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

on chaotic simulated annealing chen and aihara 1995 proposed a chaotic simulated annealing approach to solving optimization problems by adding a negative self coupling to a network model proposed earlier by aihara et al and gradually removing this negative self coupling they used the transient chaos for searching and self organizing thereby achieving great improvement over other neural network approaches to optimization problems with or without simulated annealing in this paper we suggest a new approach to chaotic simulated annealing with guaranteed convergence and minimization of the energy function by gradually reducing the time step in the euler approximation of the differential equations that describe the continuous hopfield neural network this approach eliminates the need to carefully select other system parameters we also generalize the convergence theorems of chen and aihara to arbitrarily increasing neuronal input output functions and to less restrictive and yet more compact forms

domain decomposition schemes with high order accuracy and unconditional stability parallel finite difference schemes with high order accuracy and unconditional stability for solving parabolic equations are presented the schemes are based on domain decomposition method i e interface values between subdomains are computed by the explicit scheme interior values are computed by the implicit scheme the numerical stability and error are derived in the h 1 norm in one dimensional case numerical results of both one and two dimensions examining the stability accuracy and parallelism of the procedure are also presented

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

unconditional stability of parallel difference schemes with second order accuracy for parabolic equation in this paper we investigate the parallel difference schemes of parabolic equation in particular two kinds of difference schemes with intrinsic parallelism are constructed firstly we combine the values of previous two time levels at the interface points to get the dirichlet boundary condition for the sub domain problems then the values in the sub domains are calculated by fully implicit scheme and then finally the values at the interface points are computed by fully implicit scheme the unconditional stability of these schemes is proved and the convergence rate of second order is also obtained numerical results are presented to examine the accuracy stability and parallelism of the parallel schemes

chaotic simulated annealing by a neural network with a variable delay design and application in this paper we have three goals the first is to delineate the advantages of a variably delayed system the second is to find a more intuitive lyapunov function for a delayed neural network and the third is to design a delayed neural network for a quadratic cost function for delayed neural networks most researchers construct a lyapunov function based on the linear matrix inequality lmi approach however that approach is not intuitive we provide a alternative candidate lyapunov function for a delayed neural network on the other hand if we are first given a quadratic cost function we can construct a delayed neural network by suitably dividing the second order term into two parts a self feedback connection weight and a delayed connection weight to demonstrate the advantage of a variably delayed neural network we propose a transiently chaotic neural network with variable delay and show numerically that the model should possess a better searching ability than chen aihara s model wang s model and zhao s model we discuss both the chaotic and the convergent phases during the chaotic phase we simply present bifurcation diagrams for a single neuron with a constant delay and with a variable delay we show that the variably delayed model possesses the stochastic property and chaotic wandering during the convergent phase we not only provide a novel lyapunov function for neural networks with a delay the lyapunov function is independent of the lmi approach but also establish a correlation between the lyapunov function for a delayed neural network and an objective function for the traveling salesman problem

second order in time and space corrected explicit implicit domain decomposition scheme for convection diffusion equations abstract we develop a second order corrected explicit implicit domain decomposition scheme sceidd for the parallel approximation of convection diffusion equations over multi block subdomains the stability and convergence properties of the sceidd scheme are analyzed it is proved that the scheme is unconditionally stable and it is second order accurate in time as well as space furthermore three different numerical experiments are performed to verify the theoretical results in all the experiments the sceidd scheme is compared with the eipcmu2d scheme which is first order in time

the discrete frenkel kontorova model and its extensions i exact results for the ground states abstract we present a rigorous study of the classical ground states under boundary conditions of a class of one dimensional models generalizing the discrete frenkel kontorova model the extremalization equations of the energy of these models turn out to define area preserving twist maps which exhibits periodic quasi periodic and chaotic orbits for all boundary conditions we select among all the extremum solutions of the energy of the model those which correspond to the ground states of the infinite system we prove that these ground states are either periodic commensurate or quasi periodic incommensurate but are never chaotic we also prove the existence of elementary discommensurations which are minimum energy configuration of the model for certain special boundary conditions the topological structure of the whole set of ground states is described in details in addition to physical applications consequences for twist map homeomorphisms are mentioned part ii s aubry p y ledaeron and g andre will be mostly devoted to exact results on the transition by breaking of analyticity which occurs on the incommensurate ground states when the model parameters vary and on its connection with the stochasticity threshold in the corresponding twist map

