truncations of infinite matrices and algebraic series associated with some of grammars abstract we consider an algebraic system over r x of the form x a 0 x x k a k 1 x x a k x where a 0 x and a k x are in x r x and a k 1 x is in x r let a be the infinite incidence matrix associated with the algebraic system then we prove that the eigenvalues of northwest corner truncations of a are dense in some algebraic curves using this we get a result on positive algebraic series we consider the case that the coefficients of a 1 x i 0 k 1 k are positive the algebraic series generated by the algebraic system may be viewed as a function in the complex variable x then by the above fact we prove that the radius of convergence of the function equals the least positive zero of the modified discriminant of the system as an application to context free languages we show a procedure for calculating the entropy of some one counter languages other applications to dyck languages and the lukasiewicz language are also described

interface element method iem for a partitioned system with non matching interfaces abstract a novel method for non matching interfaces on the boundaries of finite elements in partitioned domains is presented by introducing interface elements in this paper the interface element method iem satisfies the continuity conditions exactly through interface element domains without recourse to lagrange multiplier technique the interface elements take an interpolation scheme used in meshless methods to join partitioned domains the moving least square mls approximations in the present study are implemented to construct the shape functions of the interface elements the compatibility of displacements on the boundaries of the finite elements and the interface elements is always preserved in this method and the completeness of the shape functions of the interface elements transfers rigid body motions and strain fields correctly moreover alignment of the boundaries of sub domains in the mls approximations and integration domains provides a consistent numerical integration the numerical examples show that the iem is a useful tool for the analysis of a partitioned system and for a global local analysis

interface element method treatment of non matching nodes at the ends of interfaces between partitioned domains abstract a methodology for interface element method iem to combine partitioned domains with non matching nodes at the ends of interfaces is presented the iem is introduced to satisfy the continuity and the compatibility conditions on non matching interfaces between partitioned finite element domains interface elements are defined on the finite elements bordering on the interfaces and the moving least square mls approximations are employed to construct the shape functions of the interface elements by modifying the shape functions of the interface elements at the ends of non matching interfaces partitioned domains are glued such that all properties of the iem are satisfied the modifications are made to sub domains and weight functions in the mls approximations the numerical examples show that the present iem is very effective for the analysis of a partitioned system and for global local analysis

exponential stability of continuous time and discrete time cellular neural networks with delays convergence characteristics of continuous time cellular neural networks with discrete delays are studied by using lyapunov functionals we obtain delay independent sufficient conditions for the networks to converge exponentially toward the equilibria associated with the constant input sources halanay type inequalities are employed to obtain sufficient conditions for the networks to be globally exponentially stable it is shown that the estimates obtained from the halanay type inequalities improve the estimates obtained from the lyapunov methods discrete time analogues of the continuous time cellular neural networks are formulated and studied it is shown that the convergence characteristics of the continuous time systems are preserved by the discrete time analogues without any restriction imposed on the uniform discretization step size

a method of finite element tearing and interconnecting and its parallel solution algorithm a novel domain decomposition approach for the parallel finite element solution of equilibrium equations is presented the spatial domain is partitioned into a set of totally disconnected subdomains each assigned to an individual processor lagrange multipliers are introduced to enforce compatibility at the interface nodes in the static case each floating subdomain induces a local singularity that is resolved in two phases first the rigid body modes are eliminated in parallel from each local problem and a direct scheme is applied concurrently to all subdomains in order to recover each partial local solution next the contributions of these modes are related to the lagrange multipliers through an orthogonality condition a parallel conjugate projected gradient algorithm is developed for the solution of the coupled system of local rigid modes components and lagrange multipliers which completes the solution of the problem when implemented on local memory multiprocessors this proposed method of tearing and interconnecting requires less interprocessor communications than the classical method of substructuring it is also suitable for parallel vector computers with shared memory moreover unlike parallel direct solvers it exhibits a degree of parallelism that is not limited by the bandwidth of the finite element system of equations

