bifurcation analysis on a survival red blood cells model in this paper we consider a model described the survival of red blood cells in animal its dynamics are studied in terms of local and global hopf bifurcations we show that a sequence of hopf bifurcations occur at the positive equilibrium as the delay crosses some critical values using the reduced system on the center manifold we also obtain that the periodic orbits bifurcating from the positive equilibrium are stable in the center manifold and all hopf bifurcations are supercritical further particular attention is focused on the continuation of local hopf bifurcation we show that global hopf bifurcations exist after the second critical value of time delay

bifurcations for a predator prey system with two delays in this paper a predator prey system with two delays is investigated by choosing the sum of two delays as a bifurcation parameter we show that hopf bifurcations can occur as crosses some critical values by deriving the equation describing the flow on the center manifold we can determine the direction of the hopf bifurcations and the stability of the bifurcating periodic solutions in addition special attention is paid to the global continuation of local hopf bifurcations using a global hopf bifurcation result of j wu symmetric functional differential equations and neural networks with memory trans amer math soc 350 1998 4799 4838 we may show the global existence of periodic solutions

bifurcation analysis on a two neuron system with distributed delays abstract a general two neuron model with distributed delays is studied in this paper its local linear stability is analyzed by using the routh hurwitz criterion if the mean delay is used as a bifurcation parameter we prove that hopf bifurcation occurs for a weak kernel this means that a family of periodic solutions bifurcates from the equilibrium when the bifurcation parameter exceeds a critical value the direction and stability of the bifurcating periodic solutions are determined by the normal form theory and the center manifold theorem some numerical simulations for justifying the theoretical analysis are also given

rates of convergence for a class of global stochastic optimization algorithms inspired and motivated by the recent advances in simulated annealing algorithms this paper analyzes the convergence rates of a class of recursive algorithms for global optimization via monte carlo methods by using perturbed liapunov function methods stability results of the algorithms are established then the rates of convergence are ascertained by examining the asymptotic properties of suitably scaled estimation error sequences

on bendixson s criterion abstract for autonomous differential equations in r n criteria are developed which preclude the existence of invariant closed curves such as periodic or homoclinic trajectories the technique is based on the study of functionals on 2 surfaces results generalize to higher dimensions a criterion of bendixson for the nonexistence of nonconstant periodic solutions in the case n 2 as an example an application to the lorenz system in r 3 is given

cooling schedules for optimal annealing a monte carlo optimization technique called simulated annealing is a descent algorithm modified by random ascent moves in order to escape local minima which are not global minima the level of randomization is determined by a control parameter t called temperature which tends to zero according to a deterministic cooling schedule we give a simple necessary and sufficient condition on the cooling schedule for the algorithm state to converge in probability to the set of globally minimum cost states in the special case that the cooling schedule has parametric form tt c log1 t the condition for convergence is that c be greater than or equal to the depth suitably defined of the deepest local minimum which is not a global minimum state

distributed representation of geometrically correlated images with compressed linear measurements this paper addresses the problem of distributed coding of images whose correlation is driven by the motion of objects or the camera positioning it concentrates on the problem where images are encoded with compressed linear measurements we propose a geometry based correlation model that describes the common information in pairs of images we assume that the constitutive components of natural images can be captured by visual features that undergo local transformations e g translation in different images we first identify prominent visual features by computing a sparse approximation of a reference image with a dictionary of geometric basis functions we then pose a regularized optimization problem in order to estimate the corresponding features in correlated images that are given by quantized linear measurements the correlation model is thus given by the relative geometric transformations between corresponding features we then propose an efficient joint decoding algorithm that reconstructs the compressed images such that they are consistent with both the quantized measurements and the correlation model experimental results show that the proposed algorithm effectively estimates the correlation between images in multiview data sets in addition the proposed algorithm provides effective decoding performance that advantageously compares to independent coding solutions and state of the art distributed coding schemes based on disparity learning

bifurcations stability and monotonicity properties of a delayed neural network model abstract a delay differential equation modelling an artificial neural network with two neurons is investigated a linear stability analysis provides parameter values yielding asymptotic stability of the stationary solutions these can lose stability through either a pitchfork or a hopf bifurcation which is shown to be supercritical at appropriate parameter values an interaction takes place between the pitchfork and hopf bifurcations conditions are also given for the set of initial conditions that converge to a stable stationary solution to be open and dense in the functional phase space analytic results are illustrated with numerical simulations