homoclinic bifurcations for the henon map abstract chaotic dynamics can be effectively studied by continuation from an anti integrable limit we use this limit to assign global symbols to orbits and use continuation from the limit to study their bifurcations we find a bound on the parameter range for which the henon map exhibits a complete binary horseshoe as well as a subshift of finite type we classify homoclinic bifurcations and study those for the area preserving case in detail simple forcing relations between homoclinic orbits are established we show that a symmetry of the map gives rise to constraints on certain sequences of homoclinic bifurcations our numerical studies also identify the bifurcations that bound intervals on which the topological entropy is apparently constant

neural networks with prescribed large time behaviour the generalized hebb rule with a non symmetrical synaptic matrix allows us to create simple neural networks with complicated large time behaviour these networks can simulate in a sense any dynamics and in particular can generate any hyperbolic attractors and invariant sets the explicit mathematical algorithm allows us by adjusting the network parameters the neuron number coupling matrix and thresholds to obtain a network with given large time dynamics

the mass preserving and modified upwind splitting ddm scheme for time dependent convectiondiffusion equations in the paper a new mass preserving and modified upwind s ddm scheme over non overlapping multi block sub domains for solving time dependent convectiondiffusion equations in two dimensions is developed and analyzed on each sub domain the intermediate fluxes on the interfaces of sub domains are firstly computed by the modified semi implicit flux schemes then the solutions and fluxes in the interiors of sub domains are computed by the modified upwind splitting implicit solution and flux coupled schemes on the theoretical aspect analyzing the mass preserving and modified upwind s ddm scheme is difficult over non overlapping multi block sub domains due to the combination of the splitting technique the conservative modified upwind technique and the domain decomposition we prove the proposed scheme to be mass conservative and unconditionally stable in discrete l2 norm and further prove its convergence and obtain error estimates numerical experiments are presented to illustrate mass conservation convergence and parallelism we propose a new mass preserving and modified upwind splitting ddm scheme in 2d the solution and flux coupled scheme is to preserve mass over multi subdomains the developed scheme is mass conservative and unconditionally stable it is of first order convergence in time step and second order convergence in space

bifurcations in mean field theory annealing in this paper we investigate bifurcation processes for the mean field theory mft annealing applied to traveling salesman problems tsps due to the symmetries of the tsp free energy function some special bifurcations occur cyclic symmetry breaking bifurcations and reverse symmetry breaking bifurcations saddle node bifurcations also occur which type of bifurcation occurs depends on the symmetry of the eigenvector that corresponds to the zero eigenvalue mode of the free energy curvature matrix at the bifurcation point in the mft annealing process a sequence of bifurcations occurs and the bifurcation structure affects the quality of the annealing solution it is shown that the annealing solution in this process is not unique in general and it is not always the optimal solution our approach can also be applied to the potts spin model and its bifurcation structure is almost the same as that of the mft the practical implications of our results are also discussed textcopyright 1996 the american physical society

persistent chaos in high dimensions an extensive statistical survey of universal approximators shows that as the dimension of a typical dissipative dynamical system is increased the number of positive lyapunov exponents increases monotonically and the number of parameter windows with periodic behavior decreases a subset of parameter space remains where noncatastrophic topological change induced by a small parameter variation becomes inevitable a geometric mechanism depending on dimension and an associated conjecture depict why topological change is expected but not catastrophic thus providing an explanation of how and why deterministic chaos persists in high dimensions

new exponential stability results for delayed neural networks with time varying delays abstract this paper presents new sufficient conditions for the uniqueness and exponential stability of the equilibrium point for delayed neural networks with time varying delays by employing a more general type of lyapunov krasovskii functional and using lmi linear matrix inequality we derive new results for exponential stability of the equilibrium point for delayed neural networks the results establish a relation between the delay time and the parameters of the network the results are compared with the previous results derived in the literature

chaos and asymptotical stability in discrete time neural networks abstract this paper aims to theoretically prove by applying marotto s theorem that both transiently chaotic neural networks tcnn and discrete time recurrent neural networks drnn have chaotic structure a significant property tcnn and drnn is that they have only one bounded fixed point when absolute values of the self feedback connection weights in tcnn and the difference time in drnn are sufficiently large we show that this unique fixed point can actually evolve into a snap back repeller which generates chaotic structure if several conditions are satisfied on the other hand by using the lyapunov functions we also derive sufficient conditions on asymptotical stability for symmetrical versions of both tcnn and drnn under which tcnn and drnn asymptotically converge to a fixed point furthermore related bifurcations are also considered in this paper since both tcnn and drnn are not special but simple and general the obtained theoretical results hold for a wide class of discrete time neural networks to demonstrate the theoretical results of this paper better several numerical simulations are provided as illustrating examples