multigrid on the interface for mortar mixed finite element methods for elliptic problems we consider mixed finite element approximations of second order elliptic equations on domains that can be described as a union of subdomains or blocks we assume that the subdomain grids are locally defined and need not match across the block boundaries specially chosen mortar finite element spaces are introduced on the interfaces for approximating the scalar variable pressure the mortars also serve as lagrange multipliers for imposing flux matching conditions the method is implemented by reducing the algebraic system to a positive definite interface problem in the mortar spaces this problem is then solved using a multigrid on the interface with conjugate gradient smoothing the algorithm is very efficient in a distributed parallel computing environment as only subdomain solves are required on each conjugate gradient iteration the standard variational assumptions for the multigrid are not satisfied since the interface bilinear forms vary from level to level we present theoretical results for the convergence of the v cycle and the w cycle computational results in two and three dimensions are given to illustrate and confirm the theory

computational chaos a prelude to computational instability abstract chaotic behavior sometimes occurs when difference equations used as approximations to ordinary differential equations are solved numerically with an excessively large time increment in two simple examples we find that as increases chaos first sets in when attractor a acquires two distinct points that map to the same point this happens when a acquires slopes of the same sign in a rectifying coordinate system at two consecutive intersections with the critical curve chaotic and quasi periodic behavior may then alternate within a range of before computational instability finally prevails bifurcations to and from chaos and transitions to computational instability are highly scheme dependent even among differencing schemes of the same order systems exhibiting computational chaos can serve as illustrative examples in more general studies of noninvertible mappings

mls based variable node elements compatible with quadratic interpolation part i formulation and application for non matching meshes two dimensional variable node elements compatible with quadratic interpolation are developed using the moving least square mls approximation the mapping from the parental domain to the physical element domain is implicitly obtained from mls approximation with the shape functions and their derivatives calculated and saved only at the numerical integration points it is shown that the present mls based variable node elements meet the patch test if a sufficiently large number of integration points are employed for numerical integration the cantilever problem with non matching meshes is chosen to check the feasibility of the present mls based variable node elements and the result is compared with that from the lower order case compatible with linear interpolation copyright 2005 john wiley sons ltd

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

surfaces generated by moving least squares methods an analysis of moving least squares m l s methods for smoothing and interpolating scattered data is presented in particular theorems are proved concerning the smoothness of interpolants and the description of m l s processes as projection methods some properties of compositions of the m l s projector with projectors associated with finiteelement schemes are also considered the analysis is accompanied by examples of univariate and bivariate problems

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

stability analysis of dynamical neural networks in this paper we use the matrix measure technique to study the stability of dynamical neural networks testable conditions for global exponential stability of nonlinear dynamical systems and dynamical neural networks are given it shows how a few well known results can be unified and generalized in a straightforward way local exponential stability of a class of dynamical neural networks is also studied we point out that the local exponential stability of any equilibrium point of dynamical neural networks is equivalent to the stability of the linearized system around that equilibrium point from this some well known and new sufficient conditions for local exponential stability of neural networks are obtained

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

global exponential stability of hybrid bidirectional associative memory neural networks with discrete delays in this paper the dynamical characteristics of hybrid bidirectional associative memory neural networks with constant transmission delays are investigated without assuming symmetry of synaptic connection weights and monotonicity and differentiability of activation functions halanay type inequalities which are different from the approach of constructing lyapunov functionals are employed to derive the delay independent sufficient conditions under which the networks converge exponentially to the equilibria associated with temporally uniform external inputs our results are less conservative and restrictive than previously known results

global stability for infinite delay lotka volterra type systems abstract in this paper sufficient conditions are established for the global stability of the saturated equilibrium of an infinite delay nonautonomous lotka volterra type system the present work is distinguished from previous work principally be allowing the system to be nonautonomous and relaxing the traditional requirement that the undelayed intraspecific competition dominates both the delayed intraspecific competition as well as the interspecific interactions we require the undelayed intraspecific competition to dominate the latter but not the former

