discrete analogue of high order periodic cohen grossberg neural networks with delay in this paper new discrete analogue of high order cohen grossberg neural networks with varying delay is obtained by analysis and approximation techniques the existence of periodic solution for discrete high order cohen grossberg neural networks with varying delay is studied by continuation theorem of coincidence degree theory and sufficient condition is given to guarantee global exponential stability of periodic solution finally an example is given to show the effectiveness of the results in this paper

asymptotical boundedness for stochastic coupled systems on networks driven by g brownian motion abstract this paper investigates a class of stochastic coupled systems on networks driven by g brownian motion g scsn in short by means of inequality techniques kth vertex g lyapunov functions and graph theory we obtain the asymptotical boundedness for g scsn moreover pth exponential stability is derived as an application a class of stochastic coupled cohen grossberg neural networks driven by g brownian motion are discussed moreover an example is given to illustrate the theory obtained

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

dynamical analysis of cohen grossberg neural networks with finite and infinite delays a model describing dynamics of cohen grossberg neural networks with finite and infinite delays is considered by means of lyapunov functionals and differential inequality techniques criteria on global asymptotic stability of this model are derived the results of this paper are new and they supplement previously known results

harmless delays in cohen grossberg neural networks without assuming monotonicity and differentiability of the activation functions and any symmetry of interconnections we establish some sufficient conditions for the globally asymptotic stability of a unique equilibrium for the cohen grossberg neural network with multiple delays lyapunov functionals and functions combined with the razumikhin technique are employed the criteria are all independent of the magnitudes of the delays and thus the delays under these conditions are harmless 2002 elsevier science b v all rights reserved msc 34d23 34k20 92b20

design of state estimator for bam fuzzy cellular neural networks with leakage and unbounded distributed delays in this paper the state estimation problem is studied for the bidirectional associative memory bam fuzzy cellular neural networks fcnns with delays where the delays include leakage and unbounded distributed delays the problem addressed is to estimate the neuron states through available output measurements such that for all admissible leakage and unbounded distributed delays the dynamics of the estimation error is globally asymptotically stable a delay dependent linear matrix inequality lmi criterion for the existence of the estimator is proposed by using the lyapunovkrasovskii functional method in addition the unknown gain matrix is determined by solving a delay dependent lmi finally numerical examples and simulations are provided to illustrate the effectiveness of the theoretical results

stability analysis of impulsive stochastic cohen grossberg neural networks driven by g brownian motion this paper is devoted to study the stability of a class of impulsive stochastic cohen grossberg neural networks driven by g brownian motion by means of g lyapunov function borel cantelli lemma an

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

approximating extent measures of points we present a general technique for approximating various descriptors of the extent of a set p of n points in rd when the dimension d is an arbitrary fixed constant for a given extent measure and a parameter e 0 it computes in time o n 1 eo 1 a subset q p of size 1 eo 1 with the property that 1 e p q p the specific applications of our technique include e approximation algorithms for i computing diameter width and smallest bounding box ball and cylinder of p ii maintaining all the previous measures for a set of moving points and iii fitting spheres and cylinders through a point set p our algorithms are considerably simpler and faster in many cases than previously known algorithms

exponential stability of delayed bi directional associative memory networks some sufficient conditions are derived for the global exponential stability in delayed bi directional associative memory bam networks by constructing suitable lyapunov functional and the inequality 2ab

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

a delayed neural network for solving linear projection equations and its analysis in this paper we present a delayed neural network approach to solve linear projection equations the lyapunov krasovskii theory for functional differential equations and the linear matrix inequality lmi approach are employed to analyze the global asymptotic stability and global exponential stability of the delayed neural network compared with the existing linear projection neural network theoretical results and illustrative examples show that the delayed neural network can effectively solve a class of linear projection equations and some quadratic programming problems

estimator design for discrete time switched neural networks with asynchronous switching and time varying delay this brief deals with the estimator design problem for discrete time switched neural networks with time varying delay one main problem is the asynchronous mode switching between the neuron state and the estimator our goal is to design a mode dependent estimator for the switched neural networks under average dwell time switching such that the estimation error system is exponentially stable with a prescribed l2 gain in the h sense from the noise signal to the estimation error a new lyapunov functional is constructed that may increase during the mismatched switchings new results on the stability and l2 gain analysis are then obtained the admissible estimator gains are computed by solving a set of linear matrix inequalities the relations among the switching law the maximal delay upper bound and the optimal h disturbance attenuation level are established the effectiveness of the proposed design method is finally illustrated by a numerical example

