exponential stability of periodic neural networks with impulsive effects and time varying delays abstract by employing young inequality and constructing suitable liapunov functions we investigate the existence and globally exponential stability of periodic neural networks with impulses and time varying delays the results extend and improve some earlier ones 1 5 12 an illustrative example and simulations are given to show the validity of the main results

multistability of second order competitive neural networks with nondecreasing saturated activation functions in this paper second order interactions are introduced into competitive neural networks nns and the multistability is discussed for second order competitive nns socnns with nondecreasing saturated activation functions firstly based on decomposition of state space cauchy convergence principle and inequality technique some sufficient conditions ensuring the local exponential stability of 2n equilibrium points are derived secondly some conditions are obtained for ascertaining equilibrium points to be locally exponentially stable and to be located in any designated region thirdly the theory is extended to more general saturated activation functions with 2r corner points and a sufficient criterion is given under which the socnns can have r 1 n locally exponentially stable equilibrium points even if there is no second order interactions the obtained results are less restrictive than those in some recent works finally three examples with their simulations are presented to verify the theoretical analysis

higher order finite element methods and pointwise error estimates for elliptic problems on surfaces we define higher order analogues to the piecewise linear surface finite element method studied in g dziuk finite elements for the beltrami operator on arbitrary surfaces in partial differential equations and calculus of variations springer verlag berlin 1988 pp 142 155 and prove error estimates in both pointwise and l 2 based norms using the laplace beltrami problem on an implicitly defined surface gamma as a model pde we define lagrange finite element methods of arbitrary degree on polynomial approximations to gamma which likewise are of arbitrary degree then we prove a priori error estimates in the l 2 h 1 and corresponding pointwise norms that demonstrate the interaction between the pde error that arises from employing a finite dimensional finite element space and the geometric error that results from approximating gamma we also consider parametric finite element approximations that are defined on gamma and thus induce no geometric error computational examples confirm the sharpness of our error estimates

multiple periodic solutions in impulsive hybrid neural networks with delays abstract the existence of multiple periodic solutions and their exponential stability are investigated for impulsive hybrid hopfield type neural networks with both time dependent and distributed delays using the leray schauder fixed point theorem and lyapunov functionals the criteria given are easily verifiable possess many adjustable parameters and depend on impulses providing flexibility for the analysis and design of delayed neural networks with impulse effects examples are given

existence and exponential stability of periodic solution for impulsive delay differential equations and applications abstract in this paper we consider a class of nonlinear impulsive delay differential equations by establishing an exponential estimate for delay differential inequality with impulsive initial condition and employing banach fixed point theorem we obtain several sufficient conditions ensuring the existence uniqueness and global exponential stability of a periodic solution for nonlinear impulsive delay differential equations furthermore the criteria are applied to analyze dynamical behavior of impulsive delay hopfield neural networks and the results show different behavior of impulsive system originating from one continuous system

stability and periodicity in high order neural networks with impulsive effects abstract in this paper the global exponential stability and periodicity are investigated for a class generalized high order neural networks with time delays and impulses some sufficient conditions are derived for checking the global exponential stability and existence of periodic solutions for this system using the generalized halanay inequality mathematical induction and a fixed point theorem the criteria given are easily verified and possess many adjustable parameters which provides flexibility for the design and analysis of the system finally an example with numerical simulation is given to show the effectiveness of the proposed method and results

determination of a term in the right hand side of parabolic equations the inverse problem of determining a term in the right hand side of parabolic equations from integral observations is investigated the observations can be regarded as generalized interior point observations which are collected in practice the problem is then reformulated as a least squares problem in coupling with a tikhonov regularization term it is proved that the tikhonov functional is frechet differentiable and a formula for the gradient is derived via an adjoint problem the variational problem is discretized by the finite element method the convergence of which is proved the discretized variational problem is numerically solved by the conjugate gradient method some numerical examples are presented for showing the efficiency of the method

