stability analysis of markovian jump stochastic bam neural networks with impulse control and mixed time delays this paper discusses the issue of stability analysis for a class of impulsive stochastic bidirectional associative memory neural networks with both markovian jump parameters and mixed time delays the jumping parameters are modeled as a continuous time discrete state markov chain based on a novel lyapunov krasovskii functional the generalized ito s formula mathematical induction and stochastic analysis theory a linear matrix inequality approach is developed to derive some novel sufficient conditions that guarantee the exponential stability in the mean square of the equilibrium point at the same time we also investigate the robustly exponential stability in the mean square of the corresponding system with unknown parameters it should be mentioned that our stability results are delay dependent which depend on not only the upper bounds of time delays but also their lower bounds moreover the derivatives of time delays are not necessarily zero or smaller than one since several free matrices are introduced in our results consequently the results obtained in this paper are not only less conservative but also generalize and improve many earlier results finally two numerical examples and their simulations are provided to show the effectiveness of the theoretical results

dissipativity analysis for singular systems with time varying delays this paper is concerned with the dissipativity analysis problem for singular systems with time varying delays a delay dependent criterion is established to guarantee the dissipativity of the underlying systems using the delay partitioning technique all the results given in this paper are not only dependent upon the time delay but also dependent upon the number of delay partitions the effectiveness and the reduced conservatism of the derived results are demonstrated by two illustrative examples

exponential stability of stochastic reaction diffusion cohen grossberg neural networks with delays abstract in this paper stochastic cohen grossberg neural network with time varying delays and reaction diffusion terms is considered the sufficient conditions are obtained to guarantee the mean value exponential stability of an equilibrium solution

stability analyses of cellular neural networks with continuous time delay the stability of cellular neural networks cnns with continuous time delay is investigated in the present paper a main theorem together with a few corollaries related to the existence and boundedness of the solution for this kind of cnns as well as its global asymptotic stability is derived some numerical simulation examples aimed at justifying the theoretical results are also given

stability of cohen grossberg neural networks with distributed delays global asymptotic stability and global exponential stability of the cohen grossberg neural networks and hopfield neural networks with infinite and finite distributed delays are investigated in this paper for hopfield neural networks with distributed delays local stability is also discussed the existence and global stability of periodic solutions of hopfield neural networks with distributed delays and periodic inputs are achieved by using the theory of dissipative systems

sampled data synchronization analysis of markovian neural networks with generally incomplete transition rates this paper investigates the problem of sampled data synchronization for markovian neural networks with generally incomplete transition rates different from traditional markovian neural networks each transition rate can be completely unknown or only its estimate value is known in this paper compared with most of existing markovian neural networks our model is more practical because the transition rates in markovian processes are difficult to precisely acquire due to the limitations of equipment and the influence of uncertain factors in addition the time dependent lyapunov krasovskii functional is proposed to synchronize drive system and response system by applying an extended jensen s integral inequality and wirtinger s inequality new delay dependent synchronization criteria are obtained which fully utilize the upper bound of variable sampling interval and the sawtooth structure information of varying input delay moreover the desired sampled data controllers are obtained finally two examples are provided to illustrate the effectiveness of the proposed method

verified integration of linear nth order odes using large steps the solution y x of an ivp for a linear ode with analytic coefficient functions is represented as a power series a high order taylor polynomial is used for an approximate numerical solution the taylor remainder series is rigorously estimated by some geometric series the method has been implemented and tested on a computer guaranteed enclosures are achieved by taking into account all roundoff errors

sampled data synchronization of markovian coupled neural networks with mode delays based on mode dependent lkf this paper investigates sampled data synchronization problem of markovian coupled neural networks with mode dependent interval time varying delays and aperiodic sampling intervals based on an enhanced input delay approach a mode dependent augmented lyapunov krasovskii functional lkf is utilized which makes the lkf matrices mode dependent as much as possible by applying an extended jensen s integral inequality and wirtinger s inequality new delay dependent synchronization criteria are obtained which fully utilizes the upper bound on variable sampling interval and the sawtooth structure information of varying input delay in addition the desired stochastic sampled data controllers can be obtained by solving a set of linear matrix inequalities finally two examples are provided to demonstrate the feasibility of the proposed method

