monodromies at infinity of confluent a hypergeometric functions abstract we study the monodromies at infinity of confluent a hypergeometric functions introduced by adolphson 2 in particular we extend the result of 38 for non confluent a hypergeometric functions to the confluent case the integral representation by rapid decay homology cycles proved in 9 will play a central role in the proof

discrete analogue of high order periodic cohen grossberg neural networks with delay in this paper new discrete analogue of high order cohen grossberg neural networks with varying delay is obtained by analysis and approximation techniques the existence of periodic solution for discrete high order cohen grossberg neural networks with varying delay is studied by continuation theorem of coincidence degree theory and sufficient condition is given to guarantee global exponential stability of periodic solution finally an example is given to show the effectiveness of the results in this paper

multistability of second order competitive neural networks with nondecreasing saturated activation functions in this paper second order interactions are introduced into competitive neural networks nns and the multistability is discussed for second order competitive nns socnns with nondecreasing saturated activation functions firstly based on decomposition of state space cauchy convergence principle and inequality technique some sufficient conditions ensuring the local exponential stability of 2n equilibrium points are derived secondly some conditions are obtained for ascertaining equilibrium points to be locally exponentially stable and to be located in any designated region thirdly the theory is extended to more general saturated activation functions with 2r corner points and a sufficient criterion is given under which the socnns can have r 1 n locally exponentially stable equilibrium points even if there is no second order interactions the obtained results are less restrictive than those in some recent works finally three examples with their simulations are presented to verify the theoretical analysis

microlocal study of topological radon transforms and real projective duality various topological properties of projective duality between real projective varieties and their duals are obtained by making use of the microlocal theory of subanalytically constructible sheaves developed by kashiwara m kashiwara index theorem for constructible sheaves asterisque 130 1985 193 209 and kashiwara schapira m kashiwara p schapira sheaves on manifolds grundlehren math wiss vol 292 springer berlin heidelberg new york 1990 in particular we prove in the real setting some results similar to the ones proved by ernstrom in the complex case l ernstrom topological radon transforms and the local euler obstruction duke math j 76 1994 1 21 for this purpose we describe the characteristic cycles of topological radon transforms of constructible functions in terms of curvatures of strata in real projective spaces

exponential stability of impulsive high order hopfield type neural networks with time varying delays this paper considers the problems of global exponential stability and exponential convergence rate for impulsive high order hopfield type neural networks with time varying delays by using the method of lyapunov functions some sufficient conditions for ensuring global exponential stability of these networks are derived and the estimated exponential convergence rate is also obtained as an illustration an numerical example is worked out using the results obtained

stability and periodicity in high order neural networks with impulsive effects abstract in this paper the global exponential stability and periodicity are investigated for a class generalized high order neural networks with time delays and impulses some sufficient conditions are derived for checking the global exponential stability and existence of periodic solutions for this system using the generalized halanay inequality mathematical induction and a fixed point theorem the criteria given are easily verified and possess many adjustable parameters which provides flexibility for the design and analysis of the system finally an example with numerical simulation is given to show the effectiveness of the proposed method and results

hopf bifurcation and stability of periodic solutions for van der pol equation with time delay abstract in this paper the van der pol equation with a time delay is considered where the time delay is regarded as a parameter it is found that hopf bifurcation occurs when this delay passes through a sequence of critical value a formula for determining the direction of the hopf bifurcation and the stability of bifurcating periodic solutions is given by using the normal form method and center manifold theorem

confluent a hypergeometric functions and rapid decay homology cycles we study confluent a hypergeometric functions introduced by adolphson in particular we give their integral representations by using rapid decay homology cycles of hien the method of toric compactifications introduced in our previous works will be used to prove our main theorem moreover we apply it to obtain a formula for the asymptotic expansions at infinity of confluent a hypergeometric functions

remote synchronization in star networks we study phase synchronization in a network motif with a starlike structure in which the central node s the hub s frequency is strongly detuned against the other peripheral nodes we find numerically and experimentally a regime of remote synchronization rs where the peripheral nodes form a phase synchronized cluster while the hub remains free with its own dynamics and serves just as a transmitter for the other nodes we explain the mechanism for this rs by the existence of a free amplitude and also show that systems with a fixed or constant amplitude such as the classic kuramoto phase oscillator are not able to generate this phenomenon further we derive an analytic expression which supports our explanation of the mechanism

design of state estimator for bam fuzzy cellular neural networks with leakage and unbounded distributed delays in this paper the state estimation problem is studied for the bidirectional associative memory bam fuzzy cellular neural networks fcnns with delays where the delays include leakage and unbounded distributed delays the problem addressed is to estimate the neuron states through available output measurements such that for all admissible leakage and unbounded distributed delays the dynamics of the estimation error is globally asymptotically stable a delay dependent linear matrix inequality lmi criterion for the existence of the estimator is proposed by using the lyapunovkrasovskii functional method in addition the unknown gain matrix is determined by solving a delay dependent lmi finally numerical examples and simulations are provided to illustrate the effectiveness of the theoretical results