numerical solution of distributed order fractional differential equations in this paper a method for the numerical solution of distributed order fdes fractional differential equations of a general form is presented the method applies to both linear and nonlinear equations the caputo type fractional derivative is employed the distributed order fde is approximated with a multi term fde which is then solved by adjusting appropriately the numerical method developed for multi term fdes by katsikadelis several example equations are solved and the response of mechanical systems described by such equations is studied the convergence and the accuracy of the method for linear and nonlinear equations are demonstrated through well corroborated numerical results

initial value boundary value problems for fractional diffusion wave equations and applications to some inverse problems abstract we consider initial value boundary value problems for fractional diffusion wave equation t u x t l u x t where 0 2 where l is a symmetric uniformly elliptic operator with t independent smooth coefficients first we establish the unique existence of the weak solution and the asymptotic behavior as the time t goes to and the proofs are based on the eigenfunction expansions second for 0 1 we apply the eigenfunction expansions and prove i stability in the backward problem in time ii the uniqueness in determining an initial value and iii the uniqueness of solution by the decay rate as t iv stability in an inverse source problem of determining t dependent factor in the source by observation at one point over 0 t

minimal surface computation using a finite element method on an embedded surface we suggest a finite element method for finding minimal surfaces based on computing a discrete laplace beltrami operator operating on the coordinates of the surface the surface is a discrete repres

existence and exponential stability of periodic solution for impulsive cohen grossberg neural networks with time varying delays abstract this paper is concerned with the existence and global exponential stability of periodic solution for impulsive cohen grossberg neural networks with periodic coefficients and time varying delays some novel criteria on the existence and global exponential stability of periodic solution are derived by using impulsive differential inequality technique and the banach fixed point theorem the results obtained improve and extend a few of recent literature in some situations two examples with numerical simulations are given to demonstrate the efficiency of proposed methods

new robust stability results for bidirectional associative memory neural networks with multiple time delays in this paper the robust stability problem is investigated for a class of bidirectional associative memory bam neural networks with multiple time delays by employing suitable lyapunov functionals and using the upper bound norm for the interconnection matrices of the neural network system some novel sufficient conditions ensuring the existence uniqueness and global robust stability of the equilibrium point are derived the obtained results impose constraint conditions on the system parameters of neural network independent of the delay parameters some numerical examples and simulation results are given to demonstrate the applicability and effectiveness of our results and to compare the results with previous robust stability results derived in the literature

data regularization for a backward time fractional diffusion problem we investigate a backward problem for a time fractional diffusion process in inhomogeneous media which aims to determine the initial status of some physical field such as temperature for slow diffusion from its present measurement data this problem is well known to be ill posed due to the rapid decay of the forward process by using the eigenfunction expansion we construct a new regularizing scheme with an explicit solution for the noisy input data with the number of truncation terms as a regularizing parameter the convergence rate depending on the choice of strategy of the regularizing parameter is given based on the asymptotic behavior of the mittag leffler function numerical implementations are presented to show the validity of the proposed scheme for several models

global exponential stability of high order hopfield type neural networks this paper studies the problem of global exponential stability for a class of high order hopfield type neural networks by utilizing lyapunov functions several sufficient conditions for the global exponential stability of equilibrium point are obtained the exponential convergence rate of the equilibrium point is also estimated as a special case several new criteria on global exponential stability for the corresponding first order hopfield neural networks are obtained those criteria generalize some of the recent results reported in the literature

exponential stability of high order bidirectional associative memory neural networks with time delays in this paper exponential stability is studied for a class of high order bidirectional associative memory bam neural networks with time delays by employing the linear matrix inequality lmi and the lyapunov functional methods several sufficient conditions are obtained for ensuring the system to be globally exponentially stable two illustrative examples are also given in the end of this paper to show the effectiveness of our results

finite element procedures for computing normals and mean curvature on triangulated surfaces and their use for mesh refinement in this paper we consider finite element approaches to computing the mean curvature vector and normal at the vertices of piecewise linear triangulated surfaces in particular we adopt a stabilizat

