on the global convergence of a class of functional differential equations with applications in neural network theory abstract we study a system of retarded functional differential equations which generalise both the hopfield neural network model as well as hybrid network models of the cellular neural network type our main results give sufficient conditions for the global asymptotic stability of such systems and are milder than previously known conditions for the hybrid models when specialised to neural networks our models allow us to consider several different types of activation functions including piecewise linear sigmoids and unbounded activations as well as the usualc smooth sigmoids these issues are vital in the applications we also study neural network models with nonconstant delaysr t

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

global exponential stability for complex valued recurrent neural networks with asynchronous time delays in this paper we investigate the global exponential stability for complex valued recurrent neural networks with asynchronous time delays by decomposing complex valued networks to real and imaginary parts and construct an equivalent real valued system the network model is described by a continuous time equation there are two main differences of this paper with previous works 1 time delays can be asynchronous i e delays between different nodes are different which make our model more general and 2 we prove the exponential convergence directly while the existence and uniqueness of the equilibrium point is just a direct consequence of the exponential convergence using three generalized norms we present some sufficient conditions for the uniqueness and global exponential stability of the equilibrium point for delayed complex valued neural networks these conditions in our results are less restrictive because of our consideration of the excitatory and inhibitory effects between neurons so previous works of other researchers can be extended finally some numerical simulations are given to demonstrate the correctness of our obtained results

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

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 multiplicity result for semilinear resonant elliptic problems with nonsmooth potential abstract we study a semilinear elliptic problem with a nonsmooth potential and resonance at the origin between two successive eigenvalues of h 0 1 z our approach is variational and is based on the nonsmooth critical point theory for locally lipschitz functions we prove the existence of at least two nontrivial solutions

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

a multiplicity theorem for problems with the p laplacian abstract we consider nonlinear elliptic equations driven by the p laplacian differential operator using degree theoretic arguments based on the degree map for operators of type s we prove the existence of two nontrivial smooth solutions one of which is of constant sign

globally asymptotical stability of discrete time analog neural networks some globally asymptotical stability criteria for the equilibrium states of a general class of discrete time dynamic neural networks with continuous states are presented using a diagonal lyapunov function approach the neural networks are assumed to have the asymmetrical weight matrices throughout the paper the resulting criteria are described by the diagonal stability of some matrices associated with the network parameters some novel stability conditions represented by either the existence of the positive diagonal solutions of the lyapunov equations or some inequalities are given using the equivalence between the diagonal stability and the schur stability for a nonnegative matrix some simplified global stability conditions are also presented finally some examples are provided for demonstrating the effectiveness of the global stability conditions presented

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

delay dependent global exponential stability for delayed recurrent neural networks this paper deals with the global exponential stability for delayed recurrent neural networks drnns by constructing an augmented lyapunov krasovskii functional and adopting the reciprocally convex combination approach and wirtinger based integral inequality delay dependent global exponential stability criteria are derived in terms of linear matrix inequalities meanwhile a general and effective method on global exponential stability analysis for drnns is given through a lemma where the exponential convergence rate can be estimated with this lemma some global asymptotic stability criteria of drnns acquired in previous studies can be generalized to global exponential stability ones finally a frequently utilized numerical example is carried out to illustrate the effectiveness and merits of the proposed theoretical results

new conditions on global stability of cohen grossberg neural networks in this letter we discuss the dynamics of the cohen grossberg neural networks we provide a new and relaxed set of sufficient conditions for the cohen grossberg networks to be absolutely stable and exponentially stable globally we also provide an estimate of the rate of convergence

multiple nontrivial solutions of semilinear strongly resonant elliptic equations fixed point theory is an important and actual topic of nonlinear analysis moreover it s well known that the contraction mapping principle formulated and proved in the phd dissertation of banach in 1920 which was published in 1922 is one of the most important theorems in classical functional analysis during the last four decades this theorem has undergone various generalizations either by relaxing the condition on contractivity or withdrawing the requirement of completeness or sometimes even both recently a very interesting generalization was obtained in 1 by changing the structure of the space itself in fact branciari 1 introduced a concept of generalized metric space by replacing the triangle inequality by a more general inequality as such any metric space is a generalized metric space but the converse is not true 1 he proved the banach s fixed point theorem in such a space for more the reader can refer to 2 11 it is also known that common fixed point theorems are generalizations of fixed point theorems thus over the past few decades there have been many researchers who have interested in generalizing fixed point theorems to coincidence point theorems and common fixed point theorems in this paper we prove some common fixed point theorems for a larger class of contractions in generalized metric spaces and improve the results obtained by lakzian and samet 12 and di bari and vetro 13

