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

global exponential periodicity of a class of recurrent neural networks with oscillating parameters and time varying delays in this paper we present the analytical results on the global exponential periodicity of a class of recurrent neural networks with oscillating parameters and time varying delays sufficient conditions are derived for ascertaining the existence uniqueness and global exponential periodicity of the oscillatory solution of such recurrent neural networks by using the comparison principle and mixed monotone operator method the periodicity results extend or improve existing stability results for the class of recurrent neural networks with and without time delays

stability and bifurcation for discrete time cohen grossberg neural network abstract this paper investigates a discrete time cohen grossberg neural network model some sufficient criteria ensuring the asymptotic stability of the equilibrium point for this model are derived moreover by choosing the appropriate bifurcation parameter we prove that neimark sacker bifurcation occurs when the bifurcation parameter exceeds a critical value we determine the direction and stability of bifurcation by applying the normal form theory and the center manifold theorem some numerical simulations for justifying the theoretical analysis are also given

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

sensitivity analysis for variational inequalities in this paper we study the behavior of the local solutions of perturbed variational inequalities governed by perturbations to both the variational inequality function and the feasible region assuming appropriate second order and regularity conditions we show that the perturbed local solution set is lipschitz continuous and directionally differentiable even when the directional differentiability is not guaranteed we are still able to describe and characterize first order information concerning the perturbed local solution set we also discuss relations to nonlinear programming sensitivity analysis

convergence under dynamical thresholds with delays necessary and sufficient conditions are obtained for the existence of a globally asymptotically stable equilibrium of a class of delay differential equations modeling the action of a neuron with dynamical threshold effects

multistability and stable asynchronous periodic oscillations in a multiple delayed neural system abstract we consider a network of three identical neurons with multiple discrete signal transmission delays the model for such a network is a system of nonlinear delay differential equations after some consideration of the absolute synchronization of the system and the global attractivity of the zero solution we present a detailed discussion about the boundaries of the stability region of the trivial solution this allows us to determine the possible codimension one bifurcations which occur in the system in particular we show the existence of standard hopf bifurcations giving rise to synchronized periodic solutions and of d 3 equivariant hopf bifurcations giving rise to three types of periodic solutions phase locked mirror reflecting and standing waves hopf hopf and hopf steady state bifurcations interactions are shown to exist and give rise to coexistence of stable synchronized and desynchronized solutions perturbation techniques coupled with the floquet theory are used to determine the stability of the phase locked oscillations

bifurcation analysis of a class of first order nonlinear delay differential equations with reflectional symmetry abstract we consider a general class of first order nonlinear delay differential equations ddes with reflectional symmetry and study completely the bifurcations of the trivial equilibrium under some generic conditions on the taylor coefficients of the dde our analysis reveals a hopf bifurcation curve terminating on a pitchfork bifurcation line at a codimension two takens bogdanov point in parameter space we compute the normal form coefficients of the reduced vector field on the centre manifold in terms of the taylor coefficients of the original dde and in contrast to many previous bifurcation analyses of ddes we also compute the unfolding parameters in terms of these coefficients for application purposes this is important since one can now identify the possible asymptotic dynamics of the dde near the bifurcation points by computing quantities which depend explicitly on the taylor coefficients of the original dde we illustrate these results using simple model systems relevant to the areas of neural networks and atmospheric physics and show that the results agree with numerical simulations

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

effect of delay on the boundary of the basin of attraction in a self excited single graded response neuron little attention has been paid in the past to the effects of interunit transmission delays representing a xonal and synaptic delays ontheboundary of the basin of attraction of stable equilibrium points in neural networks as a first step toward a better understanding of the influence of delay we study the dynamics of a single graded response neuron with a delayed excitatory self connection the behavior of this system is representative of that of a family of networks composed of graded response neurons in which most trajectories converge to stable equilibrium points for any delay value it is shown that changing the delay modifies the location of the boundary of the basin of attraction of the stable equilibrium points without affecting the stability of the equilibria the dynamics of trajectories on the boundary are also delay dependent and influence the transient regime of trajectories within the adjacent basins our results suggest that when dealing with networks with delay it is important to stud

bifurcation analysis on a discrete time tabu learning model in this paper we consider a discrete time tabu learning single neuron model after investigating the stability of the given system we demonstrate that pichfork bifurcation flip bifurcation and neimark sacker bifurcation will occur when the bifurcation parameter exceed a critical value respectively a formula is given for determining the direction and stability of neimark sacker bifurcation by applying the normal form theory and the center manifold theorem some numerical simulations for justifying the theoretical results are also provided