enrichment and coupling of the finite element and meshless methods a mixed hierarchical approximation based on finite elements and meshless methods is presented two cases are considered the first one couples regions where finite elements or meshless methods are used to interpolate continuity and consistency is preserved the second one enriches a finite element mesh with particles thus there is no need to remesh in adaptive refinement processes in both cases the same formulation is used convergence is studied and examples are shown copyright 2000 john wiley sons ltd

non conforming mesh gluing in the finite elements method a methodology to connect two or more non conforming meshes generated from a geometric model is presented the problem leads to a variational problem subject to constraints the emphasis of the work is on constraints construction two methods namely discrete connection and continuous connection are developed the relation with hybrid formulations is considered and two application examples are presented

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

general criteria for asymptotic and exponential stabilities of neural network models with unbounded delays abstract for a family of differential equations with infinite delay we give sufficient conditions for the global asymptotic and global exponential stability of an equilibrium point this family includes most of the delayed models of neural networks of cohen grossberg type with both bounded and unbounded distributed delay for which general asymptotic and exponential stability criteria are derived as illustrations the results are applied to several concrete models studied in the literature and a comparison of results is given

global exponential stability of bidirectional associative memory neural networks with distributed delays a bidirectional associative memory neural network model with distributed delays is considered by constructing a new lyapunov functional employing the homeomorphism theory m matrix theory and the inequality email protected k 1 mb k q k 0 b k 0 q k 0 with k 1 mq k r 1 and r 1 a sufficient condition is obtained to ensure the existence uniqueness and global exponential stability of the equilibrium point for the model moreover the exponential converging velocity index is estimated which depends on the delay kernel functions and the system parameters the results generalize and improve the earlier publications and remove the usual assumption that the activation functions are bounded two numerical examples are given to show the effectiveness of the obtained results

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

perron frobenius theory of some algebraic equations associated with context free grammars abstract we define the infinite matrices associated with algebraic equations in the form x a 0 x x k a k 1 x x a k x a j x x r x for each of the associated matrices we prove the following property let d x be the discriminant of the algebraic equation let d x d x a k 2 0 k k then there exists a zero r of d x such that 1 r is positive and r y for any zero y of d x 2 if d is the period of the infinite matrix associated with the algebraic equation then there are precisely d distinct zeros y of d x with y r namely r exp i 2 j d j 0 1 d 1 3 each of these is a simple zero of d x

global asymptotic stability of bam neural networks with mixed delays and impulses in this paper bam neural networks with mixed delays and impulses are considered a new set of sufficient conditions are derived by constructing suitable lyapunov functional with matrix theory for the global asymptotic stability of bam neural networks with mixed delays and impulses moreover an example is also provided to illustrate the effectiveness of the results

dynamical approach study of spurious steady state numerical solutions of nonlinear differential equations i the dynamics of time discretization and its implications for algorithm development in computational fluid dynamics abstract the goal of this paper is to utilize the theory of nonlinear dynamics approach to investigate the possible sources of errors and slow convergence and nonconvergence of steady state numerical solutions when using the time dependent approach for nonlinear hyperbolic and parabolic partial differential equations terms this interdisciplinary research belongs to a subset of a new field of study in numerical analysis sometimes referred to as the dynamics of numerics and the numerics of dynamics at the present time this new interdisciplinary topic is still the property of an isolated discipline with all too little effort spent in pointing out an underlying generality that could make it adaptable to diverse fields of applications this is the first of a series of research papers under the same topic our hope is to reach researchers in the fields of computational fluid dynamics cfd and in particular hypersonic and combustion related cfd by simple examples in which the exact solutions of the governing equations are known the application of the apparently straightforward numerical technique to genuinely nonlinear problems can be shown to lead to incorrect or misleading results one striking phenomenon is that with the same initial data the continuum and its discretized counterpart can asymptotically approach different stable solutions this behavior is especially important for employing a time dependent approach to the steady state since the initial data are usually not known and a freestream condition or an intelligent guess for the initial conditions is often used with the unique property of the different dependence of the solution on initial data for the partial differential equation and the discretized counterpart it is not easy to delineate the true physics from numerical artifacts when numerical methods are the sole source of solution procedure for the continuum part i concentrates on the dynamical behavior of time discretization for scalar nonlinear ordinary differential equations in order to motivate this new yet unconventional approach to algorithm development in cfd and to serve as an introduction for parts 11 and iii of the same series of research papers