boundedness and global exponential stability for delayed differential equations with applications the boundedness of solutions for a class of n dimensional differential equations with distributed delays is established by assuming the existence of instantaneous negative feedbacks which dominate the delay effect as an important by product some criteria for global exponential stability of equilibria are obtained the results are illustrated with applications to delayed neural networks and population dynamics models

asymptotic synchronization of a class of neural networks with reaction diffusion terms and time varying delays in this paper the problem of asymptotic synchronization for a class of neural networks with reaction diffusion terms and time varying delays is investigated using the drive response concept a control law is derived to achieve the state synchronization of two identical neural networks with reaction diffusion terms moreover we derive a sufficient asymptotic synchronization condition for the neural networks with reaction diffusion terms if reaction diffusion terms satisfy a weaker condition the synchronization condition is easy to verify and relies on the connection matrix in the driven networks and the suitable designed controller gain matrix in the response networks

stability bifurcation and global existence of a hopf bifurcating periodic solution for a class of three neuron delayed network models in this paper a system of three delay differential equations representing a hopfield type general model for three neurons with two way bidirectional time delayed connections between the neurons and time delayed self connection from each neuron to itself is studied delay independent and delay dependent sufficient conditions for linear stability instability and the occurrence of a hopf bifurcation about the trivial equilibrium are addressed the partition of the resulting parametric space into regions of stability instability and hopf bifurcation in the absence of self connection is realized to extend the local hopf branches for large delay values a particular bidirectional delayed tri neuron model without self connection is investigated sufficient conditions for global existence of multiple non constant periodic solutions are obtained for such a model using the global hopf bifurcation theorem for functional differential equations due to j wu and the bendixson criterion for higher dimensional ordinary differential equations due to li and muldowney and following the approach developed by wei and li

common asymptotic behavior of solutions and almost periodicity for discontinuous delayed and impulsive neural networks the paper considers a general neural network model with impulses at a given sequence of instants discontinuous neuron activations delays and time varying data and inputs it is shown that when the neuron interconnections satisfy an m matrix condition or a dominance condition then the state solutions and the output solutions display a common asymptotic behavior as time t it is also shown via a new technique based on prolonging the solutions of the delayed neural network to that it is possible to select a unique special solution that is globally exponentially stable and can be considered as the unique global attractor for the network finally this paper shows that for almost periodic data and inputs the selected solution is almost periodic moreover it is robust with respect to a large class of perturbations of the data analogous results also hold for periodic data and inputs a by product of the analysis is that a sequence of almost periodic impulses is able to induce in the generic case nonstationary almost periodic solutions in an otherwise globally convergent nonimpulsive neural network to the authors knowledge the results in this paper are the only available results on global exponential stability of the unique periodic or almost periodic solution for a general neural network model combining three main features i e impulses discontinuous neuron activations and delays the results in this paper are compared with several results in the literature dealing with periodicity or almost periodicity of some subclasses of the neural network model here considered and some hints for future work are given

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

lmi conditions for global asymptotic stability results for neutral type neural networks with distributed time delays abstract in this paper the global asymptotic stability of neutral type neural networks with unbounded distributed delays is analyzed by utilizing the lyapunov krasovskii functional and the linear matrix inequality lmi approach a new sufficient condition ensuring the global asymptotic stability for neutral type neural networks is obtained by using the powerful matlab lmi toolbox two examples are provided to illustrate the applicability of the stability results

a compact finite volume method and its extrapolation for elliptic equations with third boundary conditions a fourth order compact finite volume method is constructed for one and two dimensional elliptic equations with third boundary conditions in this paper taking two point boundary value problem of third kind as an example we derive some useful high accuracy post processing formulas to recover the numerical derivatives at the nodes or midpoints of the elements we also improve the accuracy of the compact finite volume scheme from order 4 to 6 based on richardson extrapolation by rigorously proving the scheme has error asymptotic expansion numerical examples verify the correctness of the theoretical analysis and also show the effectiveness of the scheme as well as its post processing formulas and extrapolation

a finite volume method for one dimensional reaction diffusion problems abstract a truly conservative finite volume method for one dimensional reaction diffusion equations is presented the method is based on piecewise second degree polynomials approximations that result in linear fluxes a symmetric mass matrix and a semi discrete system of nonlinear ordinary differential equations in time it is shown that the semi discrete method is linearly stable provided that the problem is mathematically well posed it is also shown that implicit discretizations of the time variable are stable whereas the explicit one is conditionally stable and has a smaller domain of linear stability than the standard explicit finite difference method it is also illustrated that upon lumping the mass matrix the method coincides with a finite difference discretization of the original problem a detailed formulation of the dirichlet neumann and robin boundary conditions is presented such a formulation makes use of control volumes which are here referred to as incomplete ones although the finite volume technique presented here uses a node centered formulation it can be easily extended to cell centered ones the technique is also developed for multidimensional problems

