a new method for complete stability analysis of cellular neural networks with time delay this paper presents new complete stability results for delayed cellular neural networks dcnns a novel method is proposed for complete stability analysis of dcnns by applying the m matrix theory and introducing some new estimation techniques on the solutions of dcnns a simple and improved complete stability criterion is derived the new criterion unifies the delay dependent and delay independent complete stability conditions for dcnns moreover the obtained delay dependent criterion can give a larger upper bound of the time delay than the existing ones such that the complete stability can still be retained numerical examples are presented which show that the new complete stability results for dcnns are compared favorably with the existing results

on multistability of equations with a distributed delay monotone production and the allee effect abstract we consider the delay population dynamics model d n d t f n t d n t with an increasing fecundity function f and any mortality function d where the allee effect or multistability can be observed the study includes non autonomous equations with a distributed delay attractivity of certain positive solutions persistence extinction of solutions with initial values below a threshold boundedness and oscillation are discussed

global attractivity of positive periodic solution to periodic lotka volterra competition systems with pure delay abstract we consider a periodic lotka volterra competition system without instantaneous negative feedbacks i e pure delay systems x i t x i t r i t j 1 n a i j t x j t i j t i 1 2 n we establish some 3 2 type criteria for global attractivity of a positive periodic solution of the system which generalize the well known wright s 3 2 criteria for the autonomous delay logistic equation and thereby address the open problem proposed by both kuang y kuang global stability in delayed nonautonomous lotka volterra type systems without saturated equilibria differential integral equations 9 1996 557 567 and teng z teng nonautonomous lotka volterra systems with delays j differential equations 179 2002 538 561

stability of strong travelling waves for a non local time delayed reaction diffusion equation the paper is concerned with a non local time delayed reaction diffusion equation we prove the time asymptotic stability of a travelling wavefront without a smallness assumption on its wavelength i e the so called strong wavefront by means of the technical weighted energy method when the initial perturbation around the wave is small the exponential convergent rate is also given selection of a suitable weight plays a key role in the proof

convergence to equilibria in scalar nonquasimonotone functional differential equations abstract we consider a class of scalar functional differential equations generating a strongly order preserving semiflow with respect to the exponential ordering introduced by smith and thieme it is shown that the boundedness of all solutions and the stability properties of an equilibrium are exactly the same as for the ordinary differential equation which is obtained by ignoring the delays the result on the boundedness of the solutions combined with a convergence theorem due to smith and thieme leads to explicit necessary and sufficient conditions for the convergence of all solutions starting from a dense subset of initial data under stronger conditions guaranteeing that the functional differential equation is asymptotically equivalent to a scalar ordinary differential equation a similar result is proved for the convergence of all solutions

asymptotic periodicity monotonicity and oscillation of solutions of scalar neutral functional differential equations abstract we consider the periodic scalar neutral functional differential equation d dt x t c t x t h t x t h t x t where c is continuously differentiable h is increasing in its second argument and both c and h are 1 periodic in the t variable the two time lags and are not required to be the same it is shown that under certain conditions i the set of 1 periodic solutions is an ordered arc and each solution is convergent to a periodic solution ii the asymptotic and oscillatory behaviors of each solution are completely classified in terms of the value of the first integral at the initial condition

embedding problems over abelian groups and an application to elliptic curves conditions for the solvability of certain embedding problems can be given in terms of the existence of elements with certain norm properties a classical example due to witt 1936 crelle s j 174 237 245 is that of embedding a klein extension into a dihedral extension in construction de p extensions galoisiennes d un corps de caracteristique differente de p 1987 j algebra109 508 535 massy finds this type of condition for central p extensions of an abelian group of exponent p in this paper we generalize the results of massy to the case of central p extensions of any abelian group in the last section we discuss the reason for our interest in these problems they appear in the theory of elliptic q curves if one is interested in computing representatives with especially good arithmetic properties in the isogeny class of a given curve