hopf bifurcation of an n 1 neuron bidirectional associative memory neural network model with delays recent studies on hopf bifurcations of neural networks with delays are confined to simplified neural network models consisting of only two three four five or six neurons it is well known that neural networks are complex and large scale nonlinear dynamical systems so the dynamics of the delayed neural networks are very rich and complicated although discussing the dynamics of networks with a few neurons may help us to understand large scale networks there are inevitably some complicated problems that may be overlooked if simplified networks are carried over to large scale networks in this paper a general delayed bidirectional associative memory neural network model with n 1 neurons is considered by analyzing the associated characteristic equation the local stability of the trivial steady state is examined and then the existence of the hopf bifurcation at the trivial steady state is established by applying the normal form theory and the center manifold reduction explicit formulae are derived to determine the direction and stability of the bifurcating periodic solution furthermore the paper highlights situations where the hopf bifurcations are particularly critical in the sense that the amplitude and the period of oscillations are very sensitive to errors due to tolerances in the implementation of neuron interconnections it is shown that the sensitivity is crucially dependent on the delay and also significantly influenced by the feature of the number of neurons numerical simulations are carried out to illustrate the main results

asymptotically linear elliptic equations without nonresonance conditions abstract in this paper we are concerned with the existence of nontrivial solutions of a semilinear elliptic equation when the nonresonance condition at infinity is not satisfied we consider a strongly resonant case in the first part and a sort of resonance under density assumptions in the second part

improved stability criteria for a class of neural networks with variable delays and impulsive perturbations this paper further investigates the problem of stability analysis for a kind of neural networks with variable delays and nonlinear impulses with the help of m matrix the homeomorphism theory some effective inequalities and analysis techniques certain novel criteria on the existence uniqueness and exponential stability of the equilibrium point have been established moreover these criteria possess adjustable real parameters which extend and improve many existing results in the literature in the end two numerical examples are provided to illustrate the validation of the theoretical results

on equilibria stability and instability of hopfield neural networks existence and uniqueness of equilibrium as well as its stability and instability of a continuous time hopfield neural network are studied a set of new and simple sufficient conditions are derived

multiple solutions for nonlinear elliptic equations at resonance with a nonsmooth potential abstract in this paper we study a nonlinear elliptic problem at resonance driven by the p laplacian and with a nonsmooth potential hemivariational inequality our approach is variational and it is based on the nonsmooth critical point theory for locally lipschitz functions due to chang we prove a theorem guaranteeing the existence of one solution which is smooth and strictly positive then by strengthening the assumptions we establish a multiplicity result providing the existence of at least two distinct solutions our hypotheses permit resonance and asymmetric behavior at and as a byproduct of our analysis we obtain an nonlinear and nonsmooth generalization of a result of brezis nirenberg about h 0 1 versus c 0 1 minimizers of a smooth functional

stability analysis of cohen grossberg neural networks without assuming boundedness and differentiability of the activation functions and any symmetry of interconnections we employ lyapunov functions to establish some sufficient conditions ensuring existence uniqueness global asymptotic stability and even global exponential stability of equilibria for the cohen grossberg neural networks with and without delays our results are not only presented in terms of system parameters and can be easily verified and also less restrictive than previously known criteria and can be applied to neural networks including hopfield neural networks bidirectional association memory neural networks and cellular neural networks

estimate of exponential convergence rate and exponential stability for neural networks estimates of exponential convergence rate and exponential stability are studied for a class of neural networks which includes hopfield neural networks and cellular neural networks both local and global exponential convergence are discussed theorems for estimation of the exponential convergence rate are established and the bounds on the rate of convergence are given the domains of attraction in the case of local exponential convergence are obtained simple conditions are presented for checking exponential stability of the neural networks

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

dynamical analysis of cohen grossberg neural networks with finite and infinite delays a model describing dynamics of cohen grossberg neural networks with finite and infinite delays is considered by means of lyapunov functionals and differential inequality techniques criteria on global asymptotic stability of this model are derived the results of this paper are new and they supplement previously known results