hopf bifurcation and stability for a delayed tri neuron network model a neural network model with three neurons and a single time delay is considered its linear stability is investigated and hopf bifurcations are demonstrated by analyzing the corresponding characteristic equation in particular the explicit formulae determining the stability and the direction of periodic solutions bifurcating from hopf bifurcations are obtained by applying the normal form theory and the center manifold theorem in order to illustrate our theoretical analysis some numerical simulations are also included in the end

synchronized hopf bifurcation analysis in a neural network model with delays we consider the synchronized periodic oscillation in a ring neural network model with two different delays in self connection and nearest neighbor coupling employing the center manifold theorem and normal form method introduced by hassard et al we give an algorithm for determining the hopf bifurcation properties using the global hopf bifurcation theorem for fde due to wu and bendixson s criterion for high dimensional ode due to li and muldowney we obtain several groups of conditions that guarantee the model have multiple synchronized periodic solutions when the transfer coefficient or time delay is sufficiently large

global stochastic optimization with low dispersion point sets this study concerns a generic model free stochastic optimization problem requiring the minimization of a risk function defined on a given bounded domain in a euclidean space smoothness assumptions regarding the risk function are hypothesized and members of the underlying space of probabilities are presumed subject to a large deviation principle however the risk function may well be nonconvex and multimodal a general approach to finding the risk minimizer on the basis of decision observation pairs is proposed it consists of repeatedly observing pairs over a collection of design points principles are derived for choosing the number of these design points on the basis of an observation budget and for allocating the observations between these points in both prescheduled and adaptive settings on the basis of these principles large deviation type bounds of the minimizer in terms of sample size are established

s1 degree and global hopf bifurcation theory of functional differential equations abstract the recently developed s 1 degree and bifrucation theory are applied to provide a purely topological argument of a global hopf bifurcation theory for functional differential equations of mixed type in the special case where the equation is of retarded type the established result represents an analog of alexander and yorke s global hopf bifurcation theorem which has been obtained by chow fiedler mallet paret and nussbaum using different approaches

slowly oscillating periodic solutions for a delayed frustrated network of two neurons in this article we study a delayed frustrated network of two neurons we obtain a two dimensional closed disk bordered by a slowly oscillating periodic orbit and we give a complete description about the dynamics of the flow restricted to this closed disk

weighted means in stochastic approximation of minima weighted averages of kiefer wolfowitz type procedures which are driven by larger step lengths than usual can achieve the optimal rate of convergence a priori knowledge of a lower bound on the smallest eigenvalue of the hessian matrix is avoided the asymptotic mean squared error of the weighted averaging algorithm is the same as would emerge using a newton type adaptive algorithm several different gradient estimates are considered one of them leads to a vanishing asymptotic bias this gradient estimate applied with the weighted averaging algorithm usually yields a better asymptotic mean squared error than applied with the standard algorithm

global existence of periodic solutions in a tri neuron network model with delays we consider a delayed differential system that models a network of three neurons with memory using a global hopf bifurcation theorem for fde due to j wu and a bendixson s criterion for high dimensional ode due to li and muldowney we obtain a group of sufficient conditions for the system to have multiple periodic solutions when the sum of delays is sufficiently large

local hopf bifurcation and global periodic solutions in a delayed predator prey system abstract we consider a delayed predator prey system we first consider the existence of local hopf bifurcations and then derive explicit formulas which enable us to determine the stability and the direction of periodic solutions bifurcating from hopf bifurcations using the normal form theory and center manifold argument special attention is paid to the global existence of periodic solutions bifurcating from hopf bifurcations by using a global hopf bifurcation result due to wu trans amer math soc 350 1998 4799 we show that the local hopf bifurcation implies the global hopf bifurcation after the second critical value of delay finally several numerical simulations supporting the theoretical analysis are also given