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

unconditional stability of parallel alternating difference schemes for semilinear parabolic systems the general alternating schemes with intrinsic parallelism for semilinear parabolic systems are studied first we prove the a priori estimates in the discrete h 1 space of the difference solution for these schemes then the existence of the difference solution for these schemes follows from the fixed point principle finally the unconditional stability of the general alternating schemes is proved the alternating group explicit scheme the alternating segment explicit implicit scheme and the alternating segment crank nicolson scheme are the special cases of the general alternating schemes

explicit implicit conservative domain decomposition procedures for parabolic problems based on block centered finite differences domain decomposition procedures for solving parabolic equations are considered the underlying discretization consists of block centered finite differences in these procedures fluxes at subdomain interfaces are calculated from the solution at the previous time level these fluxes serve as neumann boundary data for implicit block centered discretizations in the subdomains a priori error estimates are presented and numerical results examining the stability accuracy and parallelism of the scheme are presented

snapback repellers and homoclinic orbits for multi dimensional maps abstract marotto extended li yorke s theorem on chaos from one dimension to multi dimension through introducing the notion of snapback repeller in 1978 due to a technical flaw he redefined snapback repeller in 2005 to validate this theorem this presentation provides two methodologies to facilitate the application of marotto s theorem the first one is to estimate the radius of repelling neighborhood for a repelling fixed point this estimation is of essential and practical significance as combined with numerical computations of snapback points secondly we propose a sequential graphic iteration scheme to construct homoclinic orbit for a repeller this construction allows us to track the homoclinic orbit applications of the present methodologies with numerical computation to a chaotic neural network and a predator prey model are demonstrated

the new mass conserving s ddm scheme for two dimensional parabolic equations with variable coefficients abstract in the article a new and efficient mass conserving operator splitting domain decomposition method s ddm is proposed and analyzed for solving two dimensional variable coefficient parabolic equations with reaction term the domain is divided into multiple non overlapping block divided subdomains on each block divided subdomain the interface fluxes are first computed explicitly by local multi point weighted schemes and the solutions in the interior of subdomain are computed by the one directional operator splitting implicit schemes at each time step the scheme is proved to satisfy mass conservation over the whole domain of domain decomposition by combining with some auxiliary lemmas and applying the energy method we analyze theoretically the stability of our scheme and prove it to have second order accuracy in space step in the l2 norm numerical experiments are performed to illustrate its accuracy conservation stability efficiency and parallelism our scheme not only keeps the excellent advantages of the non overlapping domain decomposition and the operator splitting technique but also preserves the global mass

difference graphs of block adi method the block alternating direction implicit adi method is the parallelization of the well known adi method which is suitable for the distributed memory multiprocessors with a minimal cost of communications the difference graphs of the block adi method are introduced in this paper and a general procedure is obtained to design a block adi method and at the same time a new proof of unconditional stability of the block adi method is given

finite time non fragile passivity control for neural networks with time varying delay abstract in this paper the problem of finite time non fragile passivity control for neural networks with time varying delay is studied we construct a new lyapunov krasovskii function with triple and four integral terms and then utilizing wirtinger type inequality technique the sufficient conditions for finite time boundedness and finite time passivity are derived furthermore a non fragile state feedback controller is designed such that the closed loop system is finite time passive moreover the proposed sufficient conditions can be simplified into the form of linear matrix inequalities lmis using matlab lmi toolbox finally three numerical examples are presented to illustrate the effectiveness of the proposed criteria

