erratum to existence and attractivity of almost periodic solutions for cellular neural networks with distributed delays and variable coefficients by combining the theory of the exponential dichotomy and liapunov function we study the existence and attractivity of almost periodic solutions for cellular neural networks cnns with distributed delays and variable coefficientsdx idt b i t x i t j 1 na i j t f j x j t j 1 nb i j t f j m j 0 k i j u x j t u du i i t we obtain some sufficient conditions to ensure that for the networks there exists a unique almost periodic solution and all its solutions converge to such an almost periodic solution an example is given to illustrate that the conditions of our results are feasible

the existence of almost periodic solutions of certain perturbation systems abstract certain almost periodic perturbation systems are considered in this paper by using the roughness theory of exponential dichotomies and the contraction mapping principle some sufficient conditions are obtained for the existence and uniqueness of almost periodic solution of the above systems our results generalize those in j k hale ordinary differential equations krieger huntington 1980 c he existence of almost periodic solutions of perturbation systems ann differential equations 9 1992 173 181 m lin the existence of almost periodic solution and bounded solution of perturbation systems acta math sinica 22a 2002 61 70 in chinese w a coppel almost periodic properties of ordinary differential equations ann math pura appl 76 1967 27 50 a m fink almost periodic differential equations lecture notes in math vol 377 springer verlag new york 1974 y xia f chen a chen j cao existence and global attractivity of an almost periodic ecological model appl math comput 157 2004 449 475

attractor minimal sets for non autonomous delay functional differential equations with applications for neural networks the dynamics of a class of non autonomous convex or concave and monotone delay functional differential systems is studied in particular we provide an attractivity result when two completely st

positive periodic solutions of a class of functional differential systems with feedback controls abstract in this paper by using the upper and lower solutions method we investigate the existence and nonexistence of positive periodic solutions of infinite delay functional differential system with a parameter and feedback controls x t a t x t f t x t x g t x t u t x t u t b t u t e t x t x h t x t

on proximinality of subspaces and the lineability of the set of norm attaining functionals of banach spaces abstract we show that for every 1 n there exists a banach space x n containing proximinal subspaces of codimension n but no proximinal finite codimensional subspaces of higher codimension moreover the set of norm attaining functionals of x n contains n dimensional subspaces but no subspace of higher dimension this gives an n by n version of the solutions given by read and rmoutil to problems of singer and godefroy we also study the existence of strongly proximinal subspaces of finite codimension showing that for every 1 n and 1 k n there is a banach space x n k containing proximinal subspaces of finite codimension up to n but not higher and containing strongly proximinal subspaces of finite codimension up to k but not higher finally we deal with possible infinite dimensional versions of the previous results showing among other results that there are non separable banach spaces whose set of norm attaining functionals contains infinite dimensional separable linear subspaces but no non separable subspaces

existence and global attractivity of almost periodic solutions for neural field with time delay in this paper the problem of existence and attractivity of almost periodic solutions for delayed neural field dnf with variable coefficients is discussed first the model of dnf is established as a modified neural field model secondly by combining the theory of the exponential dichotomy employing banach fixed point theory and using differential inequality technique some conditions for the the existence and attractivity of almost periodic solutions for the dnf are proposed

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

stability and bifurcation in a neural network model with two delays abstract a simple neural network model with two delays is considered linear stability of the model is investigated by analyzing the associated characteristic transcendental equation for the case without self connection it is found that the hopf bifurcation occurs when the sum of the two delays varies and passes a sequence of critical values the stability and direction of the hopf bifurcation are determined by applying the normal form theory and the center manifold theorem an example is given and numerical simulations are performed to illustrate the obtained results

hankel operators and toeplitz operators on the bergman space abstract we consider in this paper the question of when the semi commutator t fg t f t g on the bergman space with bounded harmonic symbols is compact several conditions equivalent to compactness of t fg t f t g are given as a consequence we prove a conjecture of axler that for bounded analytic functions f and g on the unit disk t fg t g t f is compact iff either f or g is constant on each gleason part p m except d

global stability of almost periodic solutions of hopfield neural networks with neutral time varying delays in this paper the global stability and almost periodicity are investigated for hopfield neural networks with neutral time varying delays some sufficient conditions are obtained for the existence and globally exponential stability of almost periodic solution by employing fixed point theorem and differential inequality techniques the results of this paper are new and they complement previously known results