asymptotic global behavior for stochastic approximation and diffusions with slowly decreasing noise effects global minimization via monte carlo the asymptotic behavior of the systems x n 1 x n a n b x n xi n a n sigma x n psi n and dy bar b y dt sqrt a t sigma y dw is studied where psi n is i i d gaussian xi n is a correlated bounded sequence of random variables and a n approx a 0 log a 1 n without xi n such algorithms are versions of the simulated annealing method for global optimization when the objective function values can only be sampled via monte carlo the discrete algorithm is a combination of stochastic approximation and simulated annealing our forms are appropriate the psi n are the annealing variables and xi n is the sampling noise for large a 0 a full asymptotic analysis is presented via the theory of large deviations mean escape time after arbitrary time n from neighborhoods of stable sets of the algorithm mean transition times after arbitrary time n from a neighborhood of one stable set to another a

delay induced periodicity in a neural netlet of excitation and inhibition abstract the dynamical behaviour of a two neuron netlet of excitation and inhibition with a transmission delay is investigated it is shown that in the absence of delay the netlet relaxes to the trivial resting state if the delay is of sufficient magnitude the network is excited to a temporally periodic cyclic behaviour the analytical mechanism for the onset of cyclic behaviour is through a hopf type bifurcation approximate solusions to the periodic output of the netlet is calculated stability of the temporally periodic cycle is investigated it is shown that the bifurcation is supercritical a related discrete version of the continuous time system is formulated it is found that the discrete system also displays a cyclic behaviour results of a number of computer simulations are displayed graphically the article concludes with a brief neurobiological discussion

bifurcation and global periodic solutions in a delayed facultative mutualism system abstract a facultative mutualism system with a discrete delay is considered by analyzing the associated characteristic equation its linear stability is investigated and hopf bifurcations are demonstrated some explicit formulae are obtained by applying the normal form theory and center manifold reduction such formulae enable us to determine the stability and the direction of the bifurcating periodic solutions bifurcating from hopf bifurcations furthermore a global hopf bifurcation result due to wu j wu symmetric functional differential equations and neural networks with memory trans amer math soc 350 1998 4799 4838 is employed to study the global existence of periodic solutions it is shown that the local hopf bifurcation implies the global hopf bifurcation after the third critical value 1 1 of delay finally numerical simulations supporting the theoretical analysis are given

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

a simulated annealing algorithm with constant temperature for discrete stochastic optimization we present a modification of the simulated annealing algorithm designed for solving discrete stochastic optimization problems like the original simulated annealing algorithm our method has the hill climbing feature so it can find global optimal solutions to discrete stochastic optimization problems with many local solutions however our method differs from the original simulated annealing algorithm in that it uses a constant rather than decreasing temperature we consider two approaches for estimating the optimal solution the first approach uses the number of visits the algorithm makes to the different states divided by a normalizer to estimate the optimal solution the second approach uses the state that has the best average estimated objective function value as estimate of the optimal solution we show that both variants of our method are guaranteed to converge almost surely to the set of global optimal solutions and discuss how our work applies in the discrete deterministic optimization setting we also show how both variants can be applied for solving discrete optimization problems when the objective function values are estimated using either transient or steady state simulation finally we include some encouraging numerical results documenting the behavior of the two variants of our algorithm when applied for solving two versions of a particular discrete stochastic optimization problem and compare their performance with that of other variants of the simulated annealing algorithm designed for solving discrete stochastic optimization problems

global random optimization by simultaneous perturbation stochastic approximation we examine the theoretical and numerical global convergence properties of a certain ldquogradient freerdquo stochastic approximation algorithm called the ldquosimultaneous perturbation stochastic approximation spsa rdquo that has performed well in complex optimization problems we establish two theorems on the global convergence of spsa the first involving the well known method of injected noise the second theorem establishes conditions under which ldquobasicrdquo spsa without injected noise can achieve convergence in probability to a global optimum a result with important practical benefits