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

absolute exponential stability of recurrent neural networks with generalized activation function in this paper the recurrent neural networks rnns with a generalized activation function class is proposed in this proposed model every component of the neuron s activation function belongs to a convex hull which is bounded by two odd symmetric piecewise linear functions that are convex or concave over the real space all of the convex hulls are composed of generalized activation function classes the novel activation function class is not only with a more flexible and more specific description of the activation functions than other function classes but it also generalizes some traditional activation function classes the absolute exponential stability aest of the rnn with a generalized activation function class is studied through three steps the first step is to demonstrate the global exponential stability ges of the equilibrium point of original rnn with a generalized activation function being equivalent to that of rnn under all vertex functions of convex hull the second step transforms the rnn under every vertex activation function into neural networks under an array of saturated linear activation functions because the ges of the equilibrium point of three systems are equivalent the next stability analysis focuses on the ges of the equilibrium point of rnn system under an array of saturated linear activation functions the last step is to study both the existence of equilibrium point and the ges of the rnn under saturated linear activation functions using the theory of m matrix in the end a two neuron rnn with a generalized activation function is constructed to show the effectiveness of our results

asymptotic stability of continuous time systems with saturation nonlinearities abstract a new criterion is established for global asymptotic stability of second order systems modeled by equations of the type dot x ax where is the saturation function the derivation is based on the bendixon s theorem on limit cycles and a closer study of the trajectories of the systems applications to stabilization of more general cascade nonlinear systems are also discussed

parameter identification of tsk neuro fuzzy models abstract in the framework of the tsk neuro fuzzy model a combination of the two well known identification methods are employed for parameter estimation of the neuro fuzzy inference system namely the series parallel and the parallel configurations the presented paper proposes two new possible configurations for identifying the parameters of the tsk neuro fuzzy model using the combinations of these two existing configurations one of the proposed configurations constitutes the series parallel configuration to the premise part and the parallel configuration to the consequent part of the neuro fuzzy model termed as ps p configuration the second one is composed of the series parallel configuration to the consequent part and the parallel configuration to the premise part of the neuro fuzzy model termed as cs p configuration the presented work mainly deals with a comparative study of the proposed configurations and the existing configurations in the context of parameter identification of the tsk neuro fuzzy model on three different benchmark examples moreover it investigates upper bound of the learning rates using the lyapunov stability theorem to assure the stability and the convergence of the model learning process implementation of the modified mountain clustering mmc and the cluster validity function yields initial models to restrict the upper bound during the learning process it also presents a two phase adaptive learning rate

nonlinear difference equations in the numerical integration of nonlinear differential equations it is often possible to get phantom solutions which are qualitatively quite different from the true solutions whether the behaviour of a numerical solution is a true reflection of a nonlinear phenomenon being modelled by the differential equation or whether it is a mere consequence of the particular discretization method used in solving the equation is clearly a question of considerable importance this question is highlighted by recent analyses of difference equation approximations to one of the simplest nonlinear differential equations the verhulst equation

hopf bifurcation in bidirectional associative memory neural networks with delays analysis and computation in addition to giving some delay independent conditions for global stability of the bidirectional associative memory neural networks with delays we perform analysis of local stability and hopf bifurcation we also work out an algorithm for determining the direction and stability of the bifurcated periodic solutions

conditional entailment bridging two approaches to default reasoning abstract in recent years two conceptually different interpretations of default expressions have been advanced extensional interpretations in which defaults are regarded as prescriptions for extending one s set of beliefs and conditional interpretations in which defaults are regarded as beliefs whose validity is bound to a particular context the two interpretations possess virtues and limitations that are practically orthogonal to each other the conditional interpretations successfully resolve arguments of different specificity e g penguins don t fly in spite of being birds but fail to capture arguments of irrelevance e g concluding red birds fly from birds fly the opposite is true for the extensional interpretations this paper develops a new account of defaults called conditional entailment which combines the benefits of the two interpretations like prioritized circumscriptions conditional entailment resolves arguments by enforcing priorities among defaults however instead of having to be specified by the user these priorities are extracted automatically from the knowledge base similarly conditional entailment possesses a sound and complete proof theory based on interacting arguments and amenable to implementation in conventional atmss

existence of multiple solutions for quasilinear and semilinear elliptic equations has been studied by many authors cf l 3 4 161 under the assumption that g r r is a continuous function such that g t t closes finite many eigenvalues when t varies from 0 to a the existence of one nontrivial solution for 1 2 was proved by amann and zehnder 3 and thews 21 the existence of two nontrivial solutions was studied by castro and lazer lo and ambrosetti and mancini 4 most of the multiplicity results for problem 1 2 are based on the fact that 1 2 can be rewritten as