periodic bi directional cohen grossberg neural networks with distributed delays abstract some sufficient conditions are obtained for the global exponential stability of periodic solutions to periodic bi directional cohen grossberg neural networks involving distributed delays by using the lyapunov functional method and some analytical techniques these results improve and generalize some previous works and are helpful for designing a global exponential stable periodic bi directional cohen grossberg neural networks

positive periodic solutions for a class of nonlinear delay equations abstract applying the theory of topological degree sufficient and realistic conditions are obtained for the existence of positive periodic solutions of a class of neutral delays equation from those conditions an algebraic criterion of existence for a more general neutral lotka volterra equation with several delays is obtained which extends and improves the previous results in addition this method is of great interest in many applications such as biomathematics

dynamic stability analysis of stochastic fractional order memristor fuzzy bam neural networks with delay and leakage terms abstract this paper deals with the uniform stability in mean square of stochastic fractional order memristor fuzzy bam neural networks with delay and leakage terms by employing the ideas of cauchy schwartz inequality burkholder davis gundy inequality analysis technique some sufficient conditions are derived to ensure the uniform stability in mean square of such networks the existence uniqueness and stability of its equilibrium point are also showed two different fractional order derivatives between the u layer and v layer are taken into consideration synchronously with fractional order 1 2

a finite volume method with linearisation in time for the solution of advection reaction diffusion systems the numerical solution in one space dimension of advection reaction diffusion systems with nonlinear source terms may invoke a high computational cost when the presently available methods are used numerous examples of finite volume schemes with high order spatial discretisations together with various techniques for the approximation of the advection term can be found in the literature almost all such techniques result in a nonlinear system of equations as a consequence of the finite volume discretisation especially when there are nonlinear source terms in the associated partial differential equation models this work introduces a new technique that avoids having such nonlinear systems of equations generated by the spatial discretisation process when nonlinear source terms in the model equations can be expanded in positive powers of the dependent function of interest the basis of this method is a new linearisation technique for the temporal integration of the nonlinear source terms as a supplementation of a more typical finite volume method the resulting linear system of equations is shown to be both accurate and significantly faster than methods that necessitate the use of solvers for nonlinear system of equations

impulsive stabilization of high order hopfield type neural networks with time varying delays this paper studies the problems of global exponential stability for impulsive high order hopfield type neural networks nns with time varying delays by employing the lyapunov razumikhin technique some criteria ensuring global exponential stability are derived our results are then used to obtain some sufficient conditions under which some nns can be forced to converge by impulsive control numerical examples are also discussed to illustrate our results

periodic attractor for reactiondiffusion high order hopfield neural networks with time varying delays this paper is concerned with a class of reactiondiffusion high order hopfield neural networks with time varying delays subject to the dirichlet boundary condition in a bounded domain easily verifiable delay independent criteria are established to ensure the existence of periodic mild solutions and the global exponential stability of the periodic mild solutions is also discussed by using the exponential dissipation property of semigroup of operators the obtained results are easy to check and they effectually complement previously known results a numerical example is given to show the effectiveness of theoretical results

convergence dynamics of stochastic cohen grossberg neural networks with unbounded distributed delays this paper addresses the issue of the convergence dynamics of stochastic cohen grossberg neural networks scgnns with white noise whose state variables are described by stochastic nonlinear integro differential equations with the help of lyapunov functional semi martingale theory and inequality techniques some novel sufficient conditions on pth moment exponential stability and almost sure exponential stability for scgnn are given furthermore as byproducts of our main results some sufficient conditions for checking stability of deterministic cgnns with unbounded distributed delays have been established especially even when the spectral radius of the coefficient matrix is greater than 1 in some cases our theory is also effective

global stability analysis in cohen grossberg neural networks with delays and inverse holder neuron activation functions in this paper a novel class of cohen grossberg neural networks with delays and inverse holder neuron activation functions are presented by using the topological degree theory and linear matrix inequality lmi technique the existence and uniqueness of equilibrium point for such cohen grossberg neural networks is investigated by constructing appropriate lyapunov function a sufficient condition which ensures the global exponential stability of the equilibrium point is established two numerical examples are provided to demonstrate the effectiveness of the theoretical results

dynamics of cohen grossberg neural networks with variable and distributed delays abstract this paper is concerned with the analysis problem for the exponential stability of a class of cohen grossberg neural networks with variable and distributed delays some sufficient conditions ensuring the existence uniqueness and exponential stability of the equilibrium point are obtained by employing brouwer s fixed point theorem and by applying the inequality technique in the results we do not assume that the activation function satisfies the boundedness and the lipschitz condition three numerical examples are given to show the effectiveness of the obtained results