chaos in numerical analysis of ordinary differential equations abstract the discretisation of the ordinary nonlinear differential equation d y d t y 1 y by the entral difference scheme is studied for fixed mesh size in the usual numerical computation this method produces some ghost solution for the long range calculation regarding this discretisation as a dynamical system in r2 these pathological behaviors are shown to be a kind of chaos in the dynamical system for any mesh size moreover some combination of the central difference scheme and the euler s scheme is studied for the above equation it gives some motivation for henon s model the usual discretisation of a second order differential equation are studied also it gives some chaotic behaviors numerically which is similar to the behavior of the orbits of the system of differential equations proposed by henon heiles

the mortar finite element method with lagrange multipliers the present paper deals with a variant of a non conforming domain decomposition technique the mortar finite element method in the opposition to the original method this variant is never conforming because of the relaxation of the matching constraints at the vertices and the edges in 3d of subdomains it is shown that written under primal hybrid formulation the approximation problem issued from a discretization of a second order elliptic equation in 2d is nonetheless well posed and provides a discrete solution that satisfies optimal error estimates with respect to natural norms finally the parallelization advantages consequence of this variant are also addressed

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

boundedness and persistence of delay differential equations with mixed nonlinearity for a nonlinear equation with several variable delays x t k 1 m f k t x h 1 t x h l t g t x t where the functions fk increase in some variables and decrease in the others we obtain conditions when a positive solution exists on 0 as well as explore boundedness and persistence of solutions finally we present sufficient conditions when a solution is unbounded examples include the mackey glass equation with non monotone feedback and two variable delays its solutions can be neither persistent nor bounded unlike the well studied case when these two delays coincide

on penalty methods for interelement constraints the problem of enforcing constraints across interelement boundaries can be treated directly in the construction of the basis or by using multiplier or penalty methods we demonstrate that the multiplier approach can induce linear dependence in the constraints and lead to a singular system of equations if appropriate precautions are not exercised the penalty method on the other hand is shown to be directly applicable to the overconstrained1 problem there are however some subtle points regarding loss of accuracy in the penalty approach we present some new results and corroborating numerical experiments to support the arguments in particular we show that there is progressive erosion of accuracy in the approximate solution using finite precision arithmetic as the penalty factor is increased beyond an optimal value this implies that a control must be applied on the size of the penalty factor these ideas are quite broadly pertinent to computation of solutions to other constrained optimization problems in which multiplier and penalty methods are used as well as the specific class of problems we consider here

an improved interface element with variable nodes for non matching finite element meshes extensive improvements of the interface element method iem are proposed for the efficient treatment of non matching finite element meshes our approach enables us to establish the master element via the moving least square mls approximation and so to remove the cumbersome process of constructing interface elements the values of shape functions and their derivatives are therefore mapped from the master element as in the conventional finite element method for the assurance of convergence and compatibility condition a patch test is demonstrated through several examples of 2d linear elasticity the convergence rate is compared between the present interface element and the previous version

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

necessary and sufficient conditions for permanence and global stability of a lotka volterra system with two delays in this paper we seek necessary and sufficient conditions for the permanence and the global asymptotic stability of a positive equilibrium for a lotka volterra system with two delays

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

central difference scheme and chaos abstract the existence of chaotic orbits is proved for area preserving diffeomorphisms of the plane defined by polynomials of degree two derived from the discretized logistic equation