multistability and convergence in delayed neural networks abstract we present the existence of 2 n stable stationary solutions for a general n dimensional delayed neural networks with several classes of activation functions the theory is obtained through formulating parameter conditions motivated by a geometrical observation positively invariant regions for the flows generated by the system and basins of attraction for these stationary solutions are established the theory is also extended to the existence of 2 n limit cycles for the n dimensional delayed neural networks with time periodic inputs it is further confirmed that quasiconvergence is generic for the networks through justifying the strongly order preserving property as the self feedback time lags are small for the neurons with negative self connection weights our theory on existence of multiple equilibria is then incorporated into this quasiconvergence for the network four numerical simulations are presented to illustrate our theory

multistability and multiperiodicity of delayed cohen grossberg neural networks with a general class of activation functions abstract in this paper by using analysis approach and decomposition of state space the multistability and multiperiodicity issues are discussed for cohen grossberg neural networks cgnns with time varying delays and a general class of activation functions where the general class of activation functions consist of nondecreasing functions with saturation s including piecewise linear functions with two corner points and standard activation functions as its special case based on the cauchy convergence principle some sufficient conditions are obtained for checking the existence and uniqueness of equilibrium points of the n neuron cgnns it is shown that the n neuron cgnns can have 2n locally exponentially stable equilibrium points located in saturation regions also some conditions are derived for ascertaining equilibrium points to be locally exponentially stable or globally exponentially attractive and to be located in any designated region as an extension of multistability some similar results are presented for ascertaining multiple periodic orbits when external inputs of the n neuron cgnns are periodic finally three examples are given to illustrate the effectiveness of the obtained results

on contact anosov flows exponential decay of correlations for co 4 contact anosov flows is established this implies in particular exponential decay of correlations for all smooth geodesic flows in strictly negative curvature

strongly order preserving semiflows generated by functional differential equations the aim of this paper is to apply some recently developed improvements in the theory of monotone dynamical systems due to the authors 12 13 j to certain systems of functional differential equations fde s which do not enjoy the quasimonotone property considered by one of us in 9 the present work extends our previous results in this direction for scalar equations in 111 to systems in the fundamental paper s m w hirsch establishes that most orbits of a strongly monotone scmiflow on a strongly ordered space x tend to the set e of equilibria employing ideas of hirsch and of h matano 7 the authors have extended the theory to obtain some improvements in the results of hirsch and matano under matano s weaker assumption that the semiflow is strongly order preserving recently in 13 we gave sufficient conditions for most orbits of a strongly order preserving semiflow to converge to an equilibrium these conditions require additional smoothness of the semiflow and a certain strong monotonicity condition for the linearized flow determined by the variational equation about each equilibrium p policik s has also given sufficient conditions for most orbits to converge for semilinear parabolic evolution equations possessing certain strong monotonicity properties in this paper wc apply the convergence results developed in 131 to nonquasimonotone fde s in this introduction wc briefly review the application of monotone dynamical systems theory to fde s enjoying the quasimonotone property this research appeared in 9 133 then we state one of the main results of this paper which applies when the quasimonotone property fails but when another property m holds some simple examples are given which

the boundary of an affine invariant submanifold we study the boundary of an affine invariant submanifold of a stratum of translation surfaces in a partial compactification consisting of all finite area abelian differentials over nodal riemann surfaces modulo zero area components the main result is a formula for the tangent space to the boundary we also prove finiteness results concerning cylinders a partial converse to the cylinder deformation theorem and a result generalizing part of the veech dichotomy

diffusive monotonicity and threshold dynamics of delayed reaction diffusion equations abstract for abstract functional differential equations and reaction diffusion equations with delay an exponential ordering is introduced which takes into account the spatial diffusion the induced monotonicity of the solution semiflows is established and applied to describe the threshold dynamics extinction or persistence convergence to positive equilibria for a nonlocal and delayed reaction diffusion population model

multistability analysis of quaternion valued neural networks with time delays this paper addresses the multistability issue for quaternion valued neural networks qvnns with time delays by using the inequality technique sufficient conditions are proposed for the boundedness and the global attractivity of delayed qvnns based on the geometrical properties of the activation functions several criteria are obtained to ensure the existence of 81 n equilibrium points 16 n of which are locally stable two numerical examples are provided to illustrate the effectiveness of the obtained results