a finite volume formulation of compact central schemes on arbitrary structured grids in the present paper a formulation allowing the use of compact schemes in the finite volume context on arbitrary meshes is presented the proposed formulation is based on the use of an implicit formula to evaluate the fluxes on the cell faces a series of numerical experiments for a 2d model convection equation a flat plate a subsonic vortical problem as well as the les simulation of channel flow has been carried out the results indicate an important improvement in obtained accuracy compared to a standard central finite volume formulation

stability in delayed cohen grossberg neural networks lmi optimization approach in this paper stability problems are further discussed for a class of delayed cohen grossberg neural networks on the basis of the linear matrix inequality lmi optimization approach and also the lyapunov krasovskii functional method combined with the halanay inequality technique several new sufficient criteria are given for ascertaining the global asymptotic stability and exponential stability of the equilibrium point for this system the proposed results are less restrictive than those given in the earlier literature and are easier to verify in practice in addition four examples and their numerical simulations are given two of them are used to demonstrate the effectiveness of the proposed results and another two show that there exist stable bifurcating periodic solutions if the given conditions do not hold

boundedness and stability for cohen grossberg neural network with time varying delays abstract in this paper a model is considered to describe the dynamics of cohen grossberg neural network with variable coefficients and time varying delays uniformly ultimate boundedness and uniform boundedness are studied for the model by utilizing the hardy inequality combining with the halanay inequality and the lyapunov functional method some new sufficient conditions are derived for the model to be globally exponentially stable the activation functions are not assumed to be differentiable or strictly increasing moreover no assumption on the symmetry of the connection matrices is necessary these criteria are important in signal processing and the design of networks

on controllability of delayed boolean control networks this paper is devoted to studying the trajectory and state controllability of boolean control networks bcns with time delay in contrast to bcns without time delay the dynamics of delayed bcns are determined by a sequence of initial states named here trajectories trajectory controllability means that there exists a control signal steering a system from an initial trajectory to a desired trajectory while state controllability means that there exists a control signal steering an initial state to a given state here both trajectory controllability and state controllability will be studied it should be noted that in this paper trajectory controllability does not mean tracking or following a given trajectory in fact it means to control bcns to a destination trajectory of length mu at the k th step using the semi tensor product of matrices the delayed bcns are first converted into an equivalent algebraic description and then some necessary and sufficient conditions are derived for the trajecto

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

existence and global exponential stability of periodic solution for impulsive cohen grossberg type bam neural networks with continuously distributed delays this paper is concerned with the existence and global exponential stability of periodic solution for a class of impulsive cohen grossberg type bam neural networks with continuously distributed delays some sufficient conditions ensuring the existence and global exponential stability of periodic solution are derived by constructing a suitable lyapunov function and a new differential inequality the proposed method can also be applied to study the impulsive cohen grossberg type bam neural networks with finite distributed delays the results in this paper extend and improve the earlier publications finally two examples with numerical simulations are given to demonstrate the obtained results

generalized lyapunov approach for convergence of neural networks with discontinuous or non lipschitz activations the paper considers a class of additive neural networks where the neuron activations are modeled by discontinuous functions or by continuous non lipschitz functions some tools are developed which enable us to apply a lyapunov like approach to differential equations with discontinuous right hand side modeling the neural network dynamics the tools include a chain rule for computing the time derivative along the neural network solutions of a nondifferentiable lyapunov function and a comparison principle for this time derivative which yields conditions for exponential convergence or convergence in finite time by means of the lyapunov like approach a general result is proved on global exponential convergence toward a unique equilibrium point of the neural network solutions moreover new results on global convergence in finite time are established which are applicable to neuron activations with jump discontinuities or neuron activations modeled by means of continuous non lipschitz holder functions

stability analysis of cohen grossberg neural network with both time varying and continuously distributed delays in this paper the cohen grossberg neural network model with both time varying and continuously distributed delays is considered without assuming both global lipschitz conditions on these activation functions and the differentiability on these time varying delays applying the idea of vector lyapunov function m matrix theory and inequality technique several new sufficient conditions are obtained to ensure the existence uniqueness and global exponential stability of equilibrium point for cohen grossberg neural network with both time varying and continuously distributed delays these results generalize and improve the earlier publications two numerical examples are given to show the effectiveness of the obtained results it is believed that these results are significant and useful for the design and applications of the cohen grossberg neural networks

dynamic of a non autonomous predator prey system with infinite delay and diffusion in the present paper a nonlinear non autonomous predator prey dispersion model with continuous delay is studied sufficient conditions which guarantee the existence of a periodic positive solution are obtained by using gaines and mawhin s continuation theorem of coincidence degree theory moreover globally asymptotically stability of the system is also obtained by means of a suitable lyapunov functional the applications show that these criteria are easily verified

