further note on global exponential stability of uncertain cellular neural networks with variable delays for cellular neural networks with time varying delays and uncertainties a recent work for exponential stability with convergence rate k of the networks is extended a new linear matrix inequality criterion for the stability which give information on the delay dependent property is derived

continuous time additive hopfield type neural networks with impulses we investigate the global stability characteristics of a system of equations modelling the dynamics of additive hopfield type neural networks with impulses in the continuous time case

design of state estimator for neural networks of neutral type in this paper the design problem of state estimator for a class of neural networks of neutral type is studied a delay dependent linear matrix inequality lmi criterion for existence of the estimator is proposed by using the lyapunov method the criterion can be easily solved by various convex optimization algorithms a numerical example with simulation results is given to show the effectiveness of 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

group analysis of self organizing maps based on functional mri using restricted frechet means studies of functional mri data are increasingly concerned with the estimation of differences in spatio temporal networks across groups of subjects or experimental conditions unsupervised clustering and independent component analysis ica have been used to identify such spatio temporal networks while these approaches have been useful for estimating these networks at the subject level comparisons over groups or experimental conditions require further methodological development in this paper we tackle this problem by showing how self organizing maps soms can be compared within a frechean inferential framework here we summarize the mean som in each group as a frechet mean with respect to a metric on the space of soms the advantage of this approach is twofold firstly it allows the visualization of the mean som in each experimental condition secondly this frechean approach permits one to draw inference on group differences using permutation of the group labels we consider the use of different distance functions and introduce one extension of the classical sum of minimum distance smd between two soms which take into account the spatial pattern of the fmri data the validity of these methods is illustrated on synthetic data through these simulations we show that the two distance functions of interest behave as expected in the sense that the ones capturing temporal and spatial aspects of the soms are more likely to reach significance under simulated scenarios characterized by temporal spatial and spatio temporal differences respectively in addition a re analysis of a classical experiment on visually triggered emotions demonstrates the usefulness of this methodology in this study the multivariate functional patterns typical of the subjects exposed to pleasant and unpleasant stimuli are found to be more similar than the ones of the subjects exposed to emotionally neutral stimuli in this re analysis the group level som output units with the smallest sample jaccard indices were compared with standard glm group specific z score maps and provided considerable levels of agreement taken together these results indicate that our proposed methods can cast new light on existing data by adopting a global analytical perspective on functional mri paradigms

stability analysis for neural networks with time varying interval delay this letter is concerned with the stability analysis of neural networks nns with time varying interval delay the relationship between the time varying delay and its lower and upper bounds is taken into account when estimating the upper bound of the derivative of lyapunov functional as a result some improved delay interval dependent stability criteria for nns with time varying interval delay are proposed numerical examples are given to demonstrate the effectiveness and the merits of the proposed method

global exponential stability of cellular neural networks with variable delays for cellular neural networks with time varying delays the problems of determining the exponential stability and estimating the exponential convergence rate are investigated by employing the lyapunov krasovskii functional and linear matrix inequality lmi technique a novel criterion for the stability which give information on the delay dependent property is derived two examples are given to demonstrate the effectiveness of the obtained results

periodic oscillatory solution of bidirectional associative memory networks with delays periodic oscillatory phenomena of bidirectional associative memory bam networks with axonal signal transmission delays are investigated by constructing suitable lyapunov functionals and some analysis techniques some simple sufficient conditions are derived ensuring the existence and uniqueness of periodic oscillatory solutions of the bam with delays and all other solutions of the bam converge exponentially to a periodic oscillatory solution these conditions are presented in terms of system parameters and have an important leading significance in the design and applications of periodic oscillatory neural circuits for the bam with delays

further results on state estimation for neural networks of neutral type with time varying delay in this paper further result on design problem of state estimator for a class of neural networks of neutral type is presented a delay dependent linear matrix inequality lmi criterion for existence of the estimator is derived a numerical simulation is given to show the effectiveness of proposed estimator

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

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

synchronization analysis in an array of asymmetric neural networks with time varying delays and nonlinear coupling in this paper the global exponential synchronization is investigated for an array of asymmetric neural networks with time varying delays and nonlinear coupling assuming neither the differentiability for time varying delays nor the symmetry for the inner coupling matrices by employing a new lyapunov krasovskii functional applying the theory of kronecker product of matrices and the technique of linear matrix inequality lmi a delay dependent sufficient condition in lmis form for checking global exponential synchronization is obtained the proposed result generalizes and improves the earlier publications an example with chaotic nodes is given to show the effectiveness of the obtained result

