robust μ stability for uncertain stochastic neural networks with unbounded time varying delays in this paper we investigate the global robust stability for uncertain stochastic neural networks with unbounded time varying delays and norm bounded parameter uncertainties a new concept of global robust stability in the mean square for neural networks is given first then by means of the linear matrix inequality lmi approach stability criteria are presented several corollaries are also derived a simple example is presented to demonstrate the effectiveness of the main result

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

delay dependent stochastic stability criteria for markovian jumping neural networks with mode dependent time varying delays and partially known transition rates abstract in this paper the problem of stochastic stability criterion of markovian jumping neural networks with mode dependent time varying delays and partially known transition rates is considered some new delay dependent stability criteria are derived by choosing a new class of lyapunov functional the obtained criteria are less conservative because free weighting matrices method and a convex optimization approach are considered finally a numerical example is given to illustrate the effectiveness of the proposed method

a graph theoretic approach to boundedness of stochastic cohen grossberg neural networks with markovian switching in this paper a novel class of stochastic cohen grossberg neural networks with markovian switching scgnnmss is investigated where the white noise and the color noise are taken into account by utilizing lyapunov method some graph theory and m matrix technique several sufficient conditions are obtained to ensure the asymptotic boundedness of the scgnnmss these criteria have a close relation to the topology property of the network and are easy to be verified in practice two numerical examples are also presented to substantiate the theoretical results

delay distribution dependent exponential stability criteria for discrete time recurrent neural networks with stochastic delay this brief is concerned with the analysis problem of global exponential stability in the mean square sense for a class of linear discrete time recurrent neural networks drnns with stochastic delay different from the prior research works the effects of both variation range and probability distribution of the time delay are involved in the proposed method first a modeling method is proposed by translating the probability distribution of the time delay into parameter matrices of the transformed drnn model where the delay is characterized by a stochastic binary distributed variable based on the new method the global exponential stability in the mean square sense for the drnns with stochastic delay is investigated by using the lyapunov krasovskii functional and exploiting some new analysis techniques a numerical example is provided to show the effectiveness and the applicability of the proposed method

novel delay dependent asymptotic stability criteria for neural networks with time varying delays the problem of delay dependent asymptotic stability criteria for neural networks nns with time varying delays is investigated an improved linear matrix inequality based on delay dependent stability test is introduced to ensure a large upper bound for time delay a new class of lyapunov function is constructed to derive a novel delay dependent stability criteria finally numerical examples are given to indicate significant improvement over some existing results

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

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

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

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

delay slope dependent stability results of recurrent neural networks by using the fact that the neuron activation functions are sector bounded and nondecreasing this brief presents a new method named the delay slope dependent method for stability analysis of a class of recurrent neural networks with time varying delays this method includes more information on the slope of neuron activation functions and fewer matrix variables in the constructed lyapunov krasovskii functional then some improved delay dependent stability criteria with less computational burden and conservatism are obtained numerical examples are given to illustrate the effectiveness and the benefits of the proposed method

some novel approaches on state estimation of delayed neural networks this paper studies the issue of state estimation for a class of neural networks nns with time varying delay a novel lyapunov krasovskii functional lkf is constructed where triple integral terms are used and a secondary delay partition approach sdpa is employed compared with the existing delay partition approaches the proposed approach can exploit more information on the time delay intervals by taking full advantage of a modified wirtinger s integral inequality mwii improved delay dependent stability criteria are derived which guarantee the existence of desired state estimator for delayed neural networks dnns a better estimator gain matrix is obtained in terms of the solution of linear matrix inequalities lmis in addition a new activation function dividing method is developed by bringing in some adjustable parameters three numerical examples with simulations are presented to demonstrate the effectiveness and merits of the proposed methods

new delay dependent stability criteria for neural networks with time varying delay in this letter a new method is proposed for stability analysis of neural networks nns with a time varying delay some less conservative delay dependent stability criteria are established by considering the additional useful terms which were ignored in previous methods when estimating the upper bound of the derivative of lyapunov functionals and introducing the new free weighting matrices numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method