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

multistability and multiperiodicity of delayed cohen grossberg neural networks with a general class of activation functions abstract in this paper by using analysis approach and decomposition of state space the multistability and multiperiodicity issues are discussed for cohen grossberg neural networks cgnns with time varying delays and a general class of activation functions where the general class of activation functions consist of nondecreasing functions with saturation s including piecewise linear functions with two corner points and standard activation functions as its special case based on the cauchy convergence principle some sufficient conditions are obtained for checking the existence and uniqueness of equilibrium points of the n neuron cgnns it is shown that the n neuron cgnns can have 2n locally exponentially stable equilibrium points located in saturation regions also some conditions are derived for ascertaining equilibrium points to be locally exponentially stable or globally exponentially attractive and to be located in any designated region as an extension of multistability some similar results are presented for ascertaining multiple periodic orbits when external inputs of the n neuron cgnns are periodic finally three examples are given to illustrate the effectiveness of the obtained results

exponential stability of impulsive high order hopfield type neural networks with time varying delays this paper considers the problems of global exponential stability and exponential convergence rate for impulsive high order hopfield type neural networks with time varying delays by using the method of lyapunov functions some sufficient conditions for ensuring global exponential stability of these networks are derived and the estimated exponential convergence rate is also obtained as an illustration an numerical example is worked out using the results obtained

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

dynamics of high order bam neural networks with and without impulses the main aim of this paper is to study the existence and global exponential stability of periodic solution for high order bidirectional associative memory bam neural networks with and without impulses easily verifiable sufficient conditions are established the method is based on coincidence degree theory as well as a priori estimates and lyapunov functional it is shown that the convergence characteristics of periodic solution for the impulsive system are preserved by the corresponding nonimpulsive system with some restriction imposed on the impulse effect numerical simulation results are given to support the theoretical predictions

periodic solutions for a class of higher order cohen grossberg type neural networks with delays sufficient conditions are obtained for the existence and global attractivity of periodic solutions of a class of higher order cohen grossberg type neural networks with delays the proof is based on gaines and mawhin s continuation theorem of coincidence degree theory the lyapunov functional and a nonsingular m matrix one example is exploited to illustrate the effectiveness of the proposed criteria

global attractivity in delayed hopfield neural network models two different approaches are employed to investigate the global attractivity of delayed hopfield neural network models without assuming the monotonicity and differentiability of the activation functions liapunov functionals and functions combined with the razumikhin technique are constructed and employed to establish sufficient conditions for global asymptotic stability independent of the delays in the case of monotone and smooth activation functions the theory of monotone dynamical systems is applied to obtain criteria for global attractivity of the delayed model such criteria depend on the magnitude of delays and show that self inhibitory connections can contribute to the global convergence

incremental clustering and dynamic information retrieval motivated by applications such as document and image classification in information retrieval we consider the problem of clustering dynamic point sets in a metric space we propose a model called incremental clustering which is based on a careful analysis of the requirements of the information retrieval application and which should also be useful in other applications the goal is to efficiently maintain clusters of small diameter as new points are inserted we analyze several natural greedy algorithms and demonstrate that they perform poorly we propose new deterministic and randomized incremental clustering algorithms which have a provably good performance and which we believe should also perform well in practice we complement our positive results with lower bounds on the performance of incremental algorithms finally we consider the dual clustering problem where the clusters are of fixed diameter and the goal is to minimize the number of clusters

global stability of neural networks with distributed delays in this paper a model describing the dynamics of recurrent neural networks with distributed delays is considered some sufficient criteria are derived ensuring the global asymptotic stability of distributed delay recurrent neural networks with more general signal propagation functions by introducing real parameters p 1 q i j 0 and r j j 0 i j 1 n and applying the properties of the m matrix and inequality techniques we do not assume that the signal propagation functions satisfy the lipschitz condition and do not require them to be bounded differentiable or strictly increasing moreover the symmetry of the connection matrix is also not necessary these criteria are independent of the delays and possess infinitely adjustable real parameters which is important in signal processing especially in moving image treatment and the design of networks