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

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

state estimation for neural networks of neutral type with interval time varying delays in this paper the design problem of state estimator for a class of neural networks of neutral type with interval time varying delays is studied the interval time varying delay does not have constraint that its derivative is less than 1 the constraint is widely used to deal with time varying delays in many papers a delay dependent linear matrix inequality lmi criterion for existence of the estimator is proposed by using lyapunov method the criterion can be easily solved by various convex optimization algorithms a numerical example is given to show the effectiveness of proposed method

robust stochastic stabilization and h control of uncertain neutral stochastic time delay systems this paper investigates the problems of robust stochastic stabilization and robust h control for uncertain neutral stochastic time delay systems with time varying norm bounded parameter uncertainties appearing in both the state and input matrices the time delay is assumed to be unknown sufficient conditions for the existence of state feedback controllers are proposed which ensure mean square asymptotic stability of the resulting closed loop system and reduce the effect of the disturbance input on the controlled output to a prescribed level for all admissible uncertainties a linear matrix inequality approach is employed to design the desired state feedback controllers furthermore in the case when time delays appear in both the state and control input results on the robust stochastic stabilization and robust h control are also presented an illustrative example is provided to show the potential of the proposed techniques

graph representations two distance sets and equiangular lines abstract using the new concepts of graph representations and heights it is shown among other results that all sufficiently large sets of equiangular lines with mutual angle arccos 1 5 are known

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

some notes on graphs whose index is close to 2 abstract we consider two classes of graphs i trees of order n and diameter d n 3 and ii unicyclic graphs of order n and girth g n 2 assuming that each graph within these classes has two vertices of degree 3 at distance k we order by the index i e spectral radius the graphs from i for any fixed k 1 k d 2 and the graphs from ii independently of k

global asymptotic stability and global exponential stability of continuous time recurrent neural networks this paper presents new results on global asymptotic stability gas and global exponential stability ges of a general class of continuous time recurrent neural networks with lipschitz continuous and monotone nondecreasing activation functions we first give three sufficient conditions for the gas of neural networks these testable sufficient conditions differ from and improve upon existing ones we then extend an existing gas result to ges one and also extend the existing ges results to more general cases with less restrictive connection weight matrices and or partially lipschitz activation functions

spectral ordering of trees with small index abstract studying graphs by means of the largest eigenvalue of the adjacency matrix the index has been a problem largely investigated in spectral graph theory here we consider trees with index in the real interval 2 2 5 and their ordering with respect to the index for such graphs we prove three indices comparisons whose order has been conjectured in belardo et al 2008 2 by doing so we prove a conjectured ordering of trees with smallest indices open since 2002 and we obtain the first 8 trees of even order with largest index

the strong law of large numbers for sequential decisions under uncertainty combines optimization and ergodic theory to characterize the optimum long run average performance that can be asymptotically attained by nonanticipating sequential decisions let x sub t be a stationary ergodic process and suppose an action b sub t must be selected in a space spl bscr with knowledge of the t past x sub 0 spl middot spl middot spl middot x sub t 1 at the beginning of every period t spl ges 0 action b sub t will incur a loss l b sub t x sub t at the end of period t when the random variable x sub t is revealed the author proves under mild integrability conditions that the optimum strategy is to select actions that minimize the conditional expected loss given the currently available information at each step the minimum long run average loss per decision can be approached arbitrarily closely by strategies that are finite order markov and under certain continuity conditions it is equal to the minimum expected loss given the infinite past if the loss l b x is bounded and continuous and if the space spl bscr is compact then the minimum can be asymptotically attained even if the distribution of the process x sub t is unknown a priori and must be learned from experience

lmi conditions for global robust stability of delayed neural networks with discontinuous neuron activations without assuming that the neuron activations are bounded some delay independent criteria for interval delayed neural networks with discontinuous neuron activations are derived to guarantee global robust stability by using the generalized lyapunov method and linear matrix inequality lmi technique the obtained results improve and extend those given in earlier literature and two numerical examples are also given to show the effectiveness of our results

strong consistency of k means clustering a random sample is divided into the k clusters that minimise the within cluster sum of squares conditions are found that ensure the almost sure convergence as the sample size increases of the set of means of the k clusters the result is proved for a more general clustering criterion