breathers in nonlinear lattices existence linear stability and quantization abstract it has been proved by the principle of anti integrable limit renamed here anti continuous limit and the implicit function theorem that under rather weak hypotheses there exist spatially localized and time periodic solutions breathers in arrays of nonlinear coupled classical oscillators provided the coupling is not too strong the models can be translationally invariant or not and be of any dimension there are also time periodic solutions corresponding to arbitrary distributions on the lattice of such solutions multibreathers the whole set of these solutions can be labeled by a discrete coding sequence the condition that the frequency of the breather or multibreather solution has no harmonics in the phonon spectrum can be discarded for a large subset of spatially extended time periodic solutions called phonobreather which correspond to special codes which can be also spatially chaotic and where no oscillator is at rest these results extend almost without change to models with coupled rotors the existence of rotobreathers which are exact solutions consisting of a single rotor rotating while the other rotors oscillate is proved there are also multirotobreather solutions and phono rotobreathers etc it is also shown that the phase of the single breathers constituting a multibreather or multirotobreather solution can be submitted to a phase torsion these new dynamical structures carry a nonzero energy flow in models with two dimensions and more the phase torsion of multibreather solutions can generate new dynamical solutions with vortices in the energy flow the dynamics of a quantum electron coupled to a classical lattice is also studied within the same approach from the anti continuous limit the existence of two kinds of polarobreathers which are spatially exponentially localized dynamical solutions is proved for a small enough electronic transfer integral the polarobreathers of the first kind include the standard static polaron the lattice configuration is static time independent when the electron is in an excited state i e the electronic oscillator oscillates periodically they can be spatially chaotic a polarobreather of the second kind corresponds to a localized periodic lattice oscillation associated with a localized quasiperiodic electronic oscillation the most simple of these solutions are those for which both the lattice oscillation and the electron wave function are mostly concentrated close to the same single site the standard floquet analysis of the linear stability of the breather and multibreather solutions is shown to be related with the band spectrum property of the newton operator involved in the implicit function theorem the krein theory of bifurcations is reinterpreted from this point of view the linear stability of the single breather and rotobreather solutions is then proved at least at small enough coupling finally it is shown that in the quantum version of translationally invariant classical models where there cannot exist in principle any strictly localized excitation there are narrow bands of excitations consisting of bound states of many bosons which are the quantum counterpart of the classical breathers the bandwidth of these excitations goes exponentially to zero with the number of bound phonons this theory provides simultaneously existence theorems and a new powerful and accurate numerical method for calculating practically any of the solutions which has been formally predicted to exist these numerical applications are currently written elsewhere

stabilization role of inhibitory self connections in a delayed neural network abstract in a delayed hopfield neural network that is strongly connected with non inhibitory interconnections fast and inhibitory self connections lead to global convergence to a unique equilibrium of the network by applying monotone dynamical systems theory and an embedding technique we prove that this conclusion remains true without the requirement of strong connectivity or non inhibitory interconnections

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

chaotic trajectories in the standard map the concept of anti integrability a rigorous proof is given in the standard map associated with a frenkel kontorowa model for the existence of chaotic trajectories with unbounded momenta for large enough coupling constant k k0 these chaotic trajectories with finite entropy per site are coded by integer sequences mi such that the sequence bi mi 1 mi 1 2mi be bounded by some integer b the bound k0 in k depends on b and can be lowered for coding sequences mi fulfilling more restrictive conditions the obtained chaotic trajectories correspond to stationary configurations of the frenkel kontorowa model with a finite non zero photon gap called gap parameter in dimensionless units this property implies that the trajectory or the configuration ui can be uniquely continued as a uniformly continuous function of the model parameter k in some neighborhood of the initial configuration a non zero gap parameter implies that the lyapunov coefficient is strictly positive when it is defined in addition the existence of dilating and contracting manifolds is proven for these chaotic trajectories exotic trajectories such as ballistic trajectories are also proven to exist as a consequence of these theorems the concept of anti integrability emerges from these theorems in the anti integrable limit which can be only defined for a discrete time dynamical system the coordinates of the trajectory at time i do not depend on the coordinates at time i 1 thus at this singular limit the existence of chaotic trajectories is trivial and the dynamical system reduces to a bernoulli shift it is well known that the kam tori of symplectic dynamical originates by continuity from the invariant tori which exists in the integrible limit under certain conditions in a similar way it appears that the chaotic trajectories of dynamical systems originate by continuity from those which exists at the anti integrable limits also under certain conditions

conservative domain decomposition procedure with unconditional stability and second order accuracy a new derivation of the conservative domain decomposition procedure for solving the parabolic equation is presented in this procedure fluxes at subdomain interfaces are calculated from the solution at the previous time level then these fluxes serve as neumann boundary data for implicit block centered discretization in the subdomain the unconditional stability and the second order accuracy of solution values as well as fluxes are proved numerical results examining the stability accuracy and parallelism of the procedure are also presented

invariant circles for the piecewise linear standard map we investigate invariant circles for a one parameter family of piecewise linear twist homeomorphisms of the annulus we show that invariant circles of all types and rotation numbers occur and we classify them into families we compute parameter ranges in which there are no invariant circles