dynamics in a periodic competitive model with stage structure in this paper we consider a time delayed periodic system which describes the competition among mature populations by appealing to theories of monotone dynamical systems periodic semiflows and uniform persistence we analyze the evolutionary behavior of the system and establish sufficient conditions for competitive coexistence and exclusion

attractors in coherent systems of differential equations abstract attractors of cooperative dynamical systems are particularly simple for example a nontrivial periodic orbit cannot be an attractor and orbits are nowhere dense this paper provides characterizations of attractors for the wider class of coherent systems defined by the property that all directed feedback loops are positive several new results for cooperative systems are obtained in the process connections with biological models are discussed

global stability and wavefronts in a cooperation model with state dependent time delay abstract this article deals with a diffusive cooperative model with state dependent delay which is assumed to be an increasing function of the population density with lower and upper bounds for the cooperative dde system the positivity and boundedness of solutions are firstly given using the comparison principle of the state dependent delay equations obtained the stability criterion of model is analyzed both from local and global points of view when the diffusion is properly introduced the existence of traveling waves is obtained by constructing a pair of upper lower solutions and schauder s fixed point theorem calculating the minimum wave speed shows that the wave is slowed down by the state dependent delay finally the traveling wavefront solutions for large wave speed are also discussed and the fronts appear to be all monotone regardless of the state dependent time delay this is an interesting property since many findings are frequently reported that delay causes a loss of monotonicity with the front developing a prominent hump in some other delay models

existence and uniqueness of a wavefront in a delayed hyperbolic parabolic model abstract we consider a class of hyperbolic parabolic equation with time delay and a non local feedback due to the maturation for the adult population density of a single species population and we show that the wave profile is described by a hybrid system that consists of an integral transformation and an ordinary differential equation we show the existence and uniqueness of a travelling wavefront of the hyperbolic parabolic system in the so called bistable case by considering the same problem for a properly parametrized parabolic system and then by considering the continuous dependence of the wave speed on the parameter involved

asymptotic behavior of matrix coefficients of admissible representations introduction 869 1 generalities on reductive groups 873 2 the infinitesimal cartan decomposition 876 3 the t radial components 880 4 differential equations satisfied by sphereical functions 885 5 asymptotic behavior of spherical functions on a 888 6 asymptotic behavior of spherical functions along the walls of a 892 7 leading characters and growth estimates on the group 898 8 admissible representations and their matrix coefficients 906 appendix 917

on attracting basins of multiple equilibria of a class of cellular neural networks in this paper we study the distribution of attraction basins of multiple equilibrium points of cellular neural networks cnns under several conditions the boundaries of the attracting basins of the stable equilibria of a completely stable cnn system are composed of the closures of the stable manifolds of unstable equilibria of n 1 dimensions as demonstrations of this idea under the conditions proposed in the literature which depicts stable and unstable equilibria we identify the attraction basin of each stable equilibrium of which the boundary is composed of the stable manifolds of the unstable equilibria precisely we also investigate the attracting basins of a simple class of symmetric 1 d cnns via identifying the unstable equilibria of which the stable manifold is n 1 dimensional and the completely stable asymmetric cnns with stable equilibria less than 2n

multistability for delayed neural networks via sequential contracting in this paper we explore a variety of new multistability scenarios in the general delayed neural network system geometric structure embedded in equations is exploited and incorporated into the analysis to elucidate the underlying dynamics criteria derived from different geometric configurations lead to disparate numbers of equilibria a new approach named sequential contracting is applied to conclude the global convergence to multiple equilibrium points of the system the formulation accommodates both smooth sigmoidal and piecewise linear activation functions several numerical examples illustrate the present analytic theory

global asymptotic behavior of a chemostat model with discrete delays this paper studies the global asymptotic behavior of an exploitative competition model between n species in a chemostat the model incorporates discrete time delays to describe the delay in the conversion of nutrient consumed to viable biomass and hence includes delays simultaneously in variables of nutrient and species concentrations in the case where only two species are engaged in competition it is shown that competitive exclusion holds for any monotone growth response functions sufficient conditions are also obtained for the model to exhibit competitive exclusion in the n species case in regard to the delay effects on the qualitative outcome of competition it is demonstrated that when the delays are relatively small the predictions of the model are identical with the predictions given by corresponding models without time delays however including large delays in the model may alter the predicted outcome of competition the techniques used also work when different removal rates are permitted an