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

convergence behavior of delayed bidirectional associative memory cellular neural networks with asymptotically periodic coefficients this paper considers the convergence behavior of delayed bam cellular neural networks with asymptotically periodic coefficients by applying mathematical analysis techniques some new sufficient conditions are obtained to ensure that solutions of the networks converge to a periodic function

connected hypergraphs with small spectral radius abstract in 1970 smith classified all connected graphs with spectral radius at most 2 here the spectral radius of a graph is the largest eigenvalue of its adjacency matrix recently the definition of spectral radius has been extended to r uniform hypergraphs in this paper we generalize smith s theorem to r uniform hypergraphs we show that the smallest limit point of the spectral radii of connected r uniform hypergraphs is r 4 r we discovered a novel method for computing the spectral radius of hypergraphs and classified all connected r uniform hypergraphs with spectral radius at most r

new lyapunov krasovskii functionals for global asymptotic stability of delayed neural networks this brief deals with the problem of global asymptotic stability for a class of delayed neural networks some new lyapunov krasovskii functionals are constructed by nonuniformly dividing the delay interval into multiple segments and choosing proper functionals with different weighting matrices corresponding to different segments in the lyapunov krasovskii functionals then using these new lyapunov krasovskii functionals some new delay dependent criteria for global asymptotic stability are derived for delayed neural networks where both constant time delays and time varying delays are treated these criteria are much less conservative than some existing results which is shown through a numerical example

lmi optimization approach on stability for delayed neural networks of neutral type in this paper the global asymptotic stability of delayed cellular neural networks of neutral type is investigated a novel delay dependent criterion for the stability using the lyapunov stability theory and linear matrix inequality lmi framework is presented since the condition is dependent on the size of time delay it is usually less conservative than delay independent ones two numerical examples are given to show the effectiveness of proposed method

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

clique inserted graphs and spectral dynamics of clique inserting abstract motivated by studying the spectra of truncated polyhedra we consider the clique inserted graphs for a regular graph g of degree r 0 the graph obtained by replacing every vertex of g with a complete graph of order r is called the clique inserted graph of g denoted as c g we obtain a formula for the characteristic polynomial of c g in terms of the characteristic polynomial of g furthermore we analyze the spectral dynamics of iterations of clique inserting on a regular graph g for any r regular graph g with r 2 let s g denote the union of the eigenvalue sets of all iterated clique inserted graphs of g we discover that the set of limit points of s g is a fractal with the maximum r and the minimum 2 and that the fractal is independent of the structure of the concerned regular graph g as long as the degree r of g is fixed it follows that for any integer r 2 there exist infinitely many connected r regular graphs or non regular graphs with r as the maximum degree with arbitrarily many distinct eigenvalues in an arbitrarily small interval around any given point in the fractal we also present a formula on the number of spanning trees of any k th iterated clique inserted graph and other related results

the strong law of large numbers for k means and best possible nets of banach valued random variables let b be a uniformly convex banach space x a b valued random variable and k a given positive integer number a random sample of x is substituted by the set of k elements which minimizes a criterion we found conditions to assure that this set converges a s as the sample size increases to the set of k elements which minimizes the same criterion for x

new approaches on stability criteria for neural networks with interval time varying delays abstract this paper concerns the problem of delay dependent stability criteria for neural networks with interval time varying delays first by constructing a newly augmented lyapunov krasovskii functional and combining with a reciprocally convex combination technique less conservative stability criterion is established in terms of linear matrix inequalities lmis which will be introduced in theorem 1 second by taking different interval of integral terms of lyapunov krasovskii functional utilized in theorem 1 further improved stability criterion is proposed in theorem 2 third a novel approach which divides the bounding of activation function into two subinterval are proposed in theorem 3 to reduce the conservatism of stability criterion finally through two well known numerical examples used in other literature it will be shown the proposed stability criteria achieves the improvements over the existing ones and the effectiveness of the proposed idea

improved delay dependent stability criterion for neural networks with time varying delay in this paper the problem of delay dependent asymptotic stability criterion for neural networks with time varying delay has been considered a new class of lyapunov functional which contains a triple integral term is constructed to derive some new delay dependent stability criteria the obtained criteria are less conservative because free weighting matrices method and a convex optimization approach are considered finally numerical examples are given to illustrate the effectiveness of the proposed method