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

new robust stability results for bidirectional associative memory neural networks with multiple time delays in this paper the robust stability problem is investigated for a class of bidirectional associative memory bam neural networks with multiple time delays by employing suitable lyapunov functionals and using the upper bound norm for the interconnection matrices of the neural network system some novel sufficient conditions ensuring the existence uniqueness and global robust stability of the equilibrium point are derived the obtained results impose constraint conditions on the system parameters of neural network independent of the delay parameters some numerical examples and simulation results are given to demonstrate the applicability and effectiveness of our results and to compare the results with previous robust stability results derived in the literature

mixed time delays dependent exponential stability for uncertain stochastic high order neural networks this paper presents a discrete and distributed time delays dependent simultaneous approach to deterministic and uncertain stochastic high order neural networks new results are proposed in terms of linear matrix inequality lmi by exploiting a novel lyapunov krasovskii functional and by making use of novel techniques for time delay systems some constraints of systems are removed and new results cover some recently published works two numerical examples are given to show the usefulness of presented approach

dynamics of high order bam neural networks with and without impulses the main aim of this paper is to study the existence and global exponential stability of periodic solution for high order bidirectional associative memory bam neural networks with and without impulses easily verifiable sufficient conditions are established the method is based on coincidence degree theory as well as a priori estimates and lyapunov functional it is shown that the convergence characteristics of periodic solution for the impulsive system are preserved by the corresponding nonimpulsive system with some restriction imposed on the impulse effect numerical simulation results are given to support the theoretical predictions

exponential stability of high order bidirectional associative memory neural networks with time delays in this paper exponential stability is studied for a class of high order bidirectional associative memory bam neural networks with time delays by employing the linear matrix inequality lmi and the lyapunov functional methods several sufficient conditions are obtained for ensuring the system to be globally exponentially stable two illustrative examples are also given in the end of this paper to show the effectiveness of our results

integral transforms with exponential kernels and laplace transform let x z y be a correspondence of complex manifolds f g we study integral transforms associated to kernels exp o with p meromor phic on z acting on formal or moderate cohomologies our main application is the laplace transform in this case x is the projective compactification of the vector space v c y is its dual space z x x y and o z w z w we obtain the isomorphisms f 0 ov f n f ov thom f v thom far n ov this content downloaded from 207 46 13 59 on mon 13 jun 2016 05 54 06 utc all use subject to http about jstor org terms 972 masaki kashiwara and pierre schapira where f is a conic and rll constructible sheaf on v and fa is its fourier sato transform some applications are discussed rims kyoto university kyoto 606 01 japan institut de mathematiques universit9 paris vi case 82 4 pl jussieu 75252 paris france e mail address schapirafmath jussieu fr this content downloaded from 207 46 13 59 on mon 13 jun 2016 05 54 06 utc all use subject to http about jstor org terms

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

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

periodic solutions for a class of higher order cohen grossberg type neural networks with delays sufficient conditions are obtained for the existence and global attractivity of periodic solutions of a class of higher order cohen grossberg type neural networks with delays the proof is based on gaines and mawhin s continuation theorem of coincidence degree theory the lyapunov functional and a nonsingular m matrix one example is exploited to illustrate the effectiveness of the proposed criteria

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

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

lmi based approach for global asymptotic stability analysis of recurrent neural networks with various delays and structures global asymptotic stability problem is studied for a class of recurrent neural networks with distributed delays satisfying lebesgue stieljies measures on the basis of linear matrix inequality the concerned network model includes many neural network models with various delays and structures as its special cases such as the delays covering the discrete delays and distributed delays and the network structures containing the neutral type networks and high order networks therefore many new stability criteria for the above neural network models have also been derived from the present stability analysis method all the obtained stability results have similar matrix inequality structures and can be easily checked three numerical examples are used to show the effectiveness of the obtained results

on controllability of delayed boolean control networks this paper is devoted to studying the trajectory and state controllability of boolean control networks bcns with time delay in contrast to bcns without time delay the dynamics of delayed bcns are determined by a sequence of initial states named here trajectories trajectory controllability means that there exists a control signal steering a system from an initial trajectory to a desired trajectory while state controllability means that there exists a control signal steering an initial state to a given state here both trajectory controllability and state controllability will be studied it should be noted that in this paper trajectory controllability does not mean tracking or following a given trajectory in fact it means to control bcns to a destination trajectory of length mu at the k th step using the semi tensor product of matrices the delayed bcns are first converted into an equivalent algebraic description and then some necessary and sufficient conditions are derived for the trajecto