neural networks orientations of the hypercube and algebraic threshold functions a class of possible generalizations of current neural networks models is described using local improvement algorithms and orientations of graphs a notation of dynamical capacity is defined and by computing bounds on the number of algebraic threshold functions it is proven that for neural networks of size n and energy function of degree d this capacity is o n sup d 1 stable states are studied and it is shown that for the same networks the storage capacity is o n sup d 1 in the case of random orientations it is proven that the expected number of stable states is exponential applications to coding theory are indicated and it is shown that usual codes can be embedded in neural networks but only at high cost cycles and their storage are also examined

synchronization in an array of linearly coupled networks with time varying delay abstract this paper studies the dynamics of a system of linearly coupled identical connected neural networks with time varying delay some sufficient conditions for synchronization of such a system are obtained based on lyapunov functional method and matrix inequality techniques which can be checked numerically very efficiently by using the matlab toolbox finally an example is provided to demonstrate the effectiveness of the proposed results

new convergence behavior of high order hopfield neural networks with time varying coefficients in this paper the convergence behavior of the delayed high order hopfield neural networks hhnns with time varying coefficients are considered some sufficient conditions are established to ensure that all solutions of the networks converge to zero point which are new and complement of previously known results

lagrange exponential stability for fuzzy cohen grossberg neural networks with time varying delays this paper focuses on the globally exponential stability in lagrange sense for takagi sugeno t s fuzzy cohen grossberg neural networks with time varying delays by employing lyapunov method and delay inequality technique we analyze two different types of activation functions which include both lipschitz function and general activation functions several easily verifiable sufficient criteria about linear matrix inequality form are obtained to guarantee the lagrange exponential stability of cohen grossberg neural networks with time varying delays which are represented by t s fuzzy models meanwhile the estimations of the globally exponentially attractive sets are given here the existence and uniqueness of the equilibrium points need not be considered finally two numerical examples with simulations are given to illustrate the effectiveness of the theoretical results

a posteriori error analysis of a cell centered finite volume method for semilinear elliptic problems in this paper we conduct a goal oriented a posteriori analysis for the error in a quantity of interest computed from a cell centered finite volume scheme for a semilinear elliptic problem the a posteriori error analysis is based on variational analysis residual errors and the adjoint problem to carry out the analysis we use an equivalence between the cell centered finite volume scheme and a mixed finite element method with special choice of quadrature

global asymptotic stability analysis of discrete time cohen grossberg neural networks based on interval systems abstract the global asymptotic stability of discrete time cohen grossberg neural networks cgnns with or without time delays is studied in this paper the cgnns are transformed into discrete time interval systems and several sufficient conditions for asymptotic stability for these interval systems are derived by constructing some suitable lyapunov functionals the conditions obtained are given in the form of linear matrix inequalities that can be checked numerically and very efficiently by using the matlab lmi control toolbox finally some illustrative numerical examples are provided to demonstrate the effectiveness of the results obtained

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

new conditions on global stability of cohen grossberg neural networks in this letter we discuss the dynamics of the cohen grossberg neural networks we provide a new and relaxed set of sufficient conditions for the cohen grossberg networks to be absolutely stable and exponentially stable globally we also provide an estimate of the rate of convergence

impulsive effects on stability of cohen grossberg neural networks with variable delays in this paper a model of impulsive cohen grossberg neural networks is first formulated by establishing some impulsive differential inequalities we investigate impulsive effects on the stability of cohen grossberg neural networks with variable delays and obtain some sufficient conditions ensuring global exponential stability of the impulsive delay system our criteria not only show that the stability still remains under certain impulsive perturbations for some continuous stable neural networks but also present an approach to stabilize the unstable neural networks by utilizing impulsive effects the results extend and improve some recent works for impulsive neural networks as well as non impulsive neural networks some examples and their simulations are given for illustration of the theoretical results

hopf bifurcation and stability of periodic solutions for van der pol equation with time delay abstract in this paper the van der pol equation with a time delay is considered where the time delay is regarded as a parameter it is found that hopf bifurcation occurs when this delay passes through a sequence of critical value a formula for determining the direction of the hopf bifurcation and the stability of bifurcating periodic solutions is given by using the normal form method and center manifold theorem

ultimate boundedness and periodicity for some partial functional differential equations with infinite delay abstract in this work we study the existence of periodic solutions for some partial functional differential equation with infinite delay we assume that the linear part is not necessarily densely defined and satisfies the known hille yosida condition firstly we give some estimates of the solutions secondly we prove that the poincare map is condensing which allows us to prove the existence of periodic solutions when the solutions are ultimately bounded

new stability criteria of neural networks with interval time varying delay a piecewise delay method abstract this paper provides improved conditions for the global asymptotic stability of a class of neural networks with interval time varying delays a piecewise delay method is firstly proposed in this method the variation interval of the time delay is divided into two subintervals by introducing its central point then by constructing a new lyapunov krasovskii functional and checking its variation in the two subintervals respectively some new delay dependent stability criteria for the addressed neural networks are derived numerical examples are provided to show that the achieved conditions are less conservative than some existing ones in the literature