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

chaotifying linear elman networks a linear model of recurrent neural networks called the elman networks is combined with the simple nonlinear modulo mod operation on its linear activated function so as to generate chaos purposely conditions on the weight matrix are obtained under which the generated chaos satisfies the mathematical definition of chaos in the sense of t y li and j a yorke 1975 some simple and representative weight matrices are constructed for designing such elman networks that can generate li yorke chaos several numerical simulations are shown to verify and visualize the design

detection of synchronization between chaotic signals an adaptive similarity based approach we present an adaptive similarity based approach to detect generalized synchronization gs with n m phase synchronization ps where n and m are integers and one of them is 1 this approach is based on the similarity index si and gaussian mixture model with the minimum description length criterion the clustering method which is shown to be superior to the closeness and connectivity of a continuous function is employed in this study to detect the existence of gs with n m ps we conducted a computer simulation and a finger lifting experiment to illustrate the effectiveness of the proposed method in the simulation of a rossler lorenz system our method outperformed the conventional si and gs with 2 1 ps within the coupled system was found in the experiment of self paced finger lifting movement cortico muscular gs with 1 2 and 1 3 ps was found between the surface electromyogram signals on the first dorsal interossei muscle and the magnetoencephalographic data in the motor area the gs with n m ps n or m 1 has been simultaneously resolved from both simulation and experiment the proposed approach thereby provides a promising means for advancing research into both nonlinear dynamics and brain science

chaos in non linear sampled data control systems in this paper sufficient conditions for chaos in non linear sampled data control systems are investigated by applying marotto s 1978 theorem and shiraiwa and kurata s 1980 theorem it is shown

dual information representation with stable firing rates and chaotic spatiotemporal spike patterns in a neural network model although various means of information representation in the cortex have been considered the fundamental mechanism for such representation is not well understood the relation between neural network dynamics and properties of information representation needs to be examined we examined spatial pattern properties of mean firing rates and spatiotemporal spikes in an interconnected spiking neural network model we found that whereas the spatiotemporal spike patterns are chaotic and unstable the spatial patterns of mean firing rates spmfr are steady and stable reflecting the internal structure of synaptic weights interestingly the chaotic instability contributes to fast stabilization of the spmfr findings suggest that there are two types of network dynamics behind neuronal spiking internally driven dynamics and externally driven dynamics when the internally driven dynamics dominate spikes are relatively more chaotic and independent of external inputs the spmfr are steady and stable when the externally driven dynamics dominate the spiking patterns are relatively more dependent on the spatiotemporal structure of external inputs these emergent properties of information representation imply that the brain may adopt a dual coding system recent experimental data suggest that internally driven and externally driven dynamics coexist and work together in the cortex

recurrent neural network as a linear attractor for pattern association we propose a linear attractor network based on the observation that similar patterns form a pipeline in the state space which can be used for pattern association to model the pipeline in the state space we present a learning algorithm using a recurrent neural network a least squares estimation approach utilizing the interdependency between neurons defines the dynamics of the network the region of convergence around the line of attraction is defined based on the statistical characteristics of the input patterns performance of the learning algorithm is evaluated by conducting several experiments in benchmark problems and it is observed that the new technique is suitable for multiple valued pattern association

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

delay dependent state estimation for delayed neural networks in this letter the delay dependent state estimation problem for neural networks with time varying delay is investigated a delay dependent criterion is established to estimate the neuron states through available output measurements such that the dynamics of the estimation error is globally exponentially stable the proposed method is based on the free weighting matrix approach and is applicable to the case that the derivative of a time varying delay takes any value an algorithm is presented to compute the state estimator finally a numerical example is given to demonstrate the effectiveness of this approach and the improvement over existing ones

splitting of separatrices for standard and semistandard mappings abstract we investigate chirikov s standard mapping which is a model for the onset of nonintegrability in nonlinear hamiltonian systems the asymptotic formula when the deviation from an integrable system is small for the angle of intersection of separatrices at a homoclinic point is derived on the basis of approximation by the green percival semistandard mapping in the complex domain computed data on the splitting of separatrices for the semi standard map are presented from which we derive the pre exponential coefficient in the formula for splitting of separatrices in the standard mapping

splitting of separatrices and symbolic dynamics for some degenerate standard like maps we consider standard like maps of class c1 with parabolic fixed points and such that the second derivative has a jump discontinuity at the fixed points an asymptotic formula for the splitting of the separatrices is obtained the structure of certain chaotic set in the stochastic layer around the separatrices is described in terms of symbolic dynamics it turns out in particular that swinging and rotating regimes of motion may alternate in time arbitrarily analogous results are stated for the so called separatrix mapping and for the more smooth standard like maps