existence of an exponential periodic attractor of periodic solutions for general bam neural networks with time varying delays and impulses abstract by applying inequality analysis technique constructing a suitable lyapunov functional and combing the continuation theorem due to mawhin and gaines some novel sufficient conditions are obtained to ensure the existence of an exponential periodic attractor of periodic solutions for general neural networks with time varying including bounded and unbounded delays and impulses an example is employed to illustrate our feasible results

new and improved results on stability of static neural networks with interval time varying delays abstract in this paper the problem of stability analysis for static neural networks with interval time varying delays is considered by the consideration of new augmented lyapunov functionals new and improved delay dependent stability criteria to guarantee the asymptotic stability of the concerned networks are proposed with the framework of linear matrix inequalities lmis which can be solved easily by standard numerical packages the enhancement of the feasible region of the proposed criteria is shown via two numerical examples by the comparison of maximum delay bounds

an analysis of global asymptotic stability of delayed cellular neural networks in this paper a new sufficient condition is given for the uniqueness and global asymptotic stability of the equilibrium point for delayed cellular neural networks dcnns this condition imposes constraints on the feedback and delayed feedback matrices of a dcnn independently of the delay parameter this result is also compared with the previous results derived in the literature

equilibrium and stability analysis of delayed neural networks under parameter uncertainties abstract this paper proposes new results for the existence uniqueness and global asymptotic stability of the equilibrium point for neural networks with multiple time delays under parameter uncertainties by using lyapunov stability theorem and applying homeomorphism mapping theorem new delay independent stability criteria are obtained the obtained results are in terms of network parameters of the neural system only and therefore they can be easily checked we also present some illustrative numerical examples to demonstrate that our result are new and improve corresponding results derived in the previous literature

impulsive delay differential inequality and stability of neural networks in this article a generalized model of neural networks involving time varying delays and impulses is considered by establishing the delay differential inequality with impulsive initial conditions and using the properties of m cone and eigenspace of the spectral radius of nonnegative matrices some new sufficient conditions for global exponential stability of impulsive delay model are obtained the results extend and improve the earlier publications an example is given to illustrate the theory

delay dependent exponential stability for a class of neural networks with time delays this paper is concerned with the exponential stability of a class of delayed neural networks described by nonlinear delay differential equations of the neutral type in terms of a linear matrix inequality lmi a sufficient condition guaranteeing the existence uniqueness and global exponential stability of an equilibrium point of such a kind of delayed neural networks is proposed this condition is dependent on the size of the time delay which is usually less conservative than delay independent ones the proposed lmi condition can be checked easily by recently developed algorithms solving lmis examples are provided to demonstrate the effectiveness and applicability of the proposed criteria

disturbance decoupling for linear time invariant systems a matrix pencil approach we give a new systematic analysis of disturbance decoupling problems for standard linear time invariant systems based on the theory of matrix pencils this approach is based on the computation of condensed forms under orthogonal equivalence transformations from these forms which can be computed in a numerically stable way we obtain new necessary and sufficient conditions that are numerically verifiable and furthermore we immediately obtain numerically stable algorithms to compute the desired compensators we present a numerical example that demonstrates the properties of the new approach

multistability of complex valued recurrent neural networks with real imaginary type activation functions this paper addresses the multistability problem of n dimensional complex valued recurrent neural networks with real imaginary type activation functions sufficient conditions are proposed for checking the existence of 2 1 2 1 n 1 equilibria under these conditions 1 1 n equilibria are locally exponentially stable and the others are unstable attractive basins of equilibria are also investigated complete attractive basins of equilibria in 1 dimensional complex valued recurrent neural networks are obtained the obtained stability results improve and extend the existing ones two numerical examples are given to illustrate the effectiveness of the obtained results

simplified exponential stability analysis for recurrent neural networks with discrete and distributed time varying delays this paper provides simplified exponential stability criteria for a class of recurrent neural networks rnns with discrete and distributed time varying delays the activation functions of the rnns are assumed to be more general and the proposed criteria are obtained by only using a integral inequality and are not involved any free weighting matrices this feature makes the computational burden largely reduced numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method

multistability and multiperiodicity of delayed bidirectional associative memory neural networks with discontinuous activation functions abstract in this paper the multistability and multiperiodicity issues are discussed for 2 n dimensional delayed bidirectional associative memory neural networks with r level discontinuous activation functions sufficient conditions are established to ensure the existence of r n locally exponentially stable equilibria as an extension of multistability conditions are established to ensure the existence of r n locally exponentially stable periodic solutions when external inputs are periodic finally two examples are given to illustrate the effectiveness of the obtained results