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

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

state estimation for coupled uncertain stochastic networks with missing measurements and time varying delays the discrete time case this paper is concerned with the problem of state estimation for a class of discrete time coupled uncertain stochastic complex networks with missing measurements and time varying delay the parameter uncertainties are assumed to be norm bounded and enter into both the network state and the network output the stochastic brownian motions affect not only the coupling term of the network but also the overall network dynamics the nonlinear terms that satisfy the usual lipschitz conditions exist in both the state and measurement equations through available output measurements described by a binary switching sequence that obeys a conditional probability distribution we aim to design a state estimator to estimate the network states such that for all admissible parameter uncertainties and time varying delays the dynamics of the estimation error is guaranteed to be globally exponentially stable in the mean square by employing the lyapunov functional method combined with the stochastic analysis approach several delay dependent criteria are established that ensure the existence of the desired estimator gains and then the explicit expression of such estimator gains is characterized in terms of the solution to certain linear matrix inequalities lmis two numerical examples are exploited to illustrate the effectiveness of the proposed estimator design schemes

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

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

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

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 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

a new criterion of delay dependent asymptotic stability for hopfield neural networks with time delay in this brief the problem of global asymptotic stability for delayed hopfield neural networks hnns is investigated a new criterion of asymptotic stability is derived by introducing a new kind of lyapunov krasovskii functional and is formulated in terms of a linear matrix inequality lmi which can be readily solved via standard software this new criterion based on a delay fractioning approach proves to be much less conservative and the conservatism could be notably reduced by thinning the delay fractioning an example is provided to show the effectiveness and the advantage of the proposed result

stability analysis of discrete time recurrent neural networks with stochastic delay this paper is concerned with the stability analysis of discrete time recurrent neural networks rnns with time delays as random variables drawn from some probability distribution by introducing the variation probability of the time delay a common delayed discrete time rnn system is transformed into one with stochastic parameters improved conditions for the mean square stability of these systems are obtained by employing new lyapunov functions and novel techniques are used to achieve delay dependence the merit of the proposed conditions lies in its reduced conservatism which is made possible by considering not only the range of the time delays but also the variation probability distribution a numerical example is provided to show the advantages of the proposed conditions

a unified framework for the construction of various matrix multisplitting iterative methods for large sparse system of linear equations abstract a unified framework for the construction of various synchronous and asynchronous parallel matrix multisplitting iterative methods suitable to the simd and mimd multiprocessor systems respectively is presented and its convergence theory is established under rather weak conditions these afford general method models and systematical convergence criterions for studying the parallel iterations in the sense of matrix multisplitting in addition how the known parallel matrix multisplitting iterative methods can be classified into this new framework and what novel ones can be generated by it are shown in detail

on the nested refinement of quadrilateral and hexahedral finite elements and the affine approximation it is shown in this paper that the optimal approximation property of bilinear or trilinear finite elements would be retained when the affine mapping is used to replace the q1 mapping on each element if the grids are refined nestedly the new method truncates the quadratic and cubic terms in reference mappings and produces constant jacobians and jacobian matrices this would avoid a shortcoming of the quadrilateral and hexahedral elements where the integrals of rational functions have to be computed or approximated numerical tests verify the analysis

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

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

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

robust synchronization of an array of coupled stochastic discrete time delayed neural networks this paper is concerned with the robust synchronization problem for an array of coupled stochastic discrete time neural networks with time varying delay the individual neural network is subject to parameter uncertainty stochastic disturbance and time varying delay where the norm bounded parameter uncertainties exist in both the state and weight matrices the stochastic disturbance is in the form of a scalar wiener process and the time delay enters into the activation function for the array of coupled neural networks the constant coupling and delayed coupling are simultaneously considered we aim to establish easy to verify conditions under which the addressed neural networks are synchronized by using the kronecker product as an effective tool a linear matrix inequality lmi approach is developed to derive several sufficient criteria ensuring the coupled delayed neural networks to be globally robustly exponentially synchronized in the mean square the lmi based conditions obtained are dependent not only on the lower bound but also on the upper bound of the time varying delay and can be solved efficiently via the matlab lmi toolbox two numerical examples are given to demonstrate the usefulness of the proposed synchronization scheme