small eigenvalues of the laplacian for algebraic measures in moduli space and mixing properties of the teichmuller flow we consider the sl 2 r action on moduli spaces of quadratic dierentials if is an sl 2 r invariant probability measure crucial information about the associated representation on l 2 and in particular ne asymptotics for decay of correlations of the diagonal action the te

limit set dichotomy and multistability for a class of cooperative neural networks with delays recent papers have pointed out the interest to study convergence in the presence of multiple equilibrium points eps multistability for neural networks nns with nonsymmetric cooperative nonnegative interconnections and neuron activations modeled by piecewise linear pl functions one basic difficulty is that the semiflows generated by such nns are monotone but due to the horizontal segments in the pl functions are not eventually strongly monotone esm this notwithstanding it has been shown that there are subclasses of irreducible interconnection matrices for which the semiflows although they are not esm enjoy convergence properties similar to those of esm semiflows the results obtained so far concern the case of cooperative nns without delays the goal of this paper is to extend some of the existing results to the relevant case of nns with delays more specifically this paper considers a class of nns with pl neuron activations concentrated delays and a nonsymmetric cooperative interconnection matrix a and delay interconnection matrix a the main result is that when a a satisfies a full interconnection condition then the generated semiflows which are monotone but not esm satisfy a limit set dichotomy analogous to that valid for esm semiflows it follows that there is an open and dense set of initial conditions in the state space of continuous functions on a compact interval for which the solutions converge toward an ep the result holds in the general case where the nns possess multiple eps i e is a result on multistability and is valid for any constant value of the delays

a periodic age structured epidemic model with a wide class of incidence rates abstract in this paper a time delayed epidemic model is formulated to describe the dynamics of seasonal diseases with age structure by the method of the spectral radius of an integral operator we define the basic reproduction number r 0 of the model it is shown that the disease is uniformly persistent and there exists at least one positive periodic state when r 0 1 while the disease will die out if r 0 1 the presented case study not only confirms the theoretical results but also demonstrates that the epidemic peak is very sensitive to the maturation period and the magnitude of seasonality which is different from the dynamics of the model without considering age heterogeneities these findings contribute to better understanding the epidemiological properties of the disease with age structure

multistability of recurrent neural networks with time varying delays and the piecewise linear activation function in this brief stability of multiple equilibria of recurrent neural networks with time varying delays and the piecewise linear activation function is studied a sufficient condition is obtained to ensure that n neuron recurrent neural networks can have 4k 1 n equilibrium points and 2k n of them are locally exponentially stable this condition improves and extends the existing stability results in the literature simulation results are also discussed in one illustrative example

asymptotic behavior of solutions of nonautonomous neutral dynamical systems abstract this paper studies the dynamics of families of monotone nonautonomous neutral functional differential equations with nonautonomous operator of great importance for their applications to the study of the long term behavior of the trajectories of problems described by this kind of equations such us compartmental systems and neural networks among many others precisely more general admissible initial conditions are included in the study to show that the solutions are asymptotically of the same type as the coefficients of the neutral and non neutral part

connected components of the moduli spaces of abelian differentials with prescribed singularities consider the moduli space of pairs c where c is a smooth compact complex curve of a given genus and is a holomorphic 1 form on c with a given list of multiplicities of zeroes we describe connected components of this space this classification is important in the study of dynamics of interval exchange transformations and billiards in rational polygons and in the study of geometry of translation surfaces

comparison theorems for neutral stochastic functional differential equations abstract the comparison theorems under wu and freedman s order are proved for neutral stochastic functional differential equations with finite or infinite delay whose drift terms satisfy the quasimonotone condition and diffusion term is the same

dynamics of sl2 ℝ over moduli space in genus two this paper classifies orbit closures and invariant measures for the natural action of sl2 r on um2 the bundle of holomorphic 1 forms over the moduli space of riemann surfaces of genus two