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

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

global exponential periodicity of a class of bidirectional associative memory networks with finite distributed delays in this paper we study the periodic oscillatory behavior of a class of bidirectional associative memory bam networks with finite distributed delays a set of criteria are proposed for determining global exponential periodicity of the proposed bam networks which assume neither differentiability nor monotonicity of the activation function of each neuron in addition our criteria are easily checkable

existence and global exponential stability of periodic solution of cellular neural networks with time varying delays by using the continuation theorem of mawhin s coincidence degree theory and gronwall s inequality some new sufficient conditions are obtained ensuring existence and global exponential stability of periodic solution of cellular neural networks with periodic coefficients and delays these results are helpful to design globally exponentially stable and oscillatory cellular neural networks

global exponential stability for a class of retarded functional differential equations with applications in neural networks in this paper the global exponential stability and asymptotic stability of retarded functional differential equations with multiple time varying delays are studied by employing several lyapunov functionals a number of sufficient conditions for these types of stability are presented our results show that these conditions are milder and more general than previously known criteria and can be applied to neural networks with a broad range of activation functions assuming neither differentiability nor strict monotonicity furthermore the results obtained for neural networks with time varying delays do not assume symmetry of the connection matrix

existence and stability of periodic solution for bam neural networks with distributed delays we use the continuation theorem of coincidence degree theory and liapunov functions to study the existence and stability of positive periodic solutions for a class of two layer heteroassociative networks called bidirectional associative memory networksdx idt a i t x i t j 1 mp j i t f j y j t t j i t y j t i i t i 1 2 n dy jdt b j t y j t i 1 nq i j t f i x i t s i j t x i t j j t j 1 2 manddx idt a i t x i t j 1 mp j i t f j 0 h j i s y j t s ds i i t i 1 2 n dy jdt b j t y j t i 1 nq i j t f i 0 k i j s x i t s ds j j t j 1 2 m

a weak coupling algorithm for seabed wave interaction analysis this paper proposes a weak coupling algorithm for the seabed wave interaction analysis this algorithm is based on the error integration over a time interval and space along fluid seabed interfaces with this weak coupling algorithm seabed wave interaction analysis can be easily carried out with a fluid solver in fluid domain and a meshless solver in seabed domain independently the fluid solver is based on a two step projection method for navier stokes equation the free surface of seawaters during wave propagation is traced through the volume of fluid vof the meshless solver is based on the biot s consolidation theory of saturated poroelasticity which considers the interaction of soil deformation and pore water pressure in seabed data exchange at the interface between fluid and porous medium domains is carried out through a point interpolation method interface condition is approximately satisfied in a variational sense through an iteration scheme between two solvers this algorithm does allow not only non matching mesh along the interface but also non matching time step in different subdomains numerical examples show that this weak coupling algorithm is able to capture the deformation of interface and improve the computation accuracy and efficiency 2004 elsevier b v all rights reserved

stability in impulsive cohen grossberg type bam neural networks with distributed delays in this paper a class of impulsive cohen grossberg type bi directional associative memory bam neural networks with distributed delays is investigated by establishing an integro differential inequality with impulsive initial conditions and employing the homeomorphism theory the m matrix theory and inequality technique some new general sufficient conditions ensuring the existence uniqueness and global exponential stability of equilibrium point for impulsive cohen grossberg type bam neural networks with distributed delays are obtained in particular the estimate of the exponential convergence rate is also provided which depends on the system parameters and impulsive disturbed intension an example is given to show the effectiveness of the results obtained here

stability results for impulsive functional differential equations with infinite delay abstract for a family of differential equations with infinitive delay and impulses we establish conditions for the existence of global solutions and for the global asymptotic and global exponential stabilities of an equilibrium point the results are used to give stability criteria for a very broad family of impulsive neural network models with both unbounded distributed delays and bounded time varying discrete delays most of the impulsive neural network models with delay recently studied are included in the general framework presented here