exponential stability for uncertain cellular neural networks with discrete and distributed time varying delays in this paper the problem of exponential stability of uncertain cellular neural networks with discrete and distribute time varying delays is considered based on the lyapunov function method and convex optimization approach a new delay dependent stability criterion with an exponential convergence rate is derived in terms of lmi linear matrix inequality three numerical examples are given to show the effectiveness of the proposed methods

existence and stability of almost periodic solution for bam neural networks with delays by using the banach fixed point theorem and constructing suitable lyapunov function some sufficient conditions are obtained ensuring existence uniqueness and global stability of almost periodic solution of the bam neural networks with variable coefficients and delays these results are helpful to design global exponential stable bam networks and almost periodic oscillatory bam networks

robust h filter design for discrete time switched systems with interval time varying delay and linear fractional perturbations lmi optimization approach in this paper the robust h filter scheme for the discrete time switched systems with interval time varying delay and linear fractional perturbations is proposed a convex optimization problem with some lmi constraints is formulated to design the stable switched filter which minimizes the h norm bound for filtering error system some nonnegative inequalities and the free weighting matrix technique are used to provide the additional degree of freedom which improves the conservativeness of the proposed results finally a numerical example is illustrated to show the use of the main results

on the spectral radius of a class of non odd bipartite even uniform hypergraphs abstract in order to investigate the non odd bipartiteness of even uniform hypergraphs starting from a simple graph g we construct a generalized power of g denoted by g k s which is obtained from g by blowing up each vertex into a s set and each edge into a k 2 s set where s k 2 when s k 2 g k s is always odd bipartite we show that g k k 2 is non odd bipartite if and only if g is non bipartite and find that g k k 2 has the same adjacency respectively signless laplacian spectral radius as g so the results involving the adjacency or signless laplacian spectral radius of a simple graph g hold for g k k 2 in particular we characterize the unique graph with minimum adjacency or signless laplacian spectral radius among all non odd bipartite hypergraphs g k k 2 of fixed order and prove that 2 5 is the smallest limit point of the non odd bipartite hypergraphs g k k 2 in addition we obtain some results for the spectral radii of the weakly irreducible nonnegative tensors

stability and bifurcation of a cohen grossberg neural network with discrete delays abstract a cohen grossberg neural network with discrete delays is investigated in this paper the qualitative analysis is given for the system and it is found that the system undergoes a sequence of hopf bifurcations by choosing the discrete time delay as a bifurcation parameter moreover by applying the normal form theory and the center manifold theorem the direction of the hopf bifurcation and the stability of bifurcating periodic solutions are obtained numerical simulations are given to illustrate the obtained results

global exponential stability and global convergence in finite time of delayed neural networks with infinite gain this paper introduces a general class of neural networks with arbitrary constant delays in the neuron interconnections and neuron activations belonging to the set of discontinuous monotone increasing and possibly unbounded functions the discontinuities in the activations are an ideal model of the situation where the gain of the neuron amplifiers is very high and tends to infinity while the delay accounts for the finite switching speed of the neuron amplifiers or the finite signal propagation speed it is known that the delay in combination with high gain nonlinearities is a particularly harmful source of potential instability the goal of this paper is to single out a subclass of the considered discontinuous neural networks for which stability is instead insensitive to the presence of a delay more precisely conditions are given under which there is a unique equilibrium point of the neural network which is globally exponentially stable for the states with a known convergence rate the conditions are easily testable and independent of the delay moreover global convergence in finite time of the state and output is investigated in doing so new interesting dynamical phenomena are highlighted with respect to the case without delay which make the study of convergence in finite time significantly more difficult the obtained results extend previous work on global stability of delayed neural networks with lipschitz continuous neuron activations and neural networks with discontinuous neuron activations but without delays

new delay dependent robust stability criterion for uncertain neural networks with time varying delays in this paper the problem of delay dependent stability of uncertain neural networks with time varying delays is considered the parameter uncertainties are time varying and assumed to be bounded in magnitude by constructing a new augmented lyapunov functional a delay dependent stability criterion for the network is derived in terms of lmi linear matrix inequality which can be easily solved by various convex optimization algorithms three numerical examples are included to show the effectiveness of proposed criterion