on infinity norms as lyapunov functions for linear systems the note presents a construction of the lyapunov function defined by l sub spl infin sup n vector norm for both continuous and discrete time linear systems in contrast to the previous results no restrictions on the positions or multiplicity of system matrix eigenvalues are required

variational methods for non differentiable functionals and their applications to partial differential equations the interest in extending the theory of nonlinear partial differential equations pde to pde with discontinuous nonlinearities dnde has been increasing daily the reasons are twofold 1 many free boundary problems may be reduced to boundary value problems of dnde cf chang 16 71 chang and jiang 9 and fleishman and mahar 121 2 sometimes in dealing with a pde problem it is beneficial to put the original pde into a large category for instance dnde cf chang 7 simply speaking a dnde is as follows

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

local c1 ω minimizers versus local w1 p ω minimizers of nonsmooth functionals abstract we study not necessarily differentiable functionals of the form j u 1 p u p d x 1 p u p d x j 1 x u d x j 2 x u d with 1 p involving locally lipschitz functions j 1 r r as well as j 2 r r we prove that local c 1 minimizers of j must be local w 1 p minimizers of j

impulsive stabilization of high order hopfield type neural networks with time varying delays this paper studies the problems of global exponential stability for impulsive high order hopfield type neural networks nns with time varying delays by employing the lyapunov razumikhin technique some criteria ensuring global exponential stability are derived our results are then used to obtain some sufficient conditions under which some nns can be forced to converge by impulsive control numerical examples are also discussed to illustrate our 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

deriving sufficient conditions for global asymptotic stability of delayed neural networks via nonsmooth analysis ii in this paper we obtain new sufficient conditions ensuring existence uniqueness and global asymptotic stability gas of the equilibrium point for a general class of delayed neural networks dnns via nonsmooth analysis which makes full use of the lipschitz property of functions defining dnns based on this new tool of nonsmooth analysis we first obtain a couple of general results concerning the existence and uniqueness of the equilibrium point then those results are applied to show that existence assumptions on the equilibrium point in some existing sufficient conditions ensuring gas are actually unnecessary and some strong assumptions such as the boundedness of activation functions in some other existing sufficient conditions can be actually dropped finally we derive some new sufficient conditions which are easy to check comparison with some related existing results is conducted and advantages are illustrated with examples throughout our paper spectral properties of the matrix a a sup spl tau play an important role which is a distinguished feature from previous studies here a and a sup spl tau are respectively the feedback and the delayed feedback matrix defining the neural network under consideration

global asymptotic stability of a class of nonautonomous integro differential systems and applications abstract in this paper we study the global asymptotic stability of a class of nonautonomous integro differential systems by constructing suitable lyapunov functionals we establish new and explicit criteria for the global asymptotic stability in the sense of definition 2 1 in the autonomous case we discuss the global asymptotic stability of a unique equilibrium of the system and in the case of periodic system we establish sufficient criteria for existence uniqueness and global asymptotic stability of a periodic solution also explored are applications of our main results to some biological and neural network models the examples show that our criteria are more general and easily applicable and improve and generalize some existing results

multiple solutions for a class of nonlinear elliptic problems with a p laplacian type operator abstract in this paper we obtain the existence of at least two solutions for a nonlinear elliptic problem on unbounded domains involving a p laplacian type operator and nonsmooth potentials our approach is variational and it is based on the nonsmooth critical point theory for locally lipschitz functions

a delayed neural network for solving linear projection equations and its analysis in this paper we present a delayed neural network approach to solve linear projection equations the lyapunov krasovskii theory for functional differential equations and the linear matrix inequality lmi approach are employed to analyze the global asymptotic stability and global exponential stability of the delayed neural network compared with the existing linear projection neural network theoretical results and illustrative examples show that the delayed neural network can effectively solve a class of linear projection equations and some quadratic programming problems

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

stability of asymmetric hopfield networks in this paper we discuss dynamical behaviors of recurrently asymmetrically connected neural networks in detail we propose an effective approach to study global and local stability of the networks many of well known existing results are unified in our framework which gives much better test conditions for global and local stability sufficient conditions for the uniqueness of the equilibrium point and its stability conditions are given too