sampled data state estimation for markovian jumping fuzzy cellular neural networks with mode dependent probabilistic time varying delays in this paper the problem of state estimation for markovian jumping fuzzy cellular neural networks fcnns using sampled data with mode dependent probabilistic time varying delays is investigated by developing a delay decomposition approach the information of the delayed states can be taken into full consideration by introducing a stochastic variable with a bernoulli distribution the information of probability distribution of the time varying delay is considered and transformed into one with deterministic time varying delay the main purpose of this paper is to estimate the neuron states through available output measurements such that the dynamics of the estimation error is globally asymptotically stable in the mean square based on the lyapunov krasovskii functional including triple integral terms and decomposed integral intervals delay distribution dependent stability criteria are obtained in terms of linear matrix inequalities lmis finally two numerical examples are given to illustrate the effectiveness of the proposed theoretical results

hypercyclic behaviour of operators in a hypercyclic c 0 semigroup abstract let t t t 0 be a hypercyclic strongly continuous semigroup of operators then each t t t 0 is hypercyclic as a single operator and it shares the set of hypercyclic vectors with the semigroup this answers in the affirmative a natural question concerning hypercyclic c 0 semigroups the analogous result for frequent hypercyclicity is also obtained

finite time h filtering for a class of discrete time markovian jump systems with switching transition probabilities subject to average dwell time switching an extension of fixed transition probability markovian switching model to combine time varying transition probabilities has offered another set of useful regime switching models this paper investigated the problem of finite time h filtering for a class of discrete time markovian jump systems with switching transition probabilities subject to average dwell time switching based on the results of finite time boundness and average dwell time a novel sufficient condition for finite time bounded of h filtering is derived and the system trajectory stays within a prescribed bound finally an example is provided to illustrate the usefulness and effectiveness of the proposed method

mean square stability of two classes of theta methods for numerical computation and simulation of delayed stochastic hopfield neural networks abstract recently the investigation on the stability of the numerical solutions to delayed stochastic differential equations has received an increasing attention but there has been little work on the stability analysis of the numerical solutions to delayed stochastic hopfield neural networks dshnns so far the aim in this paper is to study the mean square exponential stability of the split step theta sst method and the stochastic linear theta slt method for the underlying model it is proved that for any 0 1 2 there exists a constant 0 depending on such that the numerical schemes produced by the sst method and the slt method are mean square exponentially stable for 0 under the same assumptions as those to guarantee the mean square exponential stability of the underlying continuous model for the case 1 2 1 we show the same stability conclusion for all 0 to carry out the required conclusion a novel technique for the stability analysis of discrete numerical schemes with multi time delays namely the weighted sum lyapunov functional method is proposed finally a numerical example is given to illustrate the application of the suggested methods and to verify the stability conclusions obtained

new criteria for global robust stability of delayed neural networks with norm bounded uncertainties in this paper we study the global asymptotic robust stability of delayed neural networks with norm bounded uncertainties by employing the lyapunov stability theory and homeomorphic mapping theorem we derive some new types of sufficient conditions ensuring the existence uniqueness and global asymptotic stability of the equilibrium point for the class of neural networks with discrete time delays under parameter uncertainties and with respect to continuous and slope bounded activation functions an important aspect of our results is their low computational complexity as the reported results can be verified by checking some properties of symmetric matrices associated with the uncertainty sets of the network parameters the obtained results are shown to be generalizations of some of the previously published corresponding results some comparative numerical examples are also constructed to compare our results with some closely related existing literature results

global attractivity of cohen grossberg model with finite and infinite delays in this paper we have studied the global attractivity of the equilibrium of cohen grossberg model with both finite and infinite delays criteria for global attractivity are also derived by means of lyapunov functionals as a corollary we show that if the delayed system is dissipative and the coefficient matrix is vl stable then the global attractivity of the unique equilibrium is maintained provided the delays are small estimates on the allowable sizes of delays are also given applications to the hopfield neural networks with discrete delays are included

