic numerator and quadratic denominator an explicit representation of a piecewise rational interpolant with quartic numerator and quadratic denominator is presented for positivity data monotone data and convex data the shape preserving properties of the interpolant are given the interpolant is c 2 continuous spline with a shape parameter w i on each subinterval the values of w i to guarantee shape preservation are estimated a convergence analysis establishes an error bound in terms of w i and shows that the interpolant is o h 2 or o h 3 accurate several examples are supplied to support the practical value of the given interpolation method

a quasi newton trust region method the classical trust region method for unconstrained minimization can be augmented with a line search that finds a point that satisfies the wolfe conditions one can use this new method to define an algorithm that simultaneously satisfies the quasi newton condition at each iteration and maintains a positive definite approximation to the hessian of the objective function this new algorithm has strong global convergence properties and is robust and efficient in practice

existence and exponential stability of almost periodic solution for bam neural networks with variable coefficients and delays by using exponential dichotomy the banach fixed point theory constructing suitable lyapunov functional and combining yang inequality some sufficient conditions are derived ensuring existence globally exponential stability of almost periodic solution for bam neural networks with variable coefficients and delays without assuming the boundedness of signal function these results obtained are significant in design and applications of bam neural networks we extend and improve previously known results

c1 sign monotonicity and convexity preserving hermite polynomial splines of variable degree abstract this paper proposes an algorithm for constructing interpolatory hermite polynomial splines of variable degree which preserve the sign the monotonicity and the convexity of the data the polynomial segments are represented as bezier curves the degree of each segment plays the role of the tension parameter of the spline we discuss extensively the monotonicity and convexity criteria detailing a strict and a weak form of monotonicity preservation as well as their implications on the hermite interpolation we also propose a global method for estimating the nodal derivatives of the spline we evaluate the results of this method in an extensive set of examples comparing them with a number of local derivative estimation methods from the pertinent literature the algorithm is numerically stable simple to implement and it is of linear complexity since the related mathematical conditions can be expressed as linear inequalities with respect to the control points of the spline

positive quartic monotone quintic c 2 spline interpolation in one and two dimensions abstract this paper is concerned with shape preserving interpolation of discrete data by polynomial splines we show that positivity can be always preserved by quartic c2 splines and monotonicity by quintic c2 splines this is proved for one dimensional interpolation as well as for two dimensional interpolation on rectangular grids

cubic polynomial and cubic rational c1 sign monotonicity and convexity preserving hermite interpolation abstract the subject of this paper is c 1 sign monotonicity and convexity preserving spline interpolation to a set of ordered points from a real function of one real variable two solutions are proposed constructing respectively a hermite parametric polynomial cubic spline cs and a hermite cubic rational polynomial spline crs both curves are based on the shape preserving hermite variable degree spline vds gabrielides and sapidis 2018 first introduced in kaklis and pandelis 1990 and they use the bezier representation of polynomials since the cs curve is parametric the present problem also requires calculation of the y component of cs for any specific x value a robust solution to this problem is discussed in detail the crs is non parametric and it does solve the given interpolation problem with its weights which play the role of tension parameters being directly computed using the properties of the vds segments

a convexity preservingc2 parametric rational cubic interpolation ac 2 parametric rational cubic interpolantr t x t i y t j t t 1 t n to data s xj yj j 1 n is defined in terms of non negative tension parameters j j 1 n 1 letp be the polygonal line defined by the directed line segments joining the points x j y j t 1 n sufficient conditions are derived which ensure thatr t is a strictly convex function on strictly left right winding polygonal line segmentsp it is then proved that there always exist j j 1 n 1 for whichr t preserves the local left righ winding properties of any polygonal linep an example application is discussed

scattered data interpolation subject to piecewise quadratic range restrictions abstract the constriction of range restricted univariate and bivariate c1 interpolants to scattered data is considered in particular we deal with quadratic spline interpolation on a refined univariate grid respectively on a powell sabin refinement of a triangulation of the data sites subject to piecewise quadratic lower and upper obstacles to the values of the interpolant the derived sufficient conditions for the fulfillment of the range restrictions result in a system of linear inequalities for the slopes respectively gradients as parameters which is separated with respect to the data sites this system is shown to be always solvable for important special forms of the obstacles if at all in general there exist an infinite number of spline interpolants meeting the constraints the selection of a visually pleasant one is based on the minimization of a suitable choice functional

a new stability criterion for bidirectional associative memory neural networks of neutral type in the paper the global asymptotic stability of equilibrium is considered for continuous bidirectional associative memory bam neural networks of neutral type by using the lyapunov method a new stability criterion is derived in terms of linear matrix inequality lmi to ascertain the global asymptotic stability of the bam the lmi can be solved easily by various convex optimization algorithms a numerical example is illustrated to verify our result

a new sqp method of feasible directions for nonlinear programming in this paper a new sequential quadratic programming sqp method of feasible directions is proposed and analyzed for nonlinear programming where a feasible direction of descent can be derived from solving only one qp subproblem in particular this method can produce automatically a revised direction with the explicit expression which can avoid maratos effect without solving qp subproblem the theoretical analysis shows that global and superlinear convergence can be induced in the end numerical experiment is given to illustrate the effectiveness of the method