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

stable pseudomonotone variational inequality in reflexive banach spaces stability of a generalized variational inequality with either the mapping or the set perturbed is discussed in reflexive banach spaces provided that the mappings are pseudomonotone in the sense of karamardian as a byproduct generalized variational inequality having nonempty and bounded set is proved to be equivalent to the strictly feasibility

sensitivity analysis for abstract equilibrium problems we develop the general framework of sensitivity analysis for equilibrium problems in the setting of vector topological normed space our approach does not make any recourse to geometrical properties and the obtained result can be viewed as an extension and generalization of the well known results on variational inequalities in the literature even though we have worked under arbitrary constraints k with holder property that have been decisive in our treatment we have obtained in a similar spirit of domokos j math anal appl 230 1999 382 389 the best lower bound for the continuity modulus despite of the properties of the boundary of k

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

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

robustness analysis of global exponential stability of recurrent neural networks in the presence of time delays and random disturbances in recent years the global stability of recurrent neural networks rnns has been investigated extensively it is well known that time delays and external disturbances can derail the stability of rnns in this paper we analyze the robustness of global stability of rnns subject to time delays and random disturbances given a globally exponentially stable neural network the problem to be addressed here is how much time delay and noise the rnn can withstand to be globally exponentially stable in the presence of delay and noise the upper bounds of the time delay and noise intensity are characterized by using transcendental equations for the rnns to sustain global exponential stability moreover we prove theoretically that for any globally exponentially stable rnns if additive noises and time delays are smaller than the derived lower bounds arrived at here then the perturbed rnns are guaranteed to also be globally exponentially stable three numerical examples are provided to substantiate the theoretical results

dynamics of simple electronic neural networks abstract we examine systems of one and two nonlinear threshold switching elements neurons of the kind used in electronic neural networks characteristics of these systems which deviate from standard ideal models are found to induce complex dynamics when the neurons possess a finite frequency response or a transfer characteristic with a time delay underdamped transients and instability leading to oscillation can occur inertia in the neuron connections is found to cause ringing about fixed points convoluted basin boundaries instability and spontaneous oscillation and chaotic behavior when driven furthermore the collective behavior of a network of multiple neurons can be underdamped even when the individual connections are overdamped these results imply that care should be exercised in implementing networks with electronic devices or when adding inertia to enhance the performance of optimizing networks

variational conditions and the proto differentiation of partial subgradient mappings subgradient mappings have many roles in variational analysis such as the formulation of optimality conditions and in the special case of normal cone mappings the statement and analysis of variational inequalities and related expressions central to the study of perturbations of solutions to systems of conditions in which subgradient mappings appear are concepts of generalized differentiation such as proto differentiability which is unhampered by a solution mapping s potential multivaluedness this paper extends the known examples of proto differentiability by showing that a large and important class of partial subgradient mappings have this property until now the main examples have been the complete subgradient mappings associated with fully amenable functions the extension made difficult by the need to deal geometrically with projections of graphs relies on the notion of a fully amenable function having additional variables that provide a compatible parameterization the results are applied to the sensitivity analysis of generalized variational inequalities in which the underlying set need not be convex and can vary with the parameters

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

second order sensitivity analysis and asymptotic theory of parametrized nonlinear programs in this paper we study second order differential properties of an optimal value function x it is shown that under certain conditions x possesses second order directional derivatives which can be calculated by solving corresponding quadratic programs also upper and lower bounds on these derivatives are introduced under weaker assumptions in particular we show that the second order directional derivative is infinite if the corresponding quadratic program is unbounded finally sensitivity results are applied to investigate asymptotics of estimators in parametrized nonlinear programs

variational calculation of the limit cycle and its frequency in a two neuron model with delay we consider a model system of two coupled hopfield neurons which is described by delay differential equations taking into account the finite signal propagation and processing times when the delay exceeds a critical value a limit cycle emerges via a supercritical hopf bifurcation first we calculate its frequency and trajectory perturbatively by applying the poincar e lindstedt method then the perturbation series are resummed by means of the shohat expansion in good agreement with numerical values however with increasing delay the accuracy of the results from the shohat expansion worsens we thus apply variational perturbation theory vpt to the perturbation expansions to obtain more accurate results which moreover hold even in the limit of large delays

on uniqueness of kuhn tucker multipliers in nonlinear programming recently fujiwara han and mangasarian introduced a new constraint qualification which is a slight tightening of the well known mangasarian fromovitz constraint qualification we show that this new qualification is a necessary and sufficient condition for the uniqueness of kuhn tucker multipliers we also show that it implies the satisfaction of second order necessary optimality conditions at a local minimum

sensitivity analysis framework for variational inequalities in this paper a sensitivity analysis framework is developed for variational inequalities the perturbed solution to a parametric variational inequality problem is shown to be continuous and directionally differentiable under appropriate second order and regularity assumptions moreover this solution is once continuously differentiable if strict complementarity also holds