improved delay dependent asymptotic stability criteria for delayed neural networks this brief is concerned with asymptotic stability of neural networks with uncertain delays two types of uncertain delays are considered one is constant while the other is time varying the discretized lyapunov krasovskii functional lkf method is integrated with the technique of introducing the free weighting matrix between the terms of the leibniz newton formula the integrated method leads to the establishment of new delay dependent sufficient conditions in form of linear matrix inequalities for asymptotic stability of delayed neural networks dnns a numerical simulation study is conducted to demonstrate the obtained theoretical results which shows their less conservatism than the existing stability criteria

on stabilization of stochastic cohen grossberg neural networks with mode dependent mixed time delays and markovian switching the globally exponential stabilization problem is investigated for a general class of stochastic cohen grossberg neural networks with both markovian jumping parameters and mixed mode dependent time delays the mixed time delays consist of both discrete and distributed delays this paper aims to design a memoryless state feedback controller such that the closed loop system is stochastically exponentially stable in the mean square sense by introducing a new lyapunov krasovskii functional that accounts for the mode dependent mixed delays stochastic analysis is conducted in order to derive delay dependent criteria for the exponential stabilization problem three numerical examples are carried out to demonstrate the feasibility of our delay dependent stabilization criteria

state estimation for delayed neural networks in this letter the state estimation problem is studied for neural networks with time varying delays the interconnection matrix and the activation functions are assumed to be norm bounded the problem addressed is to estimate the neuron states through available output measurements such that for all admissible time delays the dynamics of the estimation error is globally exponentially stable an effective linear matrix inequality approach is developed to solve the neuron state estimation problem in particular we derive the conditions for the existence of the desired estimators for the delayed neural networks we also parameterize the explicit expression of the set of desired estimators in terms of linear matrix inequalities lmis finally it is shown that the main results can be easily extended to cope with the traditional stability analysis problem for delayed neural networks numerical examples are included to illustrate the applicability of the proposed design method

synchronization criteria for coupled neural networks with interval time varying delays and leakage delay abstract this paper considers the synchronization problem for coupled neural networks with interval time varying delays and leakage delay by construction of a suitable lyapunov krasovskii s functional and utilization of finsler s lemma novel delay dependent criteria for the synchronization of the networks are established in terms of linear matrix inequalities lmis which can be easily solved by various effective optimization algorithms two numerical examples are given to illustrate the effectiveness of the proposed methods

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

a new stability analysis of delayed cellular neural networks in this paper the global asymptotic stability of delayed cellular neural networks dcnns is investigated a novel criterion for the stability using the lyapunov stability theory and linear matrix inequality lmi framework is presented the criterion expressed by lmis is delay dependent the result is less conservative than those established in the earlier references a numerical example is given to show the effectiveness of proposed method

improved stability analysis on delayed neural networks with linear fractional uncertainties abstract the paper is concerned with robust stability for generalized neural networks gnns with both interval time varying delay and time varying distributed delay through partitioning the time delay choosing one augmented lyapunov krasovskii functional employing free weighting matrix method and convex combination the sufficient conditions are obtained to guarantee the robust stability of the concerned systems these stability criteria are presented in terms of linear matrix inequalities lmis and can be easily checked finally three numerical examples are given to demonstrate the effectiveness and reduced conservatism of the obtained results

robustness properties of k means and trimmed k means abstract the generalized k means method is based on the minimization of the discrepancy between a random variable or a sample of this random variable and a set with k points measured through a penalty function as in the m estimators setting k 1 a penalty function with unbounded derivative naturally leads to nonrobust generalized k means however surprisingly the lack of robustness extends also to the case of bounded that is generalized k means do not inherit the robustness properties of the m estimator from which they came attempting to robustify the generalized k means method the generalized trimmed k means method arises from combining k means idea with a so called impartial trimming procedure in this article study generalized k means and generalized trimmed k means performance from the viewpoint of hampel s robustness criteria that is we investigate the influence function breakdown point and qualitative robustness confirming the superiority provided by the trimming we inc