finite time stabilization for stochastic reaction diffusion systems with markovian switching via boundary control abstract this paper investigates the finite time stability fts for a class of stochastic markovian reaction diffusion systems smrdss first a boundary control strategy is put forward under the designed boundary controller a sufficient condition of fts for smrdss is provided based on the method of lyapunov krasovskii functional combined with inequality techniques when there exists the incompleteness of transition rate information we further study the problem of smrdss with partially unknown transition rates trs by adding a set of symmetric free matrices an fts criterion is also obtained for this case theoretical results show that the case of completely known trs is the special case of partially unknown trs finally simulation examples are presented to verify the validity of our derived results

accurate c 2 rational interpolants in tension a family of rational interpolants is defined for a set of real data points x i f i 1 leqq i leqq n with x 1 x 2 cdots x n each interpolant of the family is a c 2 spline with a cubic numerator and a quadratic denominator which is identified uniquely by the value of a positive tension parameter c 0 the solution constructed is nonparametric a value of c 0 close to zero will produce piecewise linear behaviour while a large value of c 0 will give approximately the cubic spline solution the method used arises from a study of other rational functional forms for effecting monotonic or convex interpolation a convergence analysis establishes an error bound in terms of c 0 and shows that o h 4 accuracy is obtained when exact boundary derivatives are prescribed several examples are supplied to support the practical value of the method

visualization of data preserving monotonicity a rational cubic function m tian y zhang j zhu q duan convexity preserving piecewise rational cubic interpolation iscias hefei china 2005 has been used to visualize monotone data in the view of monotone curves by making constraints on free parameters in the description of rational cubic function the rational cubic function is extended to rational bicubic partially blended function coons patches simple constraints are derived on free parameters in the description of rational bicubic partially blended patches to visualize the monotone data in the view of monotone surfaces the scheme of the paper is economical to compute and visually pleasant

study of a high dimensional chaotic attractor the nature of a very high dimensional chaotic attractor in an infinite dimensional phase space is examined for the purpose of studying the relationships between the physical processes occurring in the real space and the characteristics of high dimensional attractor in the phase space we introduce two complementary bases from which the attractor is observed one the lyapunov basis composed of the lyapunov vectors and the another the fourier basis composed of the fourier modes we introduce the exterior subspaces on the basis of the lyapunov vectors and observe the chaotic motion projected onto these exteriors it is shown that a certain statistical property of the projected motion changes markedly as the exterior subspace goes out of the attractor the origin of such a phenomenon is attributed to more fundamental features of our attractor which become manifest when the attractor is observed from the lyapunov basis a counterpart of the phenomenon can be observed also on the fourier basis because there is a statistical one to one correspondence between the lyapunov vectors and the fourier modes in particular a statistical property of the high pass filtered time series reflects clearly the difference between the interior and the exterior of the attractor

reliable anti synchronization conditions for bam memristive neural networks with different memductance functions this paper is concerned with anti synchronization results for a class of memristor based bidirectional associate memory bam neural networks with different memductance functions and time varying delays based on drive response system concept differential inclusions theory and lyapunov stability theory some sufficient conditions are obtained to guarantee the reliable asymptotic anti synchronization criterion for memristor based bam networks the memristive bam neural network is formulated for two types of memductance functions sufficient results are derived in terms of linear matrix inequalities lmis finally the effectiveness of the proposed criterion is demonstrated through numerical example

global asymptotic stability of bi directional associative memory networks with distributed delays in this paper several sufficient conditions are derived for the global asymptotic stability in bi directional associative memory bam networks with distributed delays by constructing suitable lyapunov functional and the young inequality technique these conditions have an important leading significance in the design and applications of globally asymptotically stable neural circuits for bam with distributed delays

hyperbolic splines and nonlinear distortion using mobius transformations we consider how to interpolate a set of monotone increasing data points x sub k y sub k so that the interpolant is a smooth invertible function and that the interpolant and its inverse have the same simple functional form we use our method to cancel jammer induced distortion in a nonlinear channel

least squares fitting gaussian type curve given the data p i t i y i i 1 m m 3 we give necessary and sufficient conditions which guarantee the existence of the weighted least squares estimate for a gaussian type function to this end we suggest a choice of the suitable initial approximation for an iterative minimization and give some numerical examples

curvature variation minimizing cubic hermite interpolants in this paper planar parametric hermite cubic interpolants with small curvature variation are studied by minimization of an appropriate approximate functional it is shown that a unique solution of the interpolation problem exists and has a nice geometric interpretation the best solution of such a problem is a quadratic geometric interpolant the optimal approximation order 4 of the solution is confirmed the approach is combined with strain energy minimization in order to obtain g 1 cubic interpolatory spline

stochastic gradient identification of polynomial wiener systems analysis and application this paper presents analytical numerical and experimental results for a stochastic gradient adaptive scheme that identifies a polynomial type nonlinear system with memory for noisy output observations the analysis includes the computation of the stationary points the mean square error surface and the stability regions of the algorithm for gaussian data convergence of the mean is studied using l sub 2 and euclidian norms monte carlo simulations confirm the theoretical predictions that show a small sensitivity to the observation noise an application is presented for the identification of a nonlinear time delayed feedback system