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

existence of periodic solutions for a system of delay differential equations abstract in this paper we mainly study the existence of periodic solutions for a system of delay differential equations representing a simple two neuron network model of hopfield type with time delayed connections between the neurons we first examine the local stability of the trivial solution propose some sufficient conditions for the uniqueness of equilibria and then apply the poincare bendixson theorem for monotone cyclic feedback delayed systems to establish the existence of periodic solutions in addition a sufficient condition that ensures the trivial solution to be globally exponentially stable is also given numerical examples are provided to support the theoretical analysis

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

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

bifurcation and category learning in network models of oscilating cortex abstract a genetic model of oscillating cortex which assumes minimal coupling justified by known anatomy is shown to function as an associative memory using previously developed theory the network has explicit excitatory neurons with local inhibitory interneuron feedback that forms a set of nonlinear oscillators coupled only by long range excitatory connections using a local hebb like learning rule for primary and higher order synapses at the ends of the long range connections the system learns to store the kinds of oscillation amplitude patterns observed in olfactory and visual cortex in olfaction these patterns emerge during respiration by a pattern forming phase transition which we characterize in the model as a multiple hopf bifurcation we argue that these bifurcations play an important role in the operation of real digital computers and neural networks and we use bifurcation theory to derive learning rules which analytically guarantee cam storage of continuous periodic sequences capacity n 2 fourier components for an n node network no spurious attractors

stability analysis for variational inequality in reflexive banach spaces this paper is devoted to the stability analysis in variational inequality we obtain some stability results for variational inequality with both the mapping and the set that are perturbed in reflexive banach spaces provided that the mappings are pseudomonotone in the sense of karamardian the stability is also discussed for the minty variational inequality as the mappings are properly quasimonotone the results in this paper generalized some known results in this area

solution differentiability for variational inequalities in this paper we study solution differentiability properties for variational inequalities we characterize frechet differentiability of perturbed solutions to parametric variational inequality problems defined on polyhedral sets our result extends the recent result of pang and it directly specializes to nonlinear complementarity problems variational inequality problems defined on perturbed sets and to nonlinear programming problems

computation of synchronized periodic solution in a bam network with two delays a bidirectional associative memory bam neural network with four neurons and two discrete delays is considered to represent an analytical method namely perturbation incremental scheme pis the expressions for the periodic solutions derived from hopf bifurcation are given by using the pis the result shows that the pis has higher accuracy than the center manifold reduction cmr with normal form for the values of time delay not far away from the hopf bifurcation point in terms of the pis the necessary and sufficient conditions of synchronized periodic solution arising from a hopf bifurcation are obtained and the synchronized periodic solution is expressed in an analytical form it can be seen that theoretical analysis is in good agreement with numerical simulation it implies that the provided method is valid and the obtained result is correct to the best of our knowledge the paper is the first one to introduce the pis to study the periodic solution derived from hopf bifurcation for a 4 d delayed system quantitatively

stability and bifurcation in a tri neuron network model with discrete and distributed delays in this paper we consider a tri neuron network model with discrete and distributed delays after discussing the distributions of the roots of the characteristic equation local stability analysis of the steady state solution leads to we analyze the stability of network models with instantaneous feedback and neural interaction history delayed neural feedback and no neural interaction history and delayed neural feedback and neural interaction history we give sufficient conditions for the linear stability of the equilibrium solution we also show that a hopf bifurcation can occur when the delays take certain critical values and we further prove that there is a positive integer k such that there are k switches from stability to instability and back to stability numerical simulations are finally performed to illustrate the obtained results

stability analysis of variational inequalities and nonlinear complementarity problems via the mixed linear complementarity problem and degree theory this paper is concerned with the mixed linear complementarity problem and the role it and its variants play in the stability analysis of the nonlinear complementarity problem and the karush kuhn tucker system of a variational inequality problem under a nonsingular assumption the mixed linear complementarity problem can be converted to the standard problem in this case the rich theory of the latter can be directly applied to the former in this work we employ degree theory to derive some sufficient conditions for the existence of a solution to the mixed linear complementarity problem in the absence of the nonsingularity property next we extend this existence theory to the mixed nonlinear complementarity problem and establish a main stability result under a certain degree theoretic assumption concerning the linearized problem we then specialize this stability result and its consequences to the parametric variational inequality problem under the assumption of a unique set of multipliers finally we

multiperiodicity and attractivity of delayed recurrent neural networks with unsaturating piecewise linear transfer functions this paper studies multiperiodicity and attractivity for a class of recurrent neural networks rnns with unsaturating piecewise linear transfer functions and variable delays using local inhibition conditions for boundedness and global attractivity are established these conditions allow coexistence of stable and unstable trajectories moreover multiperiodicity of the network is investigated by using local invariant sets it shows that under some interesting conditions there exists one periodic trajectory in each invariant set which exponentially attracts all trajectories in that region correspondingly simulations are carried out to illustrate the theories