unknown input observer design for one sided lipschitz discrete time systems subject to time delay in this paper we address the problem of unknown input observer design which simultaneously estimates state and unknown input of a class of nonlinear discrete time systems with time delay a novel approach to the state estimation problem of nonlinear systems where the nonlinearities satisfy the one sided lipschitz and quadratically inner bounded conditions is proposed this approach also allows us to reconstruct the unknown inputs of the systems the nonlinear system is first transformed to a new system which can be decomposed into unknown input free and unknown input dependent subsystems the estimation problem is then reduced to designing observer for the unknown input free subsystem rather than full order observer design in this paper we propose observer design of reduced order which is more practical and cost effective by utilizing several mathematical techniques the time delay issue as well as the bilinear terms which often emerge when designing observers for nonlinear discrete time systems are handled and less conservative observer synthesis conditions are derived in the linear matrix inequalities form two numerical examples are given to show the efficiency and high performance of our results

global stability of cellular neural networks with constant and variable delays this paper gives new conditions ensuring global asymptotic stability and global exponential stability for cellular neural networks with constant delay and variable delay respectively these conditions are derived by using the essence of piecewise linearity of the output function of cellular neural networks and by constructing lyapunov functions and functionals furthermore these conditions are significantly weaker than those given in existing literature

ramsey numbers graph eigenvalues and a conjecture of cao and yuan abstract let n be a positive integer and r n n denote the ramsey number see 15 or 11 such that any graph with at least r n n vertices contains a clique with n vertices or an independent set with n vertices we show that any graph g with order at least r n n must have its n th largest eigenvalue n g 1 and that any graph g with order at least r n 1 n 1 must have its n th smallest eigenvalue n g 0 where the bounds 1 and 0 are best possible this reveals some connection between graph spectra and ramsey numbers and enables us to give bounds of some eigenvalues for graphs with order greater than certain numbers moreover it leads to a disproof of a conjecture on limit points of graph eigenvalues posted by cao and yuan 3 in 1995 finally we post some problems for further research

existence uniqueness and exponential stability analysis for complex valued memristor based bam neural networks with time delays this article explores the exponential stability problem of complex valued bidirectional associative memory bam neural networks with time delays this analysis is on the basis of the m matrix approach the differential inclusions theory and the homeomorphism property by constructing a novel lyapunov functional a sufficient criterion for the existence uniqueness and exponential stability for the equilibrium point of the considered system is derived moreover similar results in terms of m matrix are also obtained for the exponential stability problem of delayed complex valued bam neural networks without memristors in the end two numerical examples are provided to demonstrate the availability of the obtained results

growth rates of permutation grid classes tours on graphs and the spectral radius monotone grid classes of permutations have proven very effective in helping to determine structural and enumerative properties of classical permutation pattern classes associated with grid class grid m is a graph g m known as its row column graph we prove that the exponential growth rate of grid m is equal to the square of the spectral radius of g m consequently we utilize spectral graph theoretic results to characterise all slowly growing grid classes and to show that for every 2 5 there is a grid class with growth rate arbitrarily close to to prove our main result we establish bounds on the size of certain families of tours on graphs in the process we prove that the family of tours of even length on a connected graph grows at the same rate as the family of balanced tours on the graph in which the number of times an edge is traversed in one direction is the same as the number of times it is traversed in the other direction

improved global robust stability of interval delayed neural networks via split interval generalizations abstract the problem of global robust stability of hopfield type delayed neural networks with the intervalized network parameters is revisited recently a computationally tractable i e linear matrix inequality lmi based global robust stability criterion derived from an earlier criterion based on dividing the given interval into more that two intervals has been presented in the present paper generalizations i e division of the given interval into m intervals where m is an integer greater than or equal to 2 is considered and some new lmi based global robust stability criteria are derived it is shown that in some cases m 2 may not suffice i e m 2 may be needed to realize the improvement an example showing the effectiveness of the proposed generalization is given the paper also provides a complete and systematic explanation of the split interval idea

on the distribution of the maximum eigenvalue of graphs abstract given a graph g let g denote the largest eigenvalue of the adjacency matrix of g we prove that for any 2 5 2 058 there exists a sequence of graphs g1 g2 such that limk gk thus answering a question posed by hoffman

trimmed k means an attempt to robustify quantizers a class of procedures based on impartial trimming self determined by the data is introduced with the aim of robustifying k means hence the associated clustering analysis we include a detailed study of optimal regions showing that only nonpathological regions can arise from impartial trimming procedures the asymptotic results provided in the paper focus on strong consistency of the suggested methods under widely general conditions a section is devoted to exploring the performance of the procedure to detect anomalous data in simulated data sets