fields of definition of building blocks we investigate the fields of definition up to isogeny of the abelian varieties known as building blocks these varieties are defined as the qvarieties admitting real or quaternionic multiplications of the maximal possible degree allowed by their dimensions cf pyle 2004 the shimura taniyama conjecture predicts that every such variety is isogenous to a non cm simple factor of a modular jacobian j n the obstruction to descend the field of definition of a building block up to isogeny is given by ribet in 1994 as an element in a galois cohomology group in this paper we begin by studying these elements from an abstract galois cohomological point of view and obtain results and formulas for the computation of invariants related to them when considered for the element attached to a building block these invariants give the structure of its endomorphism algebra and also complete information on the possible fields of definition up to isogeny of this building block we implemented these computations in magma for building blocks given as q simple factors up to isogeny of the jacobian of the modular curve x n using this implementation we computed a table for conductors n 500 which is described in the last section this table is a source of examples of building blocks with different behaviors and of statistical information in particular it contains many examples that answer a question posed by ribet in 1994 on the existence of a smallest field of definition up to isogeny for rm building blocks of even dimension

counting closed geodesics in strata we compute the asymptotic growth rate of the number n mathcal c r of closed geodesics of length le r in a connected component mathcal c of a stratum of quadratic differentials we prove that for any 0 le theta le 1 the number of closed geodesics gamma of length at most r such that gamma spends at least theta fraction of its time outside of a compact subset of mathcal c is exponentially smaller than n mathcal c r the theorem follows from a lattice counting statement for points x y in the moduli space mathcal m s of riemann surfaces and for 0 le theta le 1 we find an upper bound for the number of geodesic paths of length le r in mathcal c which connect a point near x to a point near y and spend at least a theta fraction of the time outside of a compact subset of mathcal c

a non local pde model for population dynamics with state selective delay local theory and global attractors we propose a non local pde model for the evolution of a single species population that involves delayed feedback where the delay such as the maturation time in the delayed birth rate is selective and the selection depends on the status of the system this delay selection in contrast with the usual state dependent delay widely used in ordinary delay differential equation ensures the lipschitz continuity of the nonlinear functional in the classical phase space we also develop the local theory and the existence and upper semi continuity of the global attractor with respect to parameters

further result on guaranteed h_ infty performance state estimation of delayed static neural networks this brief considers the guaranteed h infty performance state estimation problem of delayed static neural networks an arcak type state estimator which is more general than the widely adopted luenberger type one is chosen to tackle this issue a delay dependent criterion is derived under which the estimation error system is globally asymptotically stable with a prescribed h infty performance it is shown that the design of suitable gain matrices and the optimal performance index are accomplished by solving a convex optimization problem subject to two linear matrix inequalities compared with some previous results much better performance is achieved by our approach which is greatly benefited from introducing an additional gain matrix in the domain of activation function an example is finally given to demonstrate the advantage of the developed result

global attractivity in delayed hopfield neural network models two different approaches are employed to investigate the global attractivity of delayed hopfield neural network models without assuming the monotonicity and differentiability of the activation functions liapunov functionals and functions combined with the razumikhin technique are constructed and employed to establish sufficient conditions for global asymptotic stability independent of the delays in the case of monotone and smooth activation functions the theory of monotone dynamical systems is applied to obtain criteria for global attractivity of the delayed model such criteria depend on the magnitude of delays and show that self inhibitory connections can contribute to the global convergence

applications of the exponential ordering in the study of almost periodic delayed hopfield neural networks abstract this paper studies almost periodic neural networks of hopfield type described by delayed differential equations the authors introduce an exponential ordering to analyze the long term behavior of the solutions they prove some theorems of global convergence and deduce the stabilization role of the fast inhibitory self connections the proof which in the case of the neural networks considered in this paper requires uniform stability uses arguments of comparison of differential equations and methods of the non autonomous monotone theory of dynamical systems when the connections between different neurons are excitatory improved conditions of convergence are obtained and the stabilization role of strongly positive inputs is also shown the applicability of the results is illustrated with several numerical experiments based on two different families of neural networks