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

recurrent neural nets as dynamical boolean systems with application to associative memory discrete time discrete state recurrent neural networks are analyzed from a dynamical boolean systems point of view in order to devise new analytic and design methods for the class of both single and multilayer recurrent artificial neural networks with the proposed dynamical boolean systems analysis we are able to formulate necessary and sufficient conditions for network stability which are more general than the well known but restrictive conditions for the class of single layer networks 1 symmetric weight matrix with 2 positive diagonal and 3 asynchronous update in terms of design we use a dynamical boolean systems analysis to construct a high performance associative memory with this boolean memory we can guarantee that all fundamental memories are stored and also guarantee the size of the basin of attraction for each fundamental memory

an efficient characteristic finite difference s ddm scheme for convection diffusion equations abstract in this paper an efficient splitting domain decomposition method scheme for solving time dependent convection diffusion reaction equations is analyzed a three step method along each direction is used to solve the solution over each block divided sub domain at every time interval the new solutions are firstly solved by the quadratic interpolation then the intermediate fluxes on the interfaces of sub domains are computed by local multi point weighted average from the new solutions lastly the solutions and fluxes in the interiors of sub domains are computed by the splitting implicit characteristic difference method by some auxiliary lemmas and the defined intermediate exact solution the stability and error estimate are given in discrete l 2 norm we further prove that our scheme is of second order convergence in space and of first order convergence in time numerical experiments are presented to validate theoretical result

optimization via intermittency with a self organizing neural network one of the major obstacles in using neural networks to solve combinatorial optimization problems is the convergence toward one of the many local minima instead of the global minima in this letter we propose a technique that enables a self organizing neural network to escape from local minima by virtue of the intermittency phenomenon it gives rise to novel search dynamics that allow the system to visit multiple global minima as meta stable states numerical experiments performed suggest that the phenomenon is a combined effect of kohonen type competitive learning and the iterated softmax function operating near bifurcation the resultant intermittent search exhibits fractal characteristics when the optimization performance is at its peak in the form of 1 f signals in the time evolution of the cost as well as power law distributions in the meta stable solution states then queens problem is used as an example to illustrate the meta stable convergence process that sequentially generates in a single run 92 solutions to the 8 queens problem and 4024 solutions to the 17 queens problem

large memory capacity in chaotic artificial neural networks a view of the anti integrable limit in the literature it was reported that the chaotic artificial neural network model with sinusoidal activation functions possesses a large memory capacity as well as a remarkable ability of retrieving the stored patterns better than the conventional chaotic model with only monotonic activation functions such as sigmoidal functions this paper from the viewpoint of the anti integrable limit elucidates the mechanism inducing the superiority of the model with periodic activation functions that includes sinusoidal functions particularly by virtue of the anti integrable limit technique this paper shows that any finite dimensional neural network model with periodic activation functions and properly selected parameters has much more abundant chaotic dynamics that truly determine the model s memory capacity and pattern retrieval ability to some extent this paper mathematically and numerically demonstrates that an appropriate choice of the activation functions and control scheme can lead to a large memory capacity and better pattern retrieval ability of the artificial neural network models

cycle symmetric matrices and convergent neural networks abstract this work investigates a class of neural networks with cycle symmetric connection strength we shall show that by changing the coordinates the convergence of dynamics by fiedler and gedeon physica d 111 1998 288 is equivalent to the classical results this presentation also addresses the extension of the convergence theorem to other classes of signal functions with saturations in particular the result of cohen and grossberg ieee trans syst man cybernet smc 13 1983 815 is recast and extended with a more concise verification

efficient parallel algorithms for parabolic problems domain decomposition algorithms for parallel numerical solution of parabolic equations are studied for steady state or slow unsteady computation implicit schemes are used in order to march with large time steps parallelization is realized by approximating interface values using explicit computation various techniques are examined including a multistep second order explicit scheme and a one step high order scheme we show that the resulting schemes are of second order global accuracy in space and stable in the sense of osher or in l infty they are optimized with respect to the parallel efficiency

robust stability for interval hopfield neural networks with time delay the conventional hopfield neural network with time delay is intervalized to consider the bounded effect of deviation of network parameters and perturbations yielding a novel interval dynamic hopfield neural network idhnn model a sufficient condition related to the existence of unique equilibrium point and its robust stability is derived

global stability for cellular neural networks with time delay a sufficient condition related to the existence of a unique equilibrium point and its global asymptotic stability for cellular network networks with delay dcnns is derived it is shown that the condition relies on the feedback matrices and is independent of the delay parameter furthermore this condition is less restrictive than that given in the literature