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

exponential stability preservation in discrete time analogues of artificial neural networks with distributed delays this paper demonstrates that there is a discrete time analogue which does not require any restriction on the size of the time step in order to preserve the exponential stability of an artificial neural network with distributed delays the analysis exploits an appropriate lyapunov sequence and a discrete time system of halanay inequalities and also either a young inequality or a geometric arithmetic mean inequality to derive several sufficient conditions on the network parameters for the exponential stability of the analogue the sufficiency conditions are independent of the time step and they correspond to those that establish the exponential stability of the continuous time network

positive solutions for nonlinear hemivariational inequalities in this paper we study the existence of positive solutions for nonlinear problems driven by the p laplacian or more generally by multivalued p laplacian like operators both problems have a nonsmooth locally lipschitz potential hemivariational inequalities using variational methods based on the nonsmooth critical point theory we prove two existence results with the p laplacian and multivalued p laplacian like operators

positive solutions and multiple solutions at non resonance resonance and near resonance for hemivariational inequalities with p laplacian in this paper we study eigenvalue problems for hemivariational inequalities driven by the p laplacian differential operator we prove the existence of positive smooth solutions for both non resonant and resonant problems at the principal eigenvalue of the negative p laplacian with homogeneous dirichlet boundary condition we also examine problems which are near resonance both from the left and from the right of the principal eigenvalue for nearly resonant from the right problems we also prove a multiplicity result

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

nonmonotonic reasoning preferential models and cumulative logics abstract many systems that exhibit nonmonotonic behavior have been described and studied already in the literature the general notion of nonmonotonic reasoning though has almost always been described only negatively by the property it does not enjoy i e monotonicity we study here general patterns of nonmonotonic reasoning and try to isolate properties that could help us map the field of nonmonotonic reasoning by reference to positive properties we concentrate on a number of families of nonmonotonic consequence relations defined in the style of gentzen 13 both proof theoretic and semantic points of view are developed in parallel the former point of view was pioneered by gabbay 10 while the latter has been advocated by shoham 38 five such families are defined and characterized by representation theorems relating the two points of view one of the families of interest that of preferential relations turns out to have been studied by adams 2 the preferential models proposed here are a much stronger tool than adams probabilistic semantics the basic language used in this paper is that of propositional logic the extension of our results to first order predicate calculi and the study of the computational complexity of the decision problems described in this paper will be treated in another paper

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

global stability criterion for delayed complex valued recurrent neural networks the stability problem for delayed complex valued recurrent neural networks is considered in this paper by separating complex valued neural networks into real and imaginary parts forming an equivalent real valued system and constructing appropriate lyapunov functional a sufficient condition to ascertain the existence uniqueness and globally asymptotical stability of the equilibrium point of complex valued systems is provided in terms of linear matrix inequality meanwhile the errors in the recent work are pointed out and even if the result therein is correct it is shown that our result not only improves but also generalizes in that work numerical examples are given to show the effectiveness and merits of the present result

turbulence in multistep methods for initial value problems solving a scalar initial value problem with a numerical k step scheme amounts to iterating a k dimensional discrete dynamical system in this paper we investigate regular and chaotic behaviour of some dynamical systems associated with adams bashforth formulas applied to a simple nonlinear test equation

global stability analysis in delayed cellular neural networks abstract in this paper without assuming the boundedness monotonicity and differentiability of the activation functions we present new conditions ensuring existence uniqueness and global asymptotical stability of the equilibrium point of cellular neural network models with fixed time delays the results are applicable to both symmetric and nonsymmetric interconnection matrices and all continuous nonmonotonic neuron activation functions

what does a conditional knowledge base entail abstract this paper presents a logical approach to nonmonotonic reasoning based on the notion of a nonmonotonic consequence relation a conditional knowledge base consisting of a set of conditional assertions of the type if then represents the explicit defeasible knowledge an agent has about the way the world generally behaves we look for a plausible definition of the set of all conditional assertions entailed by a conditional knowledge base in a previous paper kraus and the authors defined and studied preferential consequence relations they noticed that not all preferential relations could be considered as reasonable inference procedures this paper studies a more restricted class of consequence relations rational relations it is argued that any reasonable nonmonotonic inference procedure should define a rational relation it is shown that the rational relations are exactly those that may be represented by a ranked preferential model or by a nonstandard probabilistic model the rational closure of a conditional knowledge base is defined and shown to provide an attractive answer to the question of the title global properties of this closure operation are proved it is a cumulative operation it is also computationally tractable this paper assumes the underlying language is propositional