local and global stability for lotka volterra systems with distributed delays and instantaneous negative feedbacks abstract this paper addresses the local and global stability of n dimensional lotka volterra systems with distributed delays and instantaneous negative feedbacks necessary and sufficient conditions for local stability independent of the choice of the delay functions are given by imposing a weak nondelayed diagonal dominance which cancels the delayed competition effect the global asymptotic stability of positive equilibria is established under conditions slightly stronger than the ones required for the linear stability for the case of monotone interactions however sharper conditions are presented this paper generalizes known results for discrete delays to systems with distributed delays several applications illustrate the results

properties of structure generating functions of automata and their applications for linear systems abstract we show a relation between the structure generating functions of r x automata and solutions of linear equations when we take the function as the set of the paths of the automaton we can use the paths as a useful tool for analyzing linear systems as an application of this theory we get mason s formula on a signal flow graph next we consider an r x automaton with infinite states and extend mason s formula to an infinite matrix besides for any infinite matrix a we define det e xa in two different ways and show that the two definitions coincide in some cases

stability conditions for scalar delay differential equations with a non delay term abstract the problem considered in the paper is exponential stability of linear equations and global attractivity of nonlinear non autonomous equations which include a non delay term and one or more delayed terms first we demonstrate that introducing a non delay term with a non negative coefficient can destroy stability of the delay equation next sufficient exponential stability conditions for linear equations with concentrated or distributed delays and global attractivity conditions for nonlinear equations are obtained the nonlinear results are applied to the mackey glass model of respiratory dynamics

global exponential stability of nonautonomous neural network models with continuous distributed delays for a family of non autonomous differential equations with distributed delays we give sufficient conditions for the global exponential stability of an equilibrium point this family includes most of the delayed models of neural networks of hopfield type with time varying coefficients and distributed delays for these models we establish sufficient conditions for their global exponential stability the existence and global exponential stability of a periodic solution is also addressed a comparison of results shows that these results are general news and add something new to some earlier publications

how delays affect neural dynamics and learning we investigate the effects of delays on the dynamics and in particular on the oscillatory properties of simple neural network models we extend previously known results regarding the effects of delays on stability and convergence properties we treat in detail the case of ring networks for which we derive simple conditions for oscillating behavior and several formulas to predict the regions of bifurcation the periods of the limit cycles and the phases of the different neurons these results in turn can readily be applied to more complex and more biologically motivated architectures such as layered networks in general the main result is that delays tend to increase the period of oscillations and broaden the spectrum of possible frequencies in a quantifiable way simulations show that the theoretically predicted values are in excellent agreement with the numerically observed behavior adaptable delays are then proposed as one additional mechanism through which neural systems could tailor their own dynamics accordingly we derive recurrent backpropagation learning formulas for the adjustment of delays and other parameters in networks with delayed interactions and discuss some possible applications

global asymptotic stability of bi directional associative memory networks with distributed delays in this paper several sufficient conditions are derived for the global asymptotic stability in bi directional associative memory bam networks with distributed delays by constructing suitable lyapunov functional and the young inequality technique these conditions have an important leading significance in the design and applications of globally asymptotically stable neural circuits for bam with distributed delays

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

an analysis on the global exponential stability and the existence of periodic solutions for non autonomous hybrid bam neural networks with distributed delays and impulses in this paper by utilizing the lyapunov functional method applying m matrix young inequality technique and other analysis techniques we analyze the exponential stability and the existence of periodic solutions for non autonomous hybrid bam neural networks with distributed delays and impulses sufficient conditions are obtained for the global exponential stability and the existence of periodic solutions for non autonomous hybrid bidirectional associative memory bam neural networks with lipschitzian activation functions without assuming their boundedness monotonicity or differentiability and subjected to impulsive state displacements at fixed instants of time finally two examples are also provided to demonstrate the effectiveness of the results obtained

vector norms as lyapunov functions for linear systems a unified theory of quadratic and piecewise linear lyapunov functions for continuous and discrete time linear systems is presented the key to this work is the description of these lyapunov functions by vector norms the main results are sufficient and necessary conditions for a vector norm to be a lyapunov function as well as a method based on these conditions of constructing such lyapunov functions