routes to chaos in high dimensional dynamical systems a qualitative numerical study this paper examines the most probable route to chaos a high dimensional dynamical systems function space time delay neural networks endowed with a probability measure in a computational setting the most probable route to chaos relative to the measure we impose on the function space as the dimension is increased is observed to be a sequence of neimark sacker bifurcations into chaos the analysis is composed of the study of an example dynamical system followed by a probabilistic study of the ensemble of dynamical systems from which the example was drawn a scenario depicting the decoupling of the stable manifolds of the torus leading up to the onset of chaos in high dimensional dissipative dynamical systems is also presented c 2006 elsevier b v all rights reserved

a class of convergent neural network dynamics abstract we consider a class of systems of differential equations in r n which exhibits convergent dynamics we find a lyapunov function and show that every bounded trajectory converges to the set of equilibria our result generalizes the results of cohen and grossberg 1983 for convergent neural networks it replaces the symmetry assumption on the matrix of weights by the assumption on the structure of the connections in the neural network we prove the convergence result also for a large class of lotka volterra systems these are naturally defined on the closed positive orthant we show that there are no heteroclinic cycles on the boundary of the positive orthant for the systems in this class

analysis of mean field annealing in substactive interference cancellation in this contribution we derive the cost function corresponding to the linear complexity subtractive interference cancellation with tangent hyperbolic tentative decisions we use the cost function to analyse the fix points of solving the subtractive interference cancellation equations the analysis show that we can control the slope of the tangent hyperbolic functions so that the corresponding cost function is convex we also show that increasing the slope can make the cost non convex going from the convex regime into the non convex regime we prove that the bifurcation of the fix points for non singular signal correlation matrices consist of the fix point of interest together with a saddle node bifurcation this proves that tracking the solution from low slopes with a convex cost gradually increasing to higher slopes with non convex cost can bring us to the best solution being very close to the optimal determined by enumeration this tracking is the idea behind annealing we show monte carlo studies with a substantial signal to noise ratio gain compared to not using annealing we also show how annealing can be used to increase capacity at a given target bit error rate in fact this capacity gain is the same obtained by improved parallel interference cancellation making us believe that the latter includes a mechanism to avoid local minima similar to annealing

exponential rm h _ infty synchronization of general discrete time chaotic neural networks with or without time delays this brief studies exponential h synchronization of a class of general discrete time chaotic neural networks with external disturbance on the basis of the drive response concept and h control theory and using lyapunov krasovskii or lyapunov functional state feedback controllers are established to not only guarantee exponential stable synchronization between two general chaotic neural networks with or without time delays but also reduce the effect of external disturbance on the synchronization error to a minimal h norm constraint the proposed controllers can be obtained by solving the convex optimization problems represented by linear matrix inequalities most discrete time chaotic systems with or without time delays such as hopfield neural networks cellular neural networks bidirectional associative memory networks recurrent multilayer perceptrons cohen grossberg neural networks chua s circuits etc can be transformed into this general chaotic neural network to be h synchronization controller designed in a unified way finally some illustrated examples with their simulations have been utilized to demonstrate the effectiveness of the proposed methods

the efficient s ddm scheme and its analysis for solving parabolic equations abstract in this paper we develop and analyze the efficient splitting domain decomposition method for solving parabolic equations the domain is divided into non overlapping multi block subdomains on interfaces of sub domains the local multilevel explicit scheme is proposed to solve the interface values of solution and then the splitting implicit scheme is proposed to solve the solution in interiors of subdomains on the theoretical aspect analyzing the s ddm scheme over non overlapping multi block sub domains is much challenging we strictly prove the stability and convergence of the s ddm scheme and obtain the optimal error estimates over non overlapping multi block subdomains numerical experiments are given to illustrate the accuracy and efficiency of the s ddm scheme the developed method takes the most attractive advantages of both the non overlapping domain decomposition and the splitting technique which overcomes the limitation of the stripe divided sub domains for parabolic equations in the previous methods the developed s ddm scheme reduces computational complexities large memory requirements and computational costs

analysis of complete stability for discrete time cellular neural networks with piecewise linear output functions this letter discusses the complete stability of discrete time cellular neural networks with piecewise linear output functions under the assumption of certain symmetry on the feedback matrix a sufficient condition of complete stability is derived by finite trajectory length because the symmetric conditions are not robust the complete stability of networks may be lost under sufficiently small perturbations the robust conditions of complete stability are also given for discrete time cellular neural networks with multiple equilibrium points and a unique equilibrium point these complete stability results are robust and available