novel global stability criteria for high order hopfield type neural networks with time varying delays abstract this paper discusses a generalized model of high order hopfield type neural networks with time varying delays some novel global stability criteria of the system is derived by using lyapunov method linear matrix inequality lmi and analytic technique the lmi based criteria obtained here are computationally more flexible and more generic than many other existing criteria a numerical example is given to illustrate our result

neural networks orientations of the hypercube and algebraic threshold functions a class of possible generalizations of current neural networks models is described using local improvement algorithms and orientations of graphs a notation of dynamical capacity is defined and by computing bounds on the number of algebraic threshold functions it is proven that for neural networks of size n and energy function of degree d this capacity is o n sup d 1 stable states are studied and it is shown that for the same networks the storage capacity is o n sup d 1 in the case of random orientations it is proven that the expected number of stable states is exponential applications to coding theory are indicated and it is shown that usual codes can be embedded in neural networks but only at high cost cycles and their storage are also examined

generalized lyapunov approach for convergence of neural networks with discontinuous or non lipschitz activations the paper considers a class of additive neural networks where the neuron activations are modeled by discontinuous functions or by continuous non lipschitz functions some tools are developed which enable us to apply a lyapunov like approach to differential equations with discontinuous right hand side modeling the neural network dynamics the tools include a chain rule for computing the time derivative along the neural network solutions of a nondifferentiable lyapunov function and a comparison principle for this time derivative which yields conditions for exponential convergence or convergence in finite time by means of the lyapunov like approach a general result is proved on global exponential convergence toward a unique equilibrium point of the neural network solutions moreover new results on global convergence in finite time are established which are applicable to neuron activations with jump discontinuities or neuron activations modeled by means of continuous non lipschitz holder functions

stability bifurcation and global existence of a hopf bifurcating periodic solution for a class of three neuron delayed network models in this paper a system of three delay differential equations representing a hopfield type general model for three neurons with two way bidirectional time delayed connections between the neurons and time delayed self connection from each neuron to itself is studied delay independent and delay dependent sufficient conditions for linear stability instability and the occurrence of a hopf bifurcation about the trivial equilibrium are addressed the partition of the resulting parametric space into regions of stability instability and hopf bifurcation in the absence of self connection is realized to extend the local hopf branches for large delay values a particular bidirectional delayed tri neuron model without self connection is investigated sufficient conditions for global existence of multiple non constant periodic solutions are obtained for such a model using the global hopf bifurcation theorem for functional differential equations due to j wu and the bendixson criterion for higher dimensional ordinary differential equations due to li and muldowney and following the approach developed by wei and li

global asymptotic stability of high order hopfield type neural networks with time delays abstract this paper studies the problem of global asymptotic stability of a class of high order hopfield type neural networks with time delays by utilizing lyapunov functionals we obtain some sufficient conditions for the global asymptotic stability of the equilibrium point of such neural networks in terms of linear matrix inequality lmi numerical examples are given to illustrate the advantages of our approach

new convergence behavior of high order hopfield neural networks with time varying coefficients in this paper the convergence behavior of the delayed high order hopfield neural networks hhnns with time varying coefficients are considered some sufficient conditions are established to ensure that all solutions of the networks converge to zero point which are new and complement of previously known results

exponential stability of impulsive cellular neural networks with time delay via lyapunov functionals this paper investigates the problem of exponential stability for a class of impulsive cellular neural networks with time delay by dividing the network state variables into subgroups according to the characters of the neural networks some sufficient conditions for exponential stability are derived by lyapunov functionals and the method of variation of parameters these conditions are given in terms of some blocks of the interconnection matrix which extend and improve some of the known results in the literature our results show that impulses may be used to stabilize the cellular neural networks with time delay if they are not stable or exponentially stable on the other hand if impulses are input disturbances criteria on the magnitude and frequency of the impulses are also established to maintain the stability property of the original system our results generalize and improve some known results two examples with numerical simulations are given to illustrate our results

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

hypergeometric d modules and twisted gaus manin systems abstract the euler koszul complex is the fundamental tool in the homological study of a hypergeometric differential systems and functions we compare euler koszul homology with d module direct images from the torus to the base space through orbits in the corresponding toric variety our approach generalizes a result by gel fand et al i m gel fand m m kapranov a v zelevinsky generalized euler integrals and a hypergeometric functions adv math 84 2 1990 255 271 mr mr1080980 92e 33015 thm 4 6 and yields a simpler more algebraic proof in the process we extend the euler koszul functor to a category of infinite toric modules and describe multigraded localizations of euler koszul homology

on irregularities of fourier transforms of regular holonomic d modules abstract we study fourier transforms of regular holonomic d modules by using the theory of fourier sato transforms of enhanced ind sheaves developed by kashiwara schapira and d agnolo kashiwara a formula for their enhanced solution complexes will be obtained moreover we show that some parts of their characteristic cycles and irregularities are expressed by the geometries of the original d modules