effective counting on translation surfaces abstract we prove an effective version of a celebrated result of eskin and masur for any sl 2 r invariant locus l of translation surfaces there exists 0 such that for almost every translation surface in l the number of saddle connections with holonomy vector of length at most t grows like c t 2 o t 2 we also provide effective versions of counting in sectors and in ellipses

monotone semiflows in scalar non quasi monotone functional differential equations abstract by introducing a stronger than pointwise ordering conditions are found under which scalar functional differential equations generate monotone semiflows even if they are not quasi monotone typically the maximum delay must be the smaller the more quasi monotonicity is violated the theory of monotone semiflows is used to show that most solutions converge to equilibrium and that stability of equilibria is essentially the same as for ordinary differential equations

canonical piecewise linear networks in this paper mapping networks will be considered from the viewpoint of the piecewise linear pwl approximation the so called canonical representation plays a kernel role in the pwl representation theory while this theory has been researched intensively in the contents of mathematics and circuit simulations little has been seen in the research area about the theoretical aspect of neural networks this paper modifies this theory and applies it as a mathematical support for mapping networks the main modification is a higher level generalization of the canonical representation with proofs of its availability in the set of pwl functions the modified theory will first be used to study the canonical pwl feature of the popular multilayer perceptron like mlpl networks second it will be seen that the generalized canonical representation is itself suitable for a network implementation which is called the standard canonical pwl network more generally the family of generalized canonical pwl networks is defined as those which may take the canonical pwl representation as a mathematical model this family is large and practically meaningful the standard canonical pwl networks may be taken as representatives in the family the modification of the pwl representation theory as well as the introduction of this theory in the theoretical study of mapping networks which provide a new concept of mapping networks i e the canonical pwl network family may be regarded as the main contributions of the paper

travelling waves for delayed reaction diffusion equations with global response we develop a new approach to obtain the existence of travelling wave solutions for reaction diffusion equations with delayed non local response the approach is based on an abstract formulation of the wave profile as a solution of an operational equation in a certain banach space coupled with an index formula of the associated fredholm operator and some careful estimation of the nonlinear perturbation the general result relates the existence of travelling wave solutions to the existence of heteroclinic connecting orbits of a corresponding functional differential equation and this result is illustrated by an application to a model describing the population growth when the species has two age classes and the diffusion of the individual during the maturation process leads to an interesting non local and delayed response for the matured population

almost totally complex points on elliptic curves let f f0 be a quadratic extension of totally real number fields and let e be an elliptic curve over f which is isogenous to its galois conjugate over f0 a quadratic extension m f is said to be almost totally complex atc if all archimedean places of f but one extend to a complex place of m the main goal of this note is to provide a new construction of a supply of darmon like points on e which are conjecturally defined over certain ring class fields of m these points are constructed by means of an extension of darmon s atr method to higher dimensional modular abelian varieties from which they inherit the following features they are algebraic provided darmon s conjectures on atr points hold true and they are explicitly computable as we illustrate with a detailed example that provides numerical evidence for the validity of our conjectures

dynamics of smooth essentially strongly order preserving semiflows with application to delay differential equations abstract in this paper we introduce a class of smooth essentially strongly order preserving semiflows and improve the limit set dichotomy for essentially strongly order preserving semiflows generic convergence and stability properties of this class of smooth essentially strongly order preserving semiflows are then developed we also establish the generalized krein rutman theorem for a compact and eventually essentially strongly positive linear operator by applying the main results of this paper to essentially cooperative and irreducible systems of delay differential equations we obtain some results on generic convergence and stability the linearized stability of an equilibrium and the existence of the most unstable manifold in these systems the obtained results improve some corresponding ones already known

nonautonomous lotka volterra systems with delays abstract the paper studies the general nonautonomous lotka volterra multispecies systems with finite delays the ultimate boundedness permanence global attractivity and existence and uniqueness of strictly positive solutions positive periodic solutions and almost periodic solutions are obtained these results are basically an extension of the known results for nonautonomous lotka volterra multispecies systems without delay to systems with delay