robust global synchronization of complex networks with neutral type delayed nodes in this paper the problems of robust global exponential synchronization for a class of complex networks with time varying delayed couplings are considered each node in the network is composed of a class of delayed neural networks described by a nonlinear delay differential equation of neutral type since model errors commonly exist in practical applications the parameter uncertainties are involved in the considered model sufficient conditions that ensure the complex networks to be robustly globally exponentially synchronized are obtained by using the lyapunov functional method and some properties of kronecker product an illustrative example is presented to show the effectiveness of the proposed approach

on improved delay dependent criterion for global stability of bidirectional associative memory neural networks with time varying delays in the paper the global robust asymptotic stability of bidirectional associative memory bam neural networks with time varying delays and uncertainties is investigated a novel stability criterion is presented based on the lyapunov method the criterion is represented in terms of linear matrix inequality lmi which can be solved easily by various optimization algorithms a numerical example is illustrated to show the effectiveness of our new result

the limit points of laplacian spectra of graphs abstract let g be a graph on n vertices denote by l g the laplacian matrix of g it is easy to see that l g is positive semidefinite symmetric and that its second smallest eigenvalue g 0 if and only if g is connected this observation let fiedler to call g the algebraic connectivity of the graph g in this paper the limit points of laplacian spectra of graphs are investigated particular attention is given to the limit points of algebraic connectivity some new results and generalizations are included

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

exponential stability analysis for uncertain neural networks with interval time varying delays in this paper the problem of exponential stability analysis for neural networks is investigated it is assumed that the considered neural networks have norm bounded parametric uncertainties and interval time varying delays by constructing a new lyapunov functional new delay dependent exponential stability criteria with an exponential convergence rate are established in terms of lmis linear matrix inequalities which can be easily solved by various convex optimization algorithms two numerical examples are included to show the effectiveness of proposed criteria

on graphs whose laplacian index does not exceed 4 5 abstract let a g and d g be the adjacency matrix and the vertex degree matrix of a graph g respectively the laplacian matrix of g is defined as l g d g a g the l index of g denoted by g is the largest root of the characteristic polynomial of l g the laplacian hoffman limit value h l is the limit of hn where the graph hn is obtained by attaching a pendant edge to the cycle c n 1 of length n 1 it is known that h l 2 where is the largest root of x 3 4 x 4 in this paper we characterize the structure of graphs whose l index does not exceed 4 5 and we completely describe those graphs whose l index does not exceed h l by doing so we complete the so called hoffman program w r t the laplacian theory of graph spectra

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

on graphs whose signless laplacian index does not exceed 4 5 abstract let a g and d g be respectively the adjacency matrix and the degree matrix of a graph g the signless laplacian matrix of g is defined as q g d g a g the q spectrum of g is the set of the eigenvalues together with their multiplicities of q g the q index of g is the maximum eigenvalue of q g the possibilities for developing a spectral theory of graphs based on the signless laplacian matrices were discussed by cvetkovic et al d cvetkovic p rowlinson s k simic signless laplacians of finite graphs linear algebra appl 423 2007 155 171 in the latter paper the authors determine the graphs whose q index is in the interval 0 4 in this paper we investigate some properties of q spectra of graphs especially for the limit points of the q index by using these results we characterize respectively the structures of graphs whose the q index lies in the intervals 4 2 5 2 5 2 and 2 4 5 where 1 3 54 6 33 1 3 54 6 33 1 3 2 382975767

the distribution of eigenvalues of graphs abstract we show that every limit point of the kth largest eigenvalues of graphs is a limit point of the k 1 th largest eigenvalues and we find out the smallest limit point of the kth largest eigenvalues and an upper bound of the limit points of the kth smallest eigenvalues for k 4 we prove that there exists a gap beyond the smallest limit point in which no point is the limit point of the kth largest eigenvalues for the third largest eigenvalues of a graph g with at least three vertices we obtain that 1 3 g 1 3 g 1 5 2 consequently if gc is not a complete bipartite graph plus isolated vertices 3 g 3 d n where d n is the complement of the double star s 1 n 3

sensitivity of optimal control for diffusion hopfield neural network in the presence of perturbation abstract with the wide investigation of hopfield neural network hnn and its control problems this paper is to control diffusion hnn system in the presence of perturbation disturbance uncertainties in the control field in particular it is try to answer the most interesting question on the sensitivity of these perturbations both in theoretical and computational aspects