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

annealing of iterative stochastic schemes annealing of general iterative stochastic schemes is studied by using wentzell s large deviation theory the convergence of this algorithm is shown under some conditions the closed form of the critical constant is specified in terms of its potential function of the mean model

attractivity multistability and bifurcation in delayed hopfieldʼs model with non monotonic feedback abstract for a system of delayed neural networks of hopfield type we deal with the study of global attractivity multistability and bifurcations in general we do not assume monotonicity conditions in the activation functions for some architectures of the network and for some families of activation functions we get optimal results on global attractivity our approach relies on a link between a system of functional differential equations and a finite dimensional discrete dynamical system for it we introduce the notion of strong attractor for a discrete dynamical system which is more restrictive than the usual concept of attractor when the dimension of the system is higher than one our principal result shows that a strong attractor of a discrete map gives a globally attractive equilibrium of a corresponding system of delay differential equations our abstract setting is not limited to applications in systems of neural networks we illustrate its use in an equation with distributed delay motivated by biological models we also obtain some results for neural systems with variable coefficients

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

diffusion for global optimization in r n we seek a global minimum of u mathbb r n to mathbb r the solution to d dt x t nabla u x t will find local minima using the idea of simulated annealing we consider th

symmetric functional differential equations and neural networks with memory we establish an analytic local hopf bifurcation theorem and a topological global hopf bifurcation theorem to detect the existence and to describe the spatial temporal pattern the asymptotic form and the global continuation of bifurcations of periodic wave solutions for functional differential equations in the presence of symmetry we apply these general results to obtain the coexistence of multiple large amplitude wave solutions for the delayed hopfield cohen grossberg model of neural networks with a symmetric circulant connection matrix

fast approximate energy minimization via graph cuts many tasks in computer vision involve assigning a label such as disparity to every pixel a common constraint is that the labels should vary smoothly almost everywhere while preserving sharp discontinuities that may exist e g at object boundaries these tasks are naturally stated in terms of energy minimization the authors consider a wide class of energies with various smoothness constraints global minimization of these energy functions is np hard even in the simplest discontinuity preserving case therefore our focus is on efficient approximation algorithms we present two algorithms based on graph cuts that efficiently find a local minimum with respect to two types of large moves namely expansion moves and swap moves these moves can simultaneously change the labels of arbitrarily large sets of pixels in contrast many standard algorithms including simulated annealing use small moves where only one pixel changes its label at a time our expansion algorithm finds a labeling within a known factor of the global minimum while our swap algorithm handles more general energy functions both of these algorithms allow important cases of discontinuity preserving energies we experimentally demonstrate the effectiveness of our approach for image restoration stereo and motion on real data with ground truth we achieve 98 percent accuracy

stability and hopf bifurcation analysis on a simplified bam neural network with delays a delay differential equation modelling a bidirectional associative memory bam neural network with three neurons is investigated its dynamics are studied in terms of local analysis and hopf bifurcation analysis by analyzing the associated characteristic equation its linear stability is investigated and hopf bifurcations are demonstrated the stability and direction of the hopf bifurcation are determined by applying the normal form theory and the center manifold reduction numerical simulation results are given to support the theoretical predictions

geometry based distributed scene representation with omnidirectional vision sensors this paper addresses the problem of efficient representation of scenes captured by distributed omnidirectional vision sensors we propose a novel geometric model to describe the correlation between different views of a 3 d scene we first approximate the camera images by sparse expansions over a dictionary of geometric atoms since the most important visual features are likely to be equivalently dominant in images from multiple cameras we model the correlation between corresponding features in different views by local geometric transforms for the particular case of omnidirectional images we define the multiview transforms between corresponding features based on shape and epipolar geometry constraints we apply this geometric framework in the design of a distributed coding scheme with side information which builds an efficient representation of the scene without communication between cameras the wyner ziv encoder partitions the dictionary into cosets of dissimilar atoms with respect to shape and position in the image the joint decoder then determines pairwise correspondences between atoms in the reference image and atoms in the cosets of the wyner ziv image in order to identify the most likely atoms to decode under epipolar geometry constraints experiments demonstrate that the proposed method leads to reliable estimation of the geometric transforms between views in particular the distributed coding scheme offers similar rate distortion performance as joint encoding at low bit rate and outperforms methods based on independent decoding of the different images

dynamics of a delayed two coupled oscillator with excitatory to excitatory connection in this paper we consider a neural network model consisting of two coupled oscillators with delayed feedback and excitatory to excitatory connection we study how the strength of the connections between the oscillators affects the dynamics of the neural network we give a full classification of all equilibria in the parameter space and obtain its linear stability by analyzing the characteristic equation of the linearized system we also investigate the spatio temporal patterns of bifurcated periodic oscillations by using the symmetric bifurcation theory of delay differential equations combined with representation theory of lie groups moreover the stability and bifurcation direction of the bifurcated periodic solutions are obtained by employing center manifold reduction and normal form theory some numerical simulations are provided to illustrate the theoretical results