the discrete and mixed minimax 2 center problems abstract letting p be a set of n points in the plane the discrete minimax 2 center problem d m m 2 c p is to find two disks centered at p 1 p 2 p that minimize the maximum of two terms namely the euclidean distance between two centers and the distance of any other point to the closer center the mixed minimax 2 center problem m m m 2 c p is when one of the two centers is not in p we present algorithms solving the d m m 2 c p and m m m 2 c p the time complexities of solving the d m m 2 c p and m m m 2 c p are o n 2 log n and o n 2 log 2 n respectively furthermore we consider two steiner minimum sum dipolar spanning tree problems in which one of the two dipoles is a steiner point and the dipoles are both steiner points these two problems are shown to be solvable in o n log n and o n time respectively

streaming with minimum space an algorithm for covering by two congruent balls in this paper we design a simple streaming algorithm for maintaining two smallest balls of equal radius in d dimension to cover a set of points in an on line fashion different from most of the traditional streaming models at any step we use the minimum amount of space by only storing the locations and the common radius of the balls previously such a geometric algorithm is only investigated for covering with one ball one center by zarrabi zadeh and chan 2006 16 we give an analysis of our algorithm which is significantly different from the one center algorithm due to the obvious possibility of grouping points wrongly under this streaming model we show that our algorithm has an approximation ratio 2 for d 1 and at most 5 611 for any fixed d 1 we also present lower bounds of 1 5 and 1 604 for the problem in the d 1 and d 1 cases respectively

global robust stability of neural networks with time varying delays in this paper we study the global robust stability of neural networks with time varying delays using the lyapunov functional method and matrix inequality technique several sufficient conditions are presented to show the existence of equilibrium and global robust stability of neural networks which is easy to apply then we give a simulation to justify the obtained results

stability analysis in lagrange sense for a non autonomous cohen grossberg neural network with mixed delays abstract the paper discusses the global exponential stability in the lagrange sense for a non autonomous cohen grossberg neural network cgnn with time varying and distributed delays the boundedness and global exponential attractivity of non autonomous cgnn with time varying and distributed delays are investigated by constructing appropriate lyapunov like functions moreover we provide verifiable criteria on the basis of considering three different types of activation function which include both bounded and unbounded activation functions these results can be applied to analyze monostable as well as multistable biology neural networks due to making no assumptions on the number of equilibria meanwhile the results obtained in this paper are more general and challenging than that of the existing references in the end an illustrative example is given to verify our results

mixed time delays dependent exponential stability for uncertain stochastic high order neural networks this paper presents a discrete and distributed time delays dependent simultaneous approach to deterministic and uncertain stochastic high order neural networks new results are proposed in terms of linear matrix inequality lmi by exploiting a novel lyapunov krasovskii functional and by making use of novel techniques for time delay systems some constraints of systems are removed and new results cover some recently published works two numerical examples are given to show the usefulness of presented approach

2n almost periodic attractors for cohen grossberg type bam neural networks with variable coefficients and distributed delays abstract in this paper a class of 2 n almost periodic attractors for cohen grossberg type bi directional associative memory bam neural networks with variable coefficients and distributed delays is discussed by imposing some new assumptions on activation functions and system parameters we split invariant basin of bam into 2 n compact convex subsets then the existence of 2 n almost periodic solutions lying in compact convex subsets is attained and some new criteria for the networks to converge toward these 2 n almost periodic solutions and exponential attracting domains are also given correspondingly finally some examples are presented to illustrate the feasibility and effectiveness of the results

global exponential stability in continuous time and discrete time delayed bidirectional neural networks convergence dynamics of continuous time bidirectional neural networks with constant transmission delays are studied without assuming the symmetry of synaptic connection weights and the monotonicity and differentiability of activation functions lyapunov functionals and halanay type inequalities are constructed and employed to derive delay independent sufficient conditions under which the continuous time networks converge exponentially to the equilibria associated with temporally uniform external inputs to the networks discrete time analogues of the continuous time networks are formulated and we study their dynamical characteristics it is shown that the convergence dynamics of the continuous time networks are preserved by the discrete time analogues without any restriction on the discretization step size several examples are given to illustrate the advantages of the discrete time analogues in numerically simulating the continuous time networks

dynamic analysis of stochastic cohen grossberg neural networks with time delays abstract in this paper we discuss stochastic cohen grossberg neural networks with time delays by constructing suitable lyapunov functional and employing the semimartingale convergence theorem we give some sufficient criteria ensuring almost sure exponential stability of the networks the results obtained are helpful to design stability of networks when stochastic noise is taken into consideration

delay dependent state estimation for delayed neural networks in this letter the delay dependent state estimation problem for neural networks with time varying delay is investigated a delay dependent criterion is established to estimate the neuron states through available output measurements such that the dynamics of the estimation error is globally exponentially stable the proposed method is based on the free weighting matrix approach and is applicable to the case that the derivative of a time varying delay takes any value an algorithm is presented to compute the state estimator finally a numerical example is given to demonstrate the effectiveness of this approach and the improvement over existing ones