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

stability of stochastic levy noise coupled systems with mixed delays in this paper based on razumikhin method stability of stochastic levy noise coupled systems with mixed delays slcsd is researched here both mixed delays and levy noise are considered into cou

stability analysis of markovian jumping stochastic cohen grossberg neural networks with mixed time delays in this letter the global asymptotical stability analysis problem is considered for a class of markovian jumping stochastic cohen grossberg neural networks cgnns with mixed delays including discrete delays and distributed delays an alternative delay dependent stability analysis result is established based on the linear matrix inequality lmi technique which can easily be checked by utilizing the numerically efficient matlab lmi toolbox neither system transformation nor free weight matrix via newton leibniz formula is required two numerical examples are included to show the effectiveness of the result

strong mixing gaussian measures for chaotic semigroups abstract in this paper we will be concerned with the problem of the existence of an invariant mixing measure considering its connection with the chaotic behavior of linear semigroups on separable banach spaces we first prove an identity characterizing invariant gaussian measure involving its covariance operator and the infinitesimal generator of the semigroup this gives an answer to a question raised by rudnicki in his inspiring review paper 32 under suitable conditions we use the proved identity to give an invariant mixing gaussian measure as distribution of a wiener integral

stability analysis and application for delayed neural networks driven by fractional brownian noise this paper deals with two types of the stability problem for the delayed neural networks driven by fractional brownian noise fbn the existence and the uniqueness of the solution to the main system with respect to fbn are proved via fixed point theory based on hilbert schmidt operator theory and analytic semigroup principle the mild solution of the stochastic neural networks is obtained by applying the stochastic analytic technique and some well known inequalities the asymptotic stability criteria and the exponential stability condition are established both numerical example and practical application for synchronization control of multiagent system are provided to illustrate the effectiveness and potential of the proposed techniques

robust stability and boundedness of stochastic differential equations with delay driven by g brownian motion this paper aims to establish the robust stability and boundedness for a class of stochastic differential equations with delay driven by g brownian motion g sddes in short whose coefficients do n

robust exponential stability of uncertain delayed neural networks with stochastic perturbation and impulse effects this paper focuses on the hybrid effects of parameter uncertainty stochastic perturbation and impulses on global stability of delayed neural networks by using the ito formula lyapunov function and halanay inequality we established several mean square stability criteria from which we can estimate the feasible bounds of impulses provided that parameter uncertainty and stochastic perturbations are well constrained moreover the present method can also be applied to general differential systems with stochastic perturbation and impulses

passivity analysis for discrete time stochastic markovian jump neural networks with mixed time delays in this paper passivity analysis is conducted for discrete time stochastic neural networks with both markovian jumping parameters and mixed time delays the mixed time delays consist of both discrete and distributed delays the markov chain in the underlying neural networks is finite piecewise homogeneous by introducing a lyapunov functional that accounts for the mixed time delays a delay dependent passivity condition is derived in terms of the linear matrix inequality approach the case of markov chain with partially unknown transition probabilities is also considered all the results presented depend upon not only discrete delay but also distributed delay a numerical example is included to demonstrate the effectiveness of the proposed methods

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

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

a note on a sum associated with the generalized hypergeometric function a new summation formula that is connected to the generalized hypergeometric function is presented the formula can be applied in the taylor series method for the solution of ordinary differential equations

stability analysis for stochastic cohen grossberg neural networks with mixed time delays in this letter the global asymptotic stability analysis problem is considered for a class of stochastic cohen grossberg neural networks with mixed time delays which consist of both the discrete and distributed time delays based on an lyapunov krasovskii functional and the stochastic stability analysis theory a linear matrix inequality lmi approach is developed to derive several sufficient conditions guaranteeing the global asymptotic convergence of the equilibrium point in the mean square it is shown that the addressed stochastic cohen grossberg neural networks with mixed delays are globally asymptotically stable in the mean square if two lmis are feasible where the feasibility of lmis can be readily checked by the matlab lmi toolbox it is also pointed out that the main results comprise some existing results as special cases a numerical example is given to demonstrate the usefulness of the proposed global stability criteria