stability analysis of impulsive stochastic cohen grossberg neural networks with mixed time delays abstract in this paper the problem of stability analysis for a class of impulsive stochastic cohen grossberg neural networks with mixed delays is considered the mixed time delays comprise both the time varying and infinite distributed delays by employing a combination of the m matrix theory and stochastic analysis technique a sufficient condition is obtained to ensure the existence uniqueness and exponential p stability of the equilibrium point for the addressed impulsive stochastic cohen grossberg neural network with mixed delays the proposed method which does not make use of the lyapunov functional is shown to be simple yet effective for analyzing the stability of impulsive or stochastic neural networks with variable and or distributed delays we then extend our main results to the case where the parameters contain interval uncertainties moreover the exponential convergence rate index is estimated which depends on the system parameters an example is given to show the effectiveness of the obtained results

stability analysis of hopfield type neural networks the paper applies several concepts in robust control research such as linear matrix inequalities edge theorem parameter dependent lyapunov function and popov criteria to investigate the stability property of hopfield type neural networks the existence and uniqueness of an equilibrium is formulated as a matrix determinant problem an induction scheme is used to find the equilibrium to verify whether the determinant is nonzero for a class of matrix a numerical range test is proposed several robust control techniques in particular linear matrix inequalities are used to characterize the local stability of the neural networks around the equilibrium the global stability of the hopfield neural networks is then addressed using a parameter dependent lyapunov function technique all these results are shown to generalize existing results in verifying the existence uniqueness of the equilibrium and local global stability of hopfield type 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

multiplicity results for semilinear elliptic problems at resonance and with jumping nonlinearities abstract in the present paper we develop a method to deal with multiple existence of solutions of nonlinear elliptic problems and give some multiple existence results for elliptic boundary value problems at resonance and problems with jumping nonlinearities

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

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

exponential stability and oscillation of hopfield graded response neural network both exponential and stochastic stabilities of the hopfield neural network are analyzed the results are especially useful for analyzing the stabilities of asymmetric neural networks a constraint on the connection matrix has been found under which the neural network has a unique and exponentially stable equilibrium given any connection matrix this constraint can be satisfied through the adjustment of the gains of the amplifiers and the resistances in the neural net circuit a one to one and smooth map between input currents and the equilibria of the neural network can be set up the above results can be applied to the master slave net to prove that the master net can find the best connection matrix for the slave net for the neural network disturbed by some noise the stochastic stability of the network is also analyzed a special asymmetric neural network formed by a closed chain of formal neurons is also studied for its stability and oscillation both stable and oscillatory dynamics are obtained in the closed chain network through the adjustment of the gains and resistances of the amplifiers

default extensions dealing with computer information a conditional knowledge base may be sometimes analyzed as a union of several pieces of information that are provided by independent sources in this case it is possible to extend separately each of these subbases via their rational closure and then glue the results together to get a rational extension of the whole base in which the specificity of its components is taken into account the resulting inference relation is free from the undesirable and counterintuitive results that can be encountered in the z system lex system or w system

stabilizing hopfield neural networks via inhibitory self connections the theory of monotone dynamical systems is employed to establish some sufficient conditions for the global attractivity of the hopfield neural networks with finite distributed delays the results show that self inhibitory connections can be used to stabilize a delayed network provided the diagonal delays corresponding to the inhibitory self connections are small enough

multistability analysis for recurrent neural networks with unsaturating piecewise linear transfer functions multistability is a property necessary in neural networks in order to enable certain applications e g decision making where monostable networks can be computationally restrictive this article focuses on the analysis of multistability for a class of recurrent neural networks with unsaturating piecewise linear transfer functions it deals fully with the three basic properties of a multistable network boundedness global attractivity and complete convergence this article makes the following contributions conditions based on local inhibition are derived that guarantee boundedness of some multistable networks conditions are established for global attractivity bounds on global attractive sets are obtained complete convergence conditions for the network are developed using novel energy like functions and simulation examples are employed to illustrate the theory thus developed

convergence of nonautonomous cohen grossberg type neural networks with variable delays this paper is concerned with the global convergence of the solutions of a nonautonomous system with variable delays arising from the description of the states of neurons in delayed cohen grossberg type in a time varying situation by exploring intrinsic features between nonautonomous system and its asymptotic equation several novel sufficient conditions are established to ensure that all solutions of the networks converge to a periodic function or a constant vector for delayed cohen grossberg type neural network nn models in time varying situation the results can be applied directly to group of nns models including hopfield nns bidirectional association memory nns and cellular nns our results are not only presented in terms of system parameters and can be easily verified but also are less restrictive than previously known criteria numerical simulations have also been presented to demonstrate the theoretical analysis

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