some uniqueness and existence results for the initial boundary value problems for the generalized time fractional diffusion equation in this paper some uniqueness and existence results for the solutions of the initial boundary value problems for the generalized time fractional diffusion equation over an open bounded domain gx 0 t email protected r n are given to establish the uniqueness of the solution a maximum principle for the generalized time fractional diffusion equation is used in turn the maximum principle is based on an extremum principle for the caputo dzherbashyan fractional derivative that is considered in the paper too another important consequence of the maximum principle is the continuous dependence of the solution on the problem data to show the existence of the solution the fourier method of the variable separation is used to construct a formal solution under certain conditions the formal solution is shown to be a generalized solution of the initial boundary value problem for the generalized time fractional diffusion equation that turns out to be a classical solution under some additional conditions

computational parametric willmore flow we propose a new algorithm for the computation of willmore flow this is the l 2 gradient flow for the willmore functional which is the classical bending energy of a surface willmore flow is described by a highly nonlinear system of pdes of fourth order for the parametrization of the surface the spatially discrete numerical scheme is stable and consistent the discretization relies on an adequate calculation of the first variation of the willmore functional together with a derivation of the second variation of the area functional which is well adapted to discretization techniques with finite elements the algorithm uses finite elements on surfaces we give numerical examples and tests for piecewise linear finite elements a convergence proof for the full algorithm remains an open question

distributed order calculus and equations of ultraslow diffusion abstract we consider equations of the form d u t x u t x f t x t 0 x r n where d is a distributed order derivative that is d t 0 1 d t d d is the caputo dzhrbashyan fractional derivative of order is a positive weight function the above equation is used in physical literature for modeling diffusion with a logarithmic growth of the mean square displacement in this work we develop a mathematical theory of such equations study the derivatives and integrals of distributed order

lmi based approach for global asymptotic stability analysis of recurrent neural networks with various delays and structures global asymptotic stability problem is studied for a class of recurrent neural networks with distributed delays satisfying lebesgue stieljies measures on the basis of linear matrix inequality the concerned network model includes many neural network models with various delays and structures as its special cases such as the delays covering the discrete delays and distributed delays and the network structures containing the neutral type networks and high order networks therefore many new stability criteria for the above neural network models have also been derived from the present stability analysis method all the obtained stability results have similar matrix inequality structures and can be easily checked three numerical examples are used to show the effectiveness of the obtained results

an algorithm for evolutionary surfaces an algorithm is presented which allows to split the calculation of the mean curvature flow of surfaces with or without boundary into a series of poisson problems on a series of surfaces this gives a new method to solve plateau s problem forh surfaces

higher order conformal decomposition fem cdfem abstract a higher order accurate finite element method is proposed which uses automatically generated meshes based on implicit level set data for the description of boundaries and interfaces in two and three dimensions the method is an alternative for fictitious domain and extended finite element methods the domain of interest is immersed in a background mesh composed by higher order elements the zero level sets are identified and meshed followed by a decomposition of the cut background elements into conforming sub elements adaptivity is a crucial ingredient of the method to guarantee the success of the mesh generation it ensures the successful decomposition of cut elements and enables improved geometry descriptions and approximations it is confirmed that higher order accurate results with optimal convergence rates are achieved with the proposed conformal decomposition finite element method cdfem

exponential stability of linear delay impulsive differential equations for an impulsive delay differential equation with bounded delay and bounded coefficients the following result is established if each solution is bounded on 0 together with its derivative for each bounded right hand side then the equation is exponentially stable an explicit stability theorem is presented

novel global stability criteria for high order hopfield type neural networks with time varying delays abstract this paper discusses a generalized model of high order hopfield type neural networks with time varying delays some novel global stability criteria of the system is derived by using lyapunov method linear matrix inequality lmi and analytic technique the lmi based criteria obtained here are computationally more flexible and more generic than many other existing criteria a numerical example is given to illustrate our result

extinction in nonautonomous t periodic competitive lotka volterra system a nonautonomous t periodic competitive lotka volterra system of n species is considered it is shown that if the coefficients are t periodic continuous and satisfy certain inequalities then any solution with strictly positive initial conditions has the property that all but one of its components vanish while the remaining component approaches the canonical solution of a certain logistic differential equation