robustness analysis of global exponential stability of recurrent neural networks in the presence of time delays and random disturbances in recent years the global stability of recurrent neural networks rnns has been investigated extensively it is well known that time delays and external disturbances can derail the stability of rnns in this paper we analyze the robustness of global stability of rnns subject to time delays and random disturbances given a globally exponentially stable neural network the problem to be addressed here is how much time delay and noise the rnn can withstand to be globally exponentially stable in the presence of delay and noise the upper bounds of the time delay and noise intensity are characterized by using transcendental equations for the rnns to sustain global exponential stability moreover we prove theoretically that for any globally exponentially stable rnns if additive noises and time delays are smaller than the derived lower bounds arrived at here then the perturbed rnns are guaranteed to also be globally exponentially stable three numerical examples are provided to substantiate the theoretical results

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

synchronization of markovian coupled neural networks with nonidentical node delays and random coupling strengths in this paper a general model of coupled neural networks with markovian jumping and random coupling strengths is introduced in the process of evolution the proposed model switches from one mode to another according to a markovian chain and all the modes have different constant time delays the coupling strengths are characterized by mutually independent random variables when compared with most of existing dynamical network models which share common time delay for all modes and have constant coupling strengths our model is more practical because different chaotic neural network models can have different time delays and coupling strength of complex networks may randomly vary around a constant due to environmental and artificial factors by designing a novel lyapunov functional and using some inequalities and the properties of random variables we derive several new sufficient synchronization criteria formulated by linear matrix inequalities the obtained criteria depend on mode delays and mathematical expectations and variances of the random coupling strengths as well numerical examples are given to demonstrate the effectiveness of the theoretical results meanwhile right continuous markovian chain is also presented

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

further results on exponential stability for impulsive switched nonlinear time delay systems with delayed impulse effects this paper is concerned with the problem of exponential stability for a class of impulsive switched nonlinear time delay systems with delayed impulse effects by using the multiple lyapunov krasovskii functionals technique some exponential stability criteria are obtained respectively for two kinds of impulsive signals destabilizing impulsive signal and stabilizing impulsive signal the derived results not only characterise the effects of delayed impulse time delay and switching on nonlinear systems but also remove some restriction conditions furthermore a more precise bound of system state is given compared with existing results on related problems the obtained results are less conservative three examples are provided to illustrate the effectiveness and the generality of the proposed results

convergence dynamics of cohen grossberg neural networks with continuously distributed delays abstract in this paper we consider the convergence dynamics of cohen grossberg neural networks cgnns with continuously distributed delays without assuming the differentiability and monotonicity of activation functions the differentiability of amplification functions and the symmetry of synaptic interconnection weights we construct suitable lyapunov functionals and employ inequality technique to establish some sufficient conditions ensuring existence uniqueness global asymptotic stability global exponential convergence and even global exponential stability of equilibria our results are not only presented in terms of system parameters and can be easily verified and also less restrictive than previously known criteria and can be applied to neural networks including hopfield neural networks bidirectional association memory neural networks and cellular neural networks

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

boundedness and global exponential stability for generalized cohen grossberg neural networks with variable delay abstract a generalized halanay inequality is established and the boundedness of generalized cohen grossberg neural networks is investigated by applying the generalized halanay inequality and lyapunov functional method new sufficient conditions are obtained ensuring the global exponential stability of the solution of the generalized cohen grossberg neural networks with variable delay three examples are also given for illustration

stochastic stability of impulsive bam neural networks with time delays the problem of stability analysis of stochastic bam neural networks with time delays and impulse effects is investigated in this paper using the lyapunov technique and the generalized hanalay inequality we characterize theoretically the aggregated effects of impulse and stability properties of the impulse free version the present approaches allow us to estimate the feasible upper bounds of impulse strengths and can also extend to the more general impulsive nonlinear systems with delays