convergence and stability for essentially strongly order preserving semiflows abstract this paper is concerned with a class of essentially strongly order preserving semiflows which are defined on an ordered metric space and are generalizations of strongly order preserving semiflows for essentially strongly order preserving semiflows we prove several principles which are analogues of the nonordering principle for limit sets the limit set dichtomy and the sequential limit set trichotomy for strongly order preserving semiflows then under certain compactness hypotheses we obtain some results on convergence quasiconvergence and stability in essentially strongly order preserving semiflows finally some applications are made to quasimonotone systems of delay differential equations and reaction diffusion equations with delay and the main advantages of our results over the classical ones are that we do not require the delicate choice of state space and the technical ignition assumption

a cooperative system which does not satisfy the limit set dichotomy the fundamental property of strongly monotone systems and strongly cooperative systems in particular is the limit set dichotomy due to hirsch if x y then either x y o r x y and both sets consist of equilibria we provide here a counterexample showing that this property need not hold for non strongly cooperative systems

new generic quasi convergence principles with applications in this paper essentially strongly order preserving and conditionally set condensing semiflows are considered obtained is a new type of generic quasi convergence principles implying the existence of an open and dense set of stable quasi convergent points when the state space is order bounded the generic quasi convergence principles are then applied to essentially cooperative and irreducible systems in the forms of ordinary differential equations and delay differential equations giving some results of theoretical and practical significance

technical communique an improved result for complete stability of delayed cellular neural networks this paper provides a new sufficient condition for the complete stability of the delayed cellular neural networks this condition imposes constraints on the parameters of the networks and the size of time delay the linear matrix inequality approach plays an important role in the proof our result recovers the known results in the earlier literature as special cases finally we give an example to illustrate the applicability of our main result

stability and convergence in strongly monotone dynamical systems soit x un systeme dynamique x est un espace topologique et le flot t t r est une famille d applications continues de sous ensembles ouverts de x dans x on decrit qualitativement le comportement asymptotique quand t des trajectoires t t x pour les etats initiaux x dans le cas de systemes ayant un principe de comparaison fort

a periodic epidemic model with age structure in a patchy environment in this paper a periodic epidemic model with age structure in a patchy environment is introduced we investigate its global dynamics in term of the basic reproduction number mathcal r 0 and show that there exists at least one positive periodic state and the disease persists when mathcal r 0 1 while the disease will die out if mathcal r 0 1 some numerical examples are given to confirm our analytic results and to show that the age and spatial heterogeneities are important factors for the global dynamics

spatial spread of rabies revisited influence of age dependent diffusion on nonlinear dynamics we consider the spatio temporal patterns of disease spread involving structured populations we start with a general model framework in population biology and spatial ecology where the individual s spatial movement behaviors depend on its maturation status and we show how delayed reaction diffusion equations with nonlocal interactions arise naturally we then consider the impact of this delayed nonlocal interaction on the disease spread by revisiting the spatial spread of rabies in continental europe during the period between 1945 and 1985 we show how the distinction of territorial patterns between juvenile and adult foxes the main carriers of the rabies under consideration yields a class of partial differential equations involving delayed and nonlocal terms that are implicitly defined by a hyperbolic parabolic equation and we show how incorporating this distinction into the model leads to a formula describing the relation of the minimal wave speed and the maturation time of foxes we show how the ho

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

existence and stability of stationary waves of a population model with strong allee effect we investigate the existence and stability of stationary waves of a nonlocal reaction diffusion population model with delay nonlocality and strong allee effect by reducing the model the conditions for existence of stationary wavefront wave pulse and inverted wave pulse are established then we show that the stationary waves of the reduced model are also the stationary waves of the general model the global stability of the stationary waves is illustrated by numerically solving the general model for different sets of parameter values

stage structured models of intra and inter specific competition within age classes abstract in some species larvae and adults experience competition in completely different ways simple stage structured models without larval competition usually yield a single delay equation for the adults using an age structured system incorporating competition among both larvae and adults we derive a system of distributed delay equations for the numbers of larvae and adults the system is neither cooperative nor reducible to a single equation for either variable positivity boundedness and uniform strong persistence are established linear stability analysis of equilibria is difficult due to the strong coupling but results are proved for small delays using monotone systems theory and exponential ordering for small delay we prove a theorem on generic convergence to equilibria which does not directly follow from standard theory but can be proved indirectly using comparison arguments finally we consider an extension to two strain competition and prove theorems on the linear stability of the boundary equilibria