global asymptotic stability of high order hopfield type neural networks with time delays abstract this paper studies the problem of global asymptotic stability of a class of high order hopfield type neural networks with time delays by utilizing lyapunov functionals we obtain some sufficient conditions for the global asymptotic stability of the equilibrium point of such neural networks in terms of linear matrix inequality lmi numerical examples are given to illustrate the advantages of our approach

identification of a time dependent source term in a distributed order time fractional equation from a nonlocal integral observation abstract the ultra slow diffusion process from internal source is governed by the inhomogeneous distributed order time fractional diffusion equation we consider an inverse problem of recovering the time dependent internal source from a nonlocal integral observation which can be regarded as the spatial average of a pointwise observation the uniqueness of the source reconstruction using observation data in a finite time interval is proven based on the energy estimate then the reconstruction problem is reformulated as a minimization problem involving a tikhonov regularizing term by deriving the explicit representation of the gradient of the cost functional in terms of an adjoint problem the conjugate gradient method is applied to obtain the numerical solution numerical results are presented to show the validity of the proposed algorithm

dynamical analysis of cohen grossberg neural networks with time delays and impulses a model describing the dynamics of cohen grossberg neural networks with time delays and impulses is considered by means of lyapunov functionals and a differential inequality technique criteria on global exponential stability of this model are derived many adjustable parameters are introduced in the criteria to provide flexibility for the design and analysis of the system the results of this paper are new and they supplement previously known results

numerical analysis for distributed order differential equations in this paper we present and analyse a numerical method for the solution of a distributed order differential equation of the general form 0 ma r d ru t dr f t where m is a positive real number and where the derivative d r is taken to be a fractional derivative of caputo type of order r we give a convergence theory for our method and conclude with some numerical examples

stabilized finite element approximation of the mean curvature vector on closed surfaces the mean curvature vector of a surface is obtained by letting the laplace beltrami operator act on the embedding of the surface in bf r 3 in this contribution we develop a stabilized finite element approximation of the mean curvature vector of certain piecewise linear surfaces which enjoys first order convergence in l 2 the stabilization involves the jump in the tangent gradient in the direction of the outer co normals at each edge in the surface mesh we consider both standard meshed surfaces and so called cut surfaces that are level sets of piecewise linear distance functions we prove a priori error estimates and verify the theoretical results numerically

finite element discretization error analysis of a surface tension force in two phase incompressible flows we consider a standard model for a stationary two phase incompressible flow with surface tension in the variational formulation of the model a linear functional which describes the surface tension force occurs this functional depends on the location and the curvature of the interface in a finite element discretization method the functional has to be approximated for an approximation method based on a laplace beltrami representation of the curvature we derive sharp bounds for the approximation error a new modified approximation method with a significantly smaller error is introduced

analyticity of solutions to a distributed order time fractional diffusion equation and its application to an inverse problem abstract this paper deals with an initial boundary value problem for a distributed order time fractional diffusion equation with the fractional derivative in the caputo sense the method of the eigenfunctions expansion in combination with the laplace transform is first employed to prove the uniqueness and existence of the solution to the initial boundary value problem and then to show its analyticity in time as an application of the analyticity of the solution a uniqueness result for an important inverse problem of determination of the weight function in the distributed order derivative contained in the time fractional diffusion equation from one interior point observation of its solution is obtained

reconstruction of the temporal component in the source term of a time fractional diffusion equation in this article we consider the reconstruction of in the time fractional diffusion equation by observation at a single point x 0 we are mainly concerned with the situation of which is practically important but has not been well investigated in literature assuming finite sign changes of and an extra observation interval we establish the multiple logarithmic stability for the problem based on a reverse convolution inequality and a lower estimate for positive solutions meanwhile we develop a fixed point iteration for the numerical reconstruction and prove its convergence the performance of the proposed method is illustrated by several numerical examples