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

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

p th moment exponential input to state stability of delayed recurrent neural networks with markovian switching via vector lyapunov function in this paper the p th moment input to state exponential stability for delayed recurrent neural networks drnns with markovian switching is studied by using stochastic analysis techniques and classical razumikhin techniques a generalized vector mathcal l operator differential inequality including cross item is obtained without additional restrictive conditions on the time varying delay the sufficient criteria on the p th moment input to state exponential stability for drnns with markovian switching are derived by means of the vector mathcal l operator differential inequality when the input is zero an improved criterion on exponential stability is obtained two numerical examples are provided to examine the correctness of the derived results

improved delay dependent stability results of recurrent neural networks abstract by using the fact that the activation functions are sector bounded and a tighter inequality this paper presents a new method to the stability analysis of a class of recurrent neural networks rnns with time varying delays this method includes more the slope of activation functions and less variables matrices in constructed lyapunov krasovskii functional with the present stability conditions the computational burden and conservatism are largely reduced both theoretical analysis and numerical example are given to illustrate the effectiveness and the benefits of the proposed method

computation of synchronized periodic solution in a bam network with two delays a bidirectional associative memory bam neural network with four neurons and two discrete delays is considered to represent an analytical method namely perturbation incremental scheme pis the expressions for the periodic solutions derived from hopf bifurcation are given by using the pis the result shows that the pis has higher accuracy than the center manifold reduction cmr with normal form for the values of time delay not far away from the hopf bifurcation point in terms of the pis the necessary and sufficient conditions of synchronized periodic solution arising from a hopf bifurcation are obtained and the synchronized periodic solution is expressed in an analytical form it can be seen that theoretical analysis is in good agreement with numerical simulation it implies that the provided method is valid and the obtained result is correct to the best of our knowledge the paper is the first one to introduce the pis to study the periodic solution derived from hopf bifurcation for a 4 d delayed system quantitatively

global exponential stability and periodic solutions of cohen grossberg neural networks with continuously distributed delays abstract convergence dynamics of cohen grossberg neural networks cgnns with continuously distributed delays are discussed without assuming the differentiability and monotonicity of activation functions the differentiability of amplification functions and the symmetry of synaptic interconnection weights by skilfully constructing suitable lyapunov functionals and employing inequality technique three sets of easily verifiable delay independent criteria to guarantee the global exponential stability of a unique equilibrium point are given and moreover by constructing poincare mapping other three sets of easily verifiable delay independent criteria to assure the existence and globally exponential stability of periodic solutions are obtained six examples are given to illustrate the theoretical results

finite time stability analysis for markovian jump memristive neural networks with partly unknown transition probabilities this paper is concerned with the finite time stochastically stability ftss analysis of markovian jump memristive neural networks with partly unknown transition probabilities in the neural networks there exist a group of modes determined by markov chain and thus the markovian jump was taken into consideration and the concept of ftss is first introduced for the memristive model by introducing a markov switching lyapunov functional and stochastic analysis theory an ftss test procedure is proposed from which we can conclude that the settling time function is a stochastic variable and its expectation is finite the system under consideration is quite general since it contains completely known and completely unknown transition probabilities as two special cases more importantly a nonlinear measure method was introduced to verify the uniqueness of the equilibrium point compared with the fixed point theorem that has been widely used in the existing results this method is more easy to implement besides the delay interval was divided into four subintervals which make full use of the information of the subsystems upper bounds of the time varying delays finally the effectiveness and superiority of the proposed method is demonstrated by two simulation examples