recursive stochastic algorithms for global optimization in r d an algorithm of the form x k 1 x k a k nabla u x k xi k b k w k where u cdot is a smooth function on mathbb r d xi k is a sequence of mathbb r d valued random variables w k is a sequence of independent standard d dimensional gaussian random variables a k a k and b k sqrt b sqrt k log log k for k large is considered an algorithm of this type arises by adding slowly decreasing white gaussian noise to a stochastic gradient algorithm it is shown under suitable conditions on u cdot xi k a and b that x k converges in probability to the set of global minima of u cdot no prior information is assumed as to what bounded region contains a global minimum the analysis is based on the asymptotic behavior of the related diffusion process dy t nabla u y t dt c t dw t where w cdot is a standard d dimensional wiener process and c t sqrt c sqrt log t for t large

geometric video approximation using weighted matching pursuit in recent years works on geometric multidimensional signal representations have established a close relation with signal expansions on redundant dictionaries for this purpose matching pursuits mp have shown to be an interesting tool recently most important limitations of mp have been underlined and alternative algorithms like weighted mp have been proposed this work explores the use of weighted mp as a new framework for motion adaptive geometric video approximations we study a novel algorithm to decompose video sequences in terms of few salient video components that jointly represent the geometric and motion content of a scene experimental coding results on highly geometric content reflect how the proposed paradigm exploits spatio temporal video geometry two dimensional weighted mp improves the representation compared to those based on 2 d mp furthermore the extracted video components represent relevant visual structures with high saliency in an example application such components are effectively used as video descriptors for the joint audio video analysis of multimedia sequences

on a planar system modelling a neuron network with memory abstract we consider a delay differential equation modelling a network of two neurons with memory the situations without self connections and two delays and with self connections and two equal delays are addressed in terms of local stability and bifurcation analysis in the first case the dynamical behavior is studied by taking one of the delays as the bifurcating parameter namely the hopf bifurcation whose existence was proven in former works occurs as the delay crosses some critical values and is completely described conditions ensuring the stability of the periodic cycles are given when self connections are present hopf and pitchfork bifurcations co exist and the equation describing the flow on the center manifold is derived

minimal instability and unstable set of a phase locked periodic orbit in a delayed neural network abstract the existence of a non trivial phase locked periodic orbit is established for a system of delay differential equations describing the dynamics of networks of two identical saturating neurons we discuss the instability and the unstable manifold of this phase locked orbit in particular we give detailed information about the spectrum of the related monodromy operator and establish the connection between the unstable manifold of the phase locked orbit and the boundary of the global extension of a three dimensional c 1 submanifold of the origin we obtain a smooth solid spindle contained in the global attractor separated by a disk bordered by the phase locked orbit major technical tools include a discrete lyapunov functional invariant manifolds and other recently developed geometric theory of delay differential equations

stability and bifurcation analysis for a delayed lotka volterra predator prey system the present paper deals with a delayed lotka volterra predator prey system by linearizing the equations and by analyzing the locations on the complex plane of the roots of the characteristic equation we find the necessary conditions that the parameters should verify in order to have the oscillations in the system in addition the normal form of the hopf bifurcation arising in the system is determined to investigate the direction and the stability of periodic solutions bifurcating from these hopf bifurcations to verify the obtained conditions a special numerical example is also included