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

existence and global attractivity of an almost periodic ecological model the almost periodic lotka volterra model with m predators and n preys is considered in this paper by constructing suitable lyapunov function some sufficient conditions are obtained for the existence and global attractivity of a unique positive almost periodic solution of this model examples show that our criteria are new general and easily verifiable

multiple almost periodic solutions in nonautonomous delayed neural networks a general methodology that involves geometric configuration of the network structure for studying multistability and multiperiodicity is developed we consider a general class of nonautonomous neural networks with delays and various activation functions a geometrical formulation that leads to a decomposition of the phase space into invariant regions is employed we further derive criteria under which the n neuron network admits 2n exponentially stable sets in addition we establish the existence of 2n exponentially stable almost periodic solutions for the system when the connection strengths time lags and external bias are almost periodic functions of time through applying the contraction mapping principle finally three numerical simulations are presented to illustrate our theory

existence and global exponential stability of almost periodic solution for cellular neural networks with variable coefficients and time varying delays in this paper we study cellular neural networks with almost periodic variable coefficients and time varying delays by using the existence theorem of almost periodic solution for general functional differential equations introducing many real parameters and applying the lyapunov functional method and the technique of young inequality we obtain some sufficient conditions to ensure the existence uniqueness and global exponential stability of almost periodic solution the results obtained in this paper are new useful and extend and improve the existing ones in previous literature

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

applications of the exponential ordering in the study of almost periodic delayed hopfield neural networks abstract this paper studies almost periodic neural networks of hopfield type described by delayed differential equations the authors introduce an exponential ordering to analyze the long term behavior of the solutions they prove some theorems of global convergence and deduce the stabilization role of the fast inhibitory self connections the proof which in the case of the neural networks considered in this paper requires uniform stability uses arguments of comparison of differential equations and methods of the non autonomous monotone theory of dynamical systems when the connections between different neurons are excitatory improved conditions of convergence are obtained and the stabilization role of strongly positive inputs is also shown the applicability of the results is illustrated with several numerical experiments based on two different families of neural networks

stability and existence of periodic solutions of periodic cellular neural networks with time vary delays by using the continuation theorem of mawhins coincidence degree theory and constructing a suitable lyapunov function some new sufficient conditions are obtained ensuring existence and global asymptotical stability of periodic solution of cellular neural networks with periodic coefficients and delays which do not require the activation functions to be differentiable and monotone nondecreasing a numerical example is given to illustrate that the criteria are feasible these results are helpful to design globally asymptotically stable and periodic oscillatory cellular neural networks

a note on stability of analog neural networks with time delays this note presents a generalized sufficient condition which guarantees stability of analog neural networks with time delays the condition is derived using a lyapunov functional and the stability criterion is stated as the equilibrium of analog neural networks with delays is globally asymptotically stable if the product of the norm of connection matrix and the maximum neuronal gain is less than one

existence and stability of almost periodic solutions in impulsive neural network models abstract the existence and global exponential stability of an almost periodic solution of an impulsive neural network model with distributed delays is considered in a matrix setting the approach transforms the original network into a matrix analysis problem where a set of sufficient conditions based on spectral radius is presented a concrete hopfield model shows the advantages in comparison with a classical norm approach

frustration stability and delay induced oscillations in a neural network model the effect of time delays on the linear stability of equilibria in an artificial neural network of hopfield type is analyzed the possibility of delay induced oscillations occurring is characterized in terms of properties of the not necessarily symmetric connection matrix of the network such oscillations are possible exactly when the network is frustrated equivalently when the signed digraph of the matrix does not require the perron property nonlinear analysis centre manifold computation of a three unit frustrated network is presented giving the nature of the bifurcations taking place a supercritical hopf bifurcation is shown to occur and a codimension two bifurcation is unfolded

existence and global attractivity of almost periodic solution for dcnns with time varying coefficients by using exponential dichotomy the banach fixed point theory and some inequality analysis technology some sufficient conditions are derived ensuring existence uniqueness and global attractivity of almost periodic solution of delayed cellular neural networks dcnns with time varying coefficients without assuming the boundedness of signal functions the results obtained have sufficient significance in design and applications of almost periodic oscillatory dcnns

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

on the exponential stability and periodic solutions of delayed cellular neural networks a set of criteria is presented for the global exponential stability and the existence of periodic solutions of delayed cellular neural networks dcnns by constructing suitable lyapunov functionals introducing many parameters and combining with the elementary inequality technique these criteria have important leading significance in the design and applications of globally stable dcnns and periodic oscillatory dcnns in addition earlier results are extended and improved other results are contained two examples are given to illustrate the theory