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

synchronization of markovian jumping stochastic complex networks with distributed time delays and probabilistic interval discrete time varying delays the paper investigates the synchronization stability problem for a class of complex dynamical networks with markovian jumping parameters and mixed time delays the complex networks consist of m modes and the networks switch from one mode to another according to a markovian chain with known transition probability the mixed time delays are composed of discrete and distributed delays the discrete time delay is assumed to be random and its probability distribution is known a priori in terms of the probability distribution of the delays the new type of system model with probability distribution dependent parameter matrices is proposed based on the stochastic analysis techniques and the properties of the kronecker product delay dependent synchronization stability criteria in the mean square are derived in the form of linear matrix inequalities which can be readily solved by using the lmi toolbox in matlab the solvability of derived conditions depends on not only the size of the delay but also the probability of the delay taking values in some intervals finally a numerical example is given to illustrate the feasibility and effectiveness of the proposed method

robust stability for interval hopfield neural networks with time delay the conventional hopfield neural network with time delay is intervalized to consider the bounded effect of deviation of network parameters and perturbations yielding a novel interval dynamic hopfield neural network idhnn model a sufficient condition related to the existence of unique equilibrium point and its robust stability is derived

delay dependent stochastic stability of delayed hopfield neural networks with markovian jump parameters in this paper the problem of stochastic stability for a class of time delay hopfield neural networks with markovian jump parameters is investigated the jumping parameters are modeled as a continuous time discrete state markov process without assuming the boundedness monotonicity and differentiability of the activation functions some results for delay dependent stochastic stability criteria for the markovian jumping hopfield neural networks mjdhnns with time delay are developed we establish that the sufficient conditions can be essentially solved in terms of linear matrix inequalities

stochastic stability of delayed neural networks with local impulsive effects in this paper the stability problem is studied for a class of stochastic neural networks nns with local impulsive effects the impulsive effects considered can be not only nonidentical in different dimensions of the system state but also various at distinct impulsive instants hence the impulses here can encompass several typical impulses in nns the aim of this paper is to derive stability criteria such that stochastic nns with local impulsive effects are exponentially stable in mean square by means of the mathematical induction method several easy to check conditions are obtained to ensure the mean square stability of nns three examples are given to show the effectiveness of the proposed stability criterion

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

asymptotic behavior of a class of reaction diffusion equations with delays abstract the authors analyze asymptotic behavior of the partial functional differential equations and the sufficient conditions on existence of global attractor of a class of reaction diffusion equations with delays are given

exponential and almost sure exponential stability of stochastic fuzzy delayed cohen grossberg neural networks in this paper we study a class of stochastic fuzzy delayed cohen grossberg neural networks two kinds of stability are discussed in our investigation one is exponential stability in the mean square and the other is almost sure exponential stability first some sufficient conditions are derived to guarantee the exponential stability in the mean square for the considered system based on the lyapunov krasovskii functional stochastic analysis theory and the ito s formula as well as the dynkin formula then we further investigate the almost sure exponential stability by employing the nonnegative semi martingale convergence theorem moreover we prove that the addressed system is both almost sure exponentially stable and exponentially stable in the mean square under suitable conditions finally three numerical examples are also given to show the effectiveness of the theoretical results in particular the simulation figures establish that fuzzy systems do have more advantages than non fuzzy systems

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

exponential periodicity and stability of neural networks with reaction diffusion terms and both variable and unbounded delays in this paper the exponential periodicity and stability of neural networks with lipschitz continuous activation functions are investigated without assuming the boundedness of the activation functions and the differentiability of time varying delays as needed in most other papers the neural networks contain reaction diffusion terms and both variable and unbounded delays some sufficient conditions ensuring the existence and uniqueness of periodic solution and stability of neural networks with reaction diffusion terms and both variable and unbounded delays are obtained by analytic methods and inequality technique furthermore the exponential converging index is also estimated the methods which does not make use of lyapunov functional is simple and valid for the periodicity and stability analysis of neural networks with variable and or unbounded delays the results extend some previous results two examples are given to show the effectiveness of the obtained results