quantization of curvature of harmonic two spheres in grassmann manifolds various pinching theorems for curvature of minimal two spheres in grassmann manifolds have been proved in particular we show that when the curvature is large then the minimal map from s2 into g m n must be either holomorphic or antiholomorphic also minimal two spheres of curvature k 2 in g 2 4 have been classified 0 introduction it is known that starting from a harmonic map f from a riemann surface into a complex grassmann manifold one can define sequences of harmonic maps by using the 0 transform and the 0 transform these sequences are called harmonic sequences cw when f is holomorphic the sequence generated by f via the 0 transform is called a pseudoholomorphic sequence and the corresponding maps are called pseudoholomorphic maps in 1980 a m din and w j zakrzewski dz and then in 1983 j eells and j c wood ec showed that all harmonic maps from s2 to the complex projective space cpf are in fact pseudoholomorphic recently f burstall j rawnsley and s salamon announced in brs that all stable harmonic maps from s2 into irreducible hermitian symmetric spaces are either holomorphic or antiholomorphic it is also known that when the target space is a general complex grassmann manifold holomorphic curves do not generate all harmonic maps cw ra on the other hand m rigoli showed in r that for a linearly full nonsingular holomorphic curve from s2 into cpn if its curvature k 4 n then k 4 n is constant then j bolton et al bjrw generalized this result to pseudoholomorphic maps and showed that for a linearly full isometric pseudoholomorphic map of position r from s2 into cpn if its curvature k 4 2r n r n then k 41 2r n r n is constant in this paper we prove various pinching theorems of curvature for harmonic maps and show that for any nonsingular harmonic map from s2 into a complex grassmann manifold if the curvature of its induced metric is large then received by the editors january 18 1988 and in revised form april 11 1988 1980 mathematics subject classification 1985 revision primary 53a10 53c55

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

hopf bifurcation and global periodic solutions in a delayed predator prey system this paper is concerned with a delayed predator prey system with same feedback delays of predator and prey species to their growth respectively we prove that a sequence of hopf bifurcations occur at the positive equilibrium as the delay increases monotonously from zero by using the theory of normal norm and center manifold reduction an explicit algorithm for determining the direction of hopf bifurcations and the stability of bifurcating periodic solutions is derived in addition the global existence results of periodic solutions bifurcating from hopf bifurcations are established by using a global hopf bifurcation result due to wu j wu symmetric functional differential equations and neural networks with memory trans amer math soc 350 1998 4799 4838 finally a numerical example supporting our theoretical prediction is also given our findings are contrasted with recent studies on a delayed predator prey system with the feedback time delay of prey species to its growth by song and wei y song j wei local hopf bifurcation and global periodic solutions in a delayed predator prey system j math anal appl 301 2005 1 21 as the feedback time delay increases monotonously from zero the positive equilibrium of the latter switches k times from stability to instability to stability in contrast the positive equilibrium of our system appears to lose the above property

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

multivariate stochastic approximation using a simultaneous perturbation gradient approximation the problem of finding a root of the multivariate gradient equation that arises in function minimization is considered when only noisy measurements of the function are available a stochastic approximation sa algorithm for the general kiefer wolfowitz type is appropriate for estimating the root the paper presents an sa algorithm that is based on a simultaneous perturbation gradient approximation instead of the standard finite difference approximation of keifer wolfowitz type procedures theory and numerical experience indicate that the algorithm can be significantly more efficient than the standard algorithms in large dimensional problems

bifurcations in a planar system of differential delay equations modeling neural activity abstract a planar system of differential delay equations modeling neural activity is investigated the stationary points and their saddle node bifurcations are estimated by an analysis of the associated characteristic equation hopf bifurcations are demonstrated at the intersection points of the saddle node and hopf bifurcation curves in an appropriate parameter plane the existence of bogdanov takens singularities is shown the properties of the bogdanov takens singularities are studied by applying the center manifold and normal form theory a numerical example illustrates the obtained results

a globally convergent stochastic approximation by combining a constrained kiefer wolfowitz search with an automatic learning algorithm it is shown that asymptotically normal convergence of an estimator to a global optimum under reasonably lenient assumptions can be attained it is enough that the objective function be smooth and locally strictly convex at its minima the central conclusion is that if theta n is the estimate produced by the method shown at the nth decision epoch then for some global minimizer theta n 1 3 theta n theta is asymptotically normally distributed this coincides with the conventional kiefer wolfowitz convergence rate to a local optimum whereas this study was motivated by needs of machine learning the basic plan would seem applicable to root finding tasks and to other types of stochastic approximation algorithms

harmonic maps of the two sphere into a complex grassmann manifold ii where qt is a complex valued one form defined up to a factor of absolute value 1 this form qp defines a complex structure on m for x e m the space f x has an orthogonal space f x of dimension n k we denote by f x and f x their corresponding projective spaces of dimensions k 1 and n k 1

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