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

stability of artificial neural networks with impulses sufficient conditions are obtained for the existence and asymptotic stability of a unique equilibrium of a hopfield type neural network with lipschitzian activation functions without assuming their boundedness monotonicity or differentiability and subjected to impulsive state displacements at fixed instants of time both the continuous time and their corresponding discrete time networks are considered the sufficient conditions of the discrete time network do not restrict the step size appearing in the discretization process and these conditions approach as the step size tends to zero those of the conditions of the continuous time networks the sufficient conditions are in terms of the parameters of the network only and are easy to verify also when the impulsive jumps are absent the results reduce to those of the non impulsive systems

stability analysis of impulsive stochastic cohen grossberg neural networks with mixed time delays abstract in this paper the problem of stability analysis for a class of impulsive stochastic cohen grossberg neural networks with mixed delays is considered the mixed time delays comprise both the time varying and infinite distributed delays by employing a combination of the m matrix theory and stochastic analysis technique a sufficient condition is obtained to ensure the existence uniqueness and exponential p stability of the equilibrium point for the addressed impulsive stochastic cohen grossberg neural network with mixed delays the proposed method which does not make use of the lyapunov functional is shown to be simple yet effective for analyzing the stability of impulsive or stochastic neural networks with variable and or distributed delays we then extend our main results to the case where the parameters contain interval uncertainties moreover the exponential convergence rate index is estimated which depends on the system parameters an example is given to show the effectiveness of the obtained results

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

exponential stability of impulsive cellular neural networks with time delay via lyapunov functionals this paper investigates the problem of exponential stability for a class of impulsive cellular neural networks with time delay by dividing the network state variables into subgroups according to the characters of the neural networks some sufficient conditions for exponential stability are derived by lyapunov functionals and the method of variation of parameters these conditions are given in terms of some blocks of the interconnection matrix which extend and improve some of the known results in the literature our results show that impulses may be used to stabilize the cellular neural networks with time delay if they are not stable or exponentially stable on the other hand if impulses are input disturbances criteria on the magnitude and frequency of the impulses are also established to maintain the stability property of the original system our results generalize and improve some known results two examples with numerical simulations are given to illustrate our results

a comprehensive review of stability analysis of continuous time recurrent neural networks stability problems of continuous time recurrent neural networks have been extensively studied and many papers have been published in the literature the purpose of this paper is to provide a comprehensive review of the research on stability of continuous time recurrent neural networks including hopfield neural networks cohen grossberg neural networks and related models since time delay is inevitable in practice stability results of recurrent neural networks with different classes of time delays are reviewed in detail for the case of delay dependent stability the results on how to deal with the constant variable delay in recurrent neural networks are summarized the relationship among stability results in different forms such as algebraic inequality forms m matrix forms linear matrix inequality forms and lyapunov diagonal stability forms is discussed and compared some necessary and sufficient stability conditions for recurrent neural networks without time delays are also discussed concluding remarks and future directions of stability analysis of recurrent neural networks are given

robust exponential stability of uncertain fuzzy cohen grossberg neural networks with time varying delays in this paper the takagi sugeno t s fuzzy model representation is extended to the stability analysis for uncertain cohen grossberg neural networks cgnns with time varying delays a novel linear matrix inequality lmi based stability criterion is obtained by using lyapunov functional theory to guarantee the exponential stability of uncertain cgnns with time varying delays which are represented by t s fuzzy models finally the proposed stability conditions are demonstrated with numerical examples

exponential stability and periodic oscillatory solution in bam networks with delays both exponential stability and periodic oscillatory solution of bidirectional associative memory bam networks with axonal signal transmission delays are considered by constructing suitable lyapunov functional and some analysis techniques some simple sufficient conditions are given ensuring the global exponential stability and the existence of periodic oscillatory solutions of bam with delays these conditions are presented in terms of system parameters and have important leading significance in the design and applications of globally exponentially stable and periodic oscillatory neural circuits for bam with delays in addition two examples are given to illustrate the results