existence and stability of traveling wave fronts in reaction advection diffusion equations with nonlocal delay this paper is concerned with the existence uniqueness and globally asymptotic stability of traveling wave fronts in the quasi monotone reaction advection diffusion equations with nonlocal delay under bistable assumption we construct various pairs of super and subsolutions and employ the comparison principle and the squeezing technique to prove that the equation has a unique nondecreasing traveling wave front up to translation which is monotonically increasing and globally asymptotically stable with phase shift the influence of advection on the propagation speed is also considered comparing with the previous results our results recovers and or improves a number of existing ones in particular these results can be applied to a reaction advection diffusion equation with nonlocal delayed effect and a diffusion population model with distributed maturation delay some new results are obtained

nonmonotone travelling waves in a single species reaction diffusion equation with delay abstract we prove the existence of a continuous family of positive and generally nonmonotone travelling fronts for delayed reaction diffusion equations u t t x u t x u t x g u t h x when g c 2 r r has exactly two fixed points x 1 0 and x 2 k 0 recently nonmonotonic waves were observed in numerical simulations by various authors here for a wide range of parameters we explain why such waves appear naturally as the delay h increases for the case of g with negative schwarzian our conditions are rather optimal we observe that the well known mackey glass type equations with diffusion fall within this subclass of as an example we consider the diffusive nicholson s blowflies equation

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

monotone semiflows generated by functional differential equations abstract this obtains sufficient condition for an autonomous functional differential equation to generate a strongly monotone semiflow on a suitable state space this allows the application to functional differential equations of very powerful recent results on strongly monotone semiflows due to hirsch and matano in addition a very striking relationship is established between such functional differential equations and corresponding ordinary differential equations an example involving a biochemical feedback loop is considered keywords stability steady states

convergence of solutions for an equation with state dependent delay abstract a result of smith and thieme shows that if a semiflow is strongly order preserving then a typical orbit converges to the set of equilibria for the equation with state dependent delay t x t f x t r x t where 0 and f and r are smooth real functions with f 0 0 and f 0 we construct a semiflow which is monotone but not strongly order preserving we prove a convergence result under a monotonicity condition different from the strong order preserving property and apply it to the above equation to obtain generic convergence

lattice point asymptotics and volume growth on teichmuller space we apply some of the ideas of the ph d thesis of g a margulis mar70 to teichmuller space let x be a point in teichmuller space and let br x be the ball of radius r centered at x with distances measured in the teichmuller metric we obtain asymptotic formulas as r tends to infinity for the volume of br x and also for the cardinality of the intersection of br x with an orbit of the mapping class group

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

convergence in smooth strongly monotone flows defined by semilinear parabolic equations on considere des equations paraboliques semi lineaires dy dt ay f y ou a est un operateur sectoriel sur un banach x ayant une resolvante compacte et f est une c 2 application de l espace des puissances fractionnaires x 0 1 dans x soit y t une solution qui est quasi convergente mais non convergente alors il existe un voisinage u de y 0 y 0 avec la propriete suivante si z u y 0 a une trajectoire bornee et soit z y 0 soit z y 0 alors la solution partant de z converge vers un equilibre

positive heteroclinics and traveling waves for scalar population models with a single delay the existence of positive heteroclinic solutions is proven for a class of scalar population models with one discrete delay traveling wave solutions for scalar delayed reaction diusion equations are also obtained as perturbations of heteroclinic solutions of the associated equation without diusion as an illustration the results are applied to the nicholson s blowflies equation with diusion n t t x d 2n x2 t x n t x pn t x e an t x in the case of p e for which the nonlinearity is non monotone

on the periodic solutions of periodic multi species competitive systems with delays the paper considers general n species periodic kolmogorov competitive systems of functional differential equations with finite or infinite delays applying schauder s fixed point theorem a criterion on the existence of the positive periodic solutions is established as applications the existence and global asymptotic stability of the single species logistic periodic model and n species lotka volterra type periodic model with delays are discussed