a novel chaotic neural network with the ability to characterize local features and its application to provide an ability to characterize local features for the chaotic neural network cnn gauss wavelet is used for the self feedback of the cnn with the dilation parameter acting as the bifurcation parameter the exponentially decaying dilation parameter and the chaotically varying translation parameter not only govern the wavelet self feedback transform but also enable the cnn to generate complex dynamics behavior preventing the network from being trapped in the local minima analysis of the energy function of the cnn indicates that the local characterization ability of the proposed cnn is effectively provided by the wavelet self feedback in the manner of inverse wavelet transform and that the proposed cnn can achieve asymptotical stability the experimental results on traveling salesman problem tsp suggest that the proposed cnn has a higher average success rate for obtaining globally optimal or near optimal solutions

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

resonances and transport in the sawtooth map we study transport in a completely chaotic hamiltonian system the hyperbolic sawtooth map analytical expressions are obtained for its cantori and resonances we show that resonances give a complete partition of phase space the flux leaking out of a resonance is given by its turnstiles whose form and areas are obtained analytically when the total flux out of a resonance becomes one third the area of an island the topology of the turnstiles changes at the same parameter value a horseshoe is formed corresponding to the orbits trapped within the resonance based on this a coding scheme for the trapped orbits is introduced and expressions for trapped ordered orbits are obtained the partial flux transferred from one resonance to another is determined by the degree of overlap of their turnstiles we calculate the survival probability within a resonance using the markov model the results are compared with results obtained numerically and from periodic orbit theory

unconditional stability of alternating difference schemes with intrinsic parallelism for two dimensional fourth order diffusion equation in this paper the parallel difference schemes for parabolic equation are studied the general alternating difference schemes with intrinsic parallelism for two dimensional fourth order diffusion equation are presented and proved to be unconditionally stable by the energy method two kinds of alternating band explicit abe1 abe2 schemes alternating band explicit implicit abe i scheme and alternating band crank nicolson abc n scheme are the special cases of the general schemes constructed here numerical experiments are performed to examine the accuracy and unconditional stability

binary partitioning perceptual grouping and restoration with semidefinite programming we introduce a novel optimization method based on semidefinite programming relaxations to the field of computer vision and apply it to the combinatorial problem of minimizing quadratic functionals in binary decision variables subject to linear constraints the approach is tuning parameter free and computes high quality combinatorial solutions using interior point methods convex programming and a randomized hyperplane technique apart from a symmetry condition no assumptions such as metric pairwise interactions are made with respect to the objective criterion as a consequence the approach can be applied to a wide range of problems applications to unsupervised partitioning figure ground discrimination and binary restoration are presented along with extensive ground truth experiments from the viewpoint of relaxation of the underlying combinatorial problem we show the superiority of our approach to relaxations based on spectral graph theory and prove performance bounds

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

mean field equations bifurcation map and route to chaos in discrete time neural networks abstract we investigate the dynamical behaviour of neural networks with asymmetric synaptic weights in the presence of random thresholds we inspect low gain dynamics before using mean field equations to study the bifurcations of the fixed points and the change of regime that occurs when varying control parameters we infer different areas with various regimes summarized by a bifurcation map in the parameter space we numerically show the occurence of chaos that arises generically by a quasi periodicity route we then discuss some features of our system in relation with biological observations such as low firing rates and refractory periods

a finite difference domain decomposition algorithm for numerical solution of the heat equation a domain decomposition algorithm for numerically solving the heat equation in one and two space dimensions is presented in this procedure interface values between subdomains are found by an explicit finite difference formula once these values are calculated interior values are determined by backward differencing in time a natural extension of this method allows for the use of different time steps in different subdomains maximum norm error estimates for these procedures are derived which demonstrate that the error incurred at the interfaces is higher order in the discretization parameters

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

bogdanov takens singularity in tri neuron network with time delay this brief reports a retarded functional differential equation modeling tri neuron network with time delay the bogdanov takens b t bifurcation is investigated by using the center manifold reduction and the normal form method we get the versal unfolding of the norm forms at the b t singularity and show that the model can exhibit pitchfork hopf homoclinic and double limit cycles bifurcations some numerical simulations are given to support the analytic results and explore chaotic dynamics finally an algorithm is given to show that chaotic tri neuron networks can be used for encrypting a color image