infinite dimensional primitive linearly compact lie superalgebras we classify open maximal subalgebras of all infinite dimensional linearly compact simple lie superalgebras this is applied to the classification of infinite dimensional lie superalgebras of vector fields acting transitively and primitively in a formal neighborhood of a point of a finite dimensional supermanifold

onset of chaos in differential delay equations abstract in the present paper we study the onset of chaos in the differential delay equation x dot t x t bx t 2 1 x 10 t 2 b 0 we develop a new numerical technique and apply it to study the global behavior of the flow on the attractor using this technique we find unstable periodic orbits connections between different periodic orbits transverse homoclinic orbits and try to explain the underlying reason for chaos

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

the capelli eigenvalue problem for lie superalgebras for a finite dimensional unital complex simple jordan superalgebra j the tits kantor koecher construction yields a 3 graded lie superalgebra mathfrak g flat cong mathfrak g flat 1 oplus mathfrak g flat 0 oplus mathfrak g flat 1 such that mathfrak g flat 1 cong j set v mathfrak g flat 1 and mathfrak g mathfrak g flat 0 in most cases the space mathscr p v of superpolynomials on v is a completely reducible and multiplicity free representation of mathfrak g and there exists a direct sum decomposition mathscr p v bigoplus lambda in omega v lambda where left v lambda right lambda in omega is a family of irreducible mathfrak g modules parametrized by a set of partitions omega in these cases one can define a natural basis left d lambda right lambda in omega of capelli operators for the algebra mathscr pd v mathfrak g of mathfrak g invariant superpolynomial differential operators on v in this paper we complete the solution to the capelli eigenvalue problem which asks for the determination of the scalar c mu lambda by which d mu acts on v lambda we associate a restricted root system varsigma to the symmetric pair mathfrak g mathfrak k that corresponds to j which is either a deformed root system of type mathsf a m n or a root system of type mathsf q n we prove a necessary and sufficient condition on the structure of varsigma for mathscr p v to be completely reducible and multiplicity free when varsigma satisfies the latter condition we obtain an explicit formula for the eigenvalue c mu lambda in terms of sergeev veselov s shifted super jack polynomials when varsigma is of type mathsf a m n and okounkov ivanov s factorial schur q polynomials when varsigma is of type mathsf q n along the way we prove that the natural map from the centre of the enveloping algebra of mathfrak g into mathscr pd v mathfrak g is surjective in all cases except when j cong f where f is the 10 dimensional exceptional jordan superalgebra

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

cooperative dynamics in a network of stochastic elements with delayed feedback networks of globally coupled noise activated bistable elements with connection time delays are considered the dynamics of these systems is studied numerically using a langevin description and analytically using 1 a gaussian approximation as well as 2 a dichotomous model the system demonstrates ordering phase transitions and multistability that is for a strong enough feedback it exhibits nontrivial stationary states and oscillatory states whose frequencies depend only on the mean of the time delay distribution function other observed dynamical phenomena include coherence resonance and in the case of nonuniform coupling strengths amplitude death and chaos furthermore an increase of the stability of the trivial equilibrium with increasing nonuniformity of the time delays is observed

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

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

stability of piecewise polynomial collocation for computing periodic solutions of delay differential equations we prove numerical stability of a class of piecewise polynomial collocation methods on nonuniform meshes for computing asymptotically stable and unstable periodic solutions of the linear delay differential equation dot y t a t y t b t y t tau f t by a periodic boundary value approach this equation arises e g in the study of the numerical stability of collocation methods for computing periodic solutions of nonlinear delay equations we obtain convergence results for the standard collocation algorithm and for two variants in particular estimates of the difference between the collocation solution and the true solution are derived for the standard collocation scheme the convergence results are unconditional that is they do not require mesh ratio restrictions numerical results that support the theoretical findings are also given