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

complicated dynamics of a ring neural network with time delays this paper studies the dynamical behavior of a ring neural network with time delays on the basis of lyapunov s method the asymptotic stability of the equilibrium is first investigated and the delay dependent criteria ensuring global stability for the ring neural network are obtained moreover based on the global hopf bifurcation theorem for fde the conditions that guarantee the global existence of periodic solutions are determined it shows that periodic solutions bifurcating from the trivial equilibrium can continue when the time delay is far away from the critical value some examples are induced to illustrate our results in addition complicated dynamics of the model are investigated with the help of numerical simulation the study results show that the model exhibits period doubling bifurcations which lead eventually to chaos and the chaos can also directly occur via the bifurcations from the quasi periodic solutions

lmi based stability criteria for neural networks with multiple time varying delays abstract in this paper the stability of neural networks with multiple time varying delays is studied a new class of lyapunov krasovskii functionals is constructed and the s procedure and free weighting matrix method are employed to derive a delay dependent stability criterion from which a delay independent criterion is obtained as a special case moreover the result is also extended to delay dependent and rate independent stability criteria for multiple unknown time varying delays finally numerical examples are given to illustrate the effectiveness of our methods and improvement over the existing ones

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

dynamics of a class of nonlinear discrete time neural networks in this paper we consider a class of delay difference systems with piecewise constant nonlinearity which includes the discrete version of an artificial neural network model of two neurons described by differential equations with piecewise constant arguments some interesting results are obtained for the periodicity and convergence of solutions of the systems

stability and hopf bifurcation analysis on a ring of four neurons with delays we consider a four neuron ring with self feedback and delays by analyzing the associated characteristic equation linear stability is investigated and hopf bifurcations are demonstrated as well as the stability and direction of the hopf bifurcation are determined by employing the normal form method and the center manifold reduction numerical simulations are presented to illustrate the results

asymptotic stability criteria for a two neuron network with different time delays in this paper the asymptotic stability of a two neuron system with different time delays has been investigated some criteria for determining the global asymptotically stability of equilibrium are derived from the theory of monotonic dynamical system and the approach of lyapunov functional for local asymptotic stability some elegant criteria are also obtained by the nyquist criteria we find that one of them depends on the length of delays while the other ones do not in the latter case the delays are sometimes called harmless delays the results obtained have leading significance in the study of neural networks composed of a large number of neurons with different time delays

dynamics of fitzhugh nagumo excitable systems with delayed coupling small lattices of n nearest neighbor coupled excitable fitzhugh nagumo systems with time delayed coupling are studied and compared with systems of fitzhugh nagumo oscillators with the same delayed coupling bifurcations of equilibria in an n 2 case are studied analytically and it is then numerically confirmed that the same bifurcations are relevant for the dynamics in the case ng2 bifurcations found include inverse and direct hopf and fold limit cycle bifurcations typical dynamics for different small time lags and coupling intensities could be excitable with a single globally stable equilibrium asymptotic oscillatory with symmetric limit cycle bistable with stable equilibrium and a symmetric limit cycle and again coherent oscillatory but nonsymmetric and phase shifted for an intermediate range of time lags inverse sub critical hopf and fold limit cycle bifurcations lead to the phenomenon of oscillator death the phenomenon does not occur in the case of fitzhugh nagumo oscillators with the same type of coupling

hopf bifurcating periodic orbits in a ring of neurons with delays in this paper we consider a ring of neurons with self feedback and delays the linear stability of the model is investigated by analyzing the associated characteristic transcendental equation based on the normal form approach and the center manifold theory we derive the formula for determining the properties of hopf bifurcating slowly oscillating periodic orbits for a ring of neurons with delays including the direction of hopf bifurcation stability of the hopf bifurcating slowly oscillating periodic orbits and so on moreover by means of the symmetric bifurcation theory of delay differential equations coupled with representation theory of standard dihedral groups we not only investigate the effect of synaptic delay of signal transmission on the pattern formation but also obtain some important results about the spontaneous bifurcation of multiple branches of periodic solutions and their spatio temporal patterns

cardinal interpolation with differences of tempered functions abstract in this paper we investigate the existence and uniqueness of cardinal interpolants associated with functions arising from the k th order iterated discrete laplacian k applied to certain radial basis functions in particular we concentrate on determining for a given radial function which functions k give rise to cardinal interpolation operators which are both bounded and invertible l 2 z 3 in addition to solving the cardinal interpolation problem cip associated with such functions k our approach provides a unified framework and simpler proofs for the cip associated with polyharmonic splines and hardy multiquadrics

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