asymptotic stability analysis of stochastic reaction diffusion cohen grossberg neural networks with mixed time delays abstract in this paper the asymptotic stability problem is studied for a class of stochastic cohen grossberg neural networks with reaction diffusion and time mixed delays by using the lyapunov krasovskii functional stochastic analysis technology and linear matrix inequalities lmis technique several sufficient conditions on the asymptotic stability for the considered system are obtained the condition not only connects with the delays and diffusion effect but also relates to the magnitude of noise therefore these stability criteria are essentially new and more effective than those given in previous conditions two examples are presented to illustrate the effectiveness and efficiency of the results

robust state estimation for uncertain neural networks with time varying delay the robust state estimation problem for a class of uncertain neural networks with time varying delay is studied in this paper the parameter uncertainties are assumed to be norm bounded based on a new bounding technique a sufficient condition is presented to guarantee the existence of the desired state estimator for the uncertain delayed neural networks the criterion is dependent on the size of the time varying delay and on the size of the time derivative of the time varying delay it is shown that the design of the robust state estimator for such neural networks can be achieved by solving a linear matrix inequality lmi which can be easily facilitated by using some standard numerical packages finally two simulation examples are given to demonstrate the effectiveness of the developed approach

stability analysis for stochastic volterra levin equations with poisson jumps fixed point approach this paper is devoted to investigate a class of stochastic volterra levin equations with poisson jumps to the best of the authors knowledge till now the stability problem for this class of new systems has not yet been solved since poisson jumps are considered the main objective of this paper is to fill the gap by using the fixed point theory we first study the existence and uniqueness of the solution as well as the pth moment exponential stability for the considered system then based on the well known borel cantelli lemma we prove that the solution is almost surely pth moment exponentially stable our results improve and generalize those given in the previous literature finally two simple examples are provided to illustrate the effectiveness of the obtained 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

exponential stability of stochastic delayed hopfield neural networks the exponential stability for stochastic delayed hopfield neural networks hnns is considered the sufficient conditions to guarantee the almost surely exponential stability and exponential stability in mean square of an equilibrium solution are given one example is also given to demonstrate our results

adaptive lag synchronization for competitive neural networks with mixed delays and uncertain hybrid perturbations this paper investigates the problem of adaptive lag synchronization for a kind of competitive neural network with discrete and distributed delays mixed delays as well as uncertain nonlinear external and stochastic perturbations hybrid perturbations a simple but robust adaptive controller is designed such that the response system can lag synchronize with a drive system based on the lyapunov stability theory and some suitable lyapunov krasovskii functionals several sufficient conditions ensuring the lag synchronization are developed our synchronization criteria are easily verified and do not need to solve any linear matrix inequality some existing results are improved and extended moreover the designed adaptive controller has better anti interference capacity and is more practical than the usual adaptive controller numerical simulations are exploited to show the effectiveness of the theoretical results

impulsive synchronization of reaction diffusion neural networks with mixed delays and its application to image encryption this paper presents a new impulsive synchronization criterion of two identical reaction diffusion neural networks with discrete and unbounded distributed delays the new criterion is established by applying an impulse time dependent lyapunov functional combined with the use of a new type of integral inequality for treating the reaction diffusion terms the impulse time dependent feature of the proposed lyapunov functional can capture more hybrid dynamical behaviors of the impulsive reaction diffusion neural networks than the conventional impulse time independent lyapunov functions functionals while the new integral inequality which is derived from wirtinger s inequality overcomes the conservatism introduced by the integral inequality used in the previous results numerical examples demonstrate the effectiveness of the proposed method later the developed impulsive synchronization method is applied to build a spatiotemporal chaotic cryptosystem that can transmit an encrypted image the experimental results verify that the proposed image encrypting cryptosystem has the advantages of large key space and high security against some traditional attacks

stability in asymmetric hopfield nets with transmission delays sufficient conditions are derived for the delay independent stability of the equilibria in hopfield s graded response networks of the type dxi t dt bixi t nj 1aijfj jxj t ij fi t i 1 2 n when the external inputs fi are held temporally uniform a generalization to continuously distributed delays is briefly indicated several illustrative examples are numerically simulated and the results of simulations are graphically displayed