ikeda hopf bifurcation revisited abstract a large variety of passive optical systems subject to a delayed feedback have appeared in the literature and are described mathematically by the same class of scalar delay differential equations ddes these equations include ikeda dde and their solutions are determined in terms of a control parameter distinct from the delay we concentrate on the first hopf bifurcation generated by a fixed delay and determine a general expression for its direction of bifurcation we then examine our result in the two limits of small and large delays for small delays we show that a hopf bifurcation to nearly sinusoidal oscillations is possible provided that the feedback rate is sufficiently high bifurcation from infinity for large delays we complement the early work by chow et al proc roy soc edinburgh a 120 1992 223 229 and hale and huang j diff equ 114 1994 1 23 by comparing analytical and numerical bifurcation diagrams as the oscillations progressively change from sine to square wave

periodic bi directional cohen grossberg neural networks with distributed delays abstract some sufficient conditions are obtained for the global exponential stability of periodic solutions to periodic bi directional cohen grossberg neural networks involving distributed delays by using the lyapunov functional method and some analytical techniques these results improve and generalize some previous works and are helpful for designing a global exponential stable periodic bi directional cohen grossberg neural networks

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

fractal uncertainty principle with explicit exponent we prove an explicit formula for the dependence of the exponent beta in the fractal uncertainty principle of bourgain dyatlov ann math 187 1 43 2018 on the dimension delta and on the regularity constant c r for the regular set in particular this implies an explicit essential spectral gap for convex co compact hyperbolic surfaces when the hausdorff dimension of the limit set is close to 1

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

harmless delays in cohen grossberg neural networks without assuming monotonicity and differentiability of the activation functions and any symmetry of interconnections we establish some sufficient conditions for the globally asymptotic stability of a unique equilibrium for the cohen grossberg neural network with multiple delays lyapunov functionals and functions combined with the razumikhin technique are employed the criteria are all independent of the magnitudes of the delays and thus the delays under these conditions are harmless 2002 elsevier science b v all rights reserved msc 34d23 34k20 92b20

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

patterns of sustained oscillations in neural networks with delayed interactions we study the cohen grossberg hopfield model of neural networks with delayed interactions when the interconnection matrix has only real and purely imaginary eigenvalues two indices the symmetry index and the antisymmetry index are introduced and are used to describe the pattern of sustained oscillations caused by the delay it is shown that the parameter plane of these indices is divided into two regions by a smooth curve across which the patterns of oscillations switch it is also shown that the stability of sustained oscillations is completely determined by the third order term of the input output relation

classification of linearly compact simple nambu poisson algebras we introduce the notion of a universal odd generalized poisson superalgebra associated with an associative algebra a by generalizing a construction made in the work of de sole and kac jpn j math 8 1 145 2013 by making use of this notion we give a complete classification of simple linearly compact generalized n nambu poisson algebras over an algebraically closed field of characteristic zero

representations of simple noncommutative jordan superalgebras i abstract in this article we begin the study of representations of simple finite dimensional noncommutative jordan superalgebras in the case of degree 3 we show that any finite dimensional representation is completely reducible and depending on the superalgebra quasiassociative or jordan then we study representations of superalgebras d t and k 3 and prove the kronecker factorization theorem for superalgebras d t in the last section we use a new approach to study noncommutative jordan representations of simple jordan superalgebras

a new n 6 superconformal algebra in this paper we construct a newn 6 superconformal algebra which extends the virasoro algebra by theso 6 current algebra by 6 odd primary fields of conformal weight 3 2 and by 10 odd primary fields of conformal weight 1 2 the commutation relations of this algebra which we will refer to asck 6 are represented by short distance operator product expansions ope we constructck 6 as a subalgebra of theso 6 superconformal algebra k6 thus giving it a natural representation as first order differential operators on the circle withn 6 extended symmetry we show thatck 6 has no nontrivial central extensions

classification of simple linearly compact kantor triple systems over the complex numbers abstract simple finite dimensional kantor triple systems over the complex numbers are classified in terms of satake diagrams we prove that every simple and linearly compact kantor triple system has finite dimension and give an explicit presentation of all the classical and exceptional systems

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

normal forms for retarded functional differential equations with parameters and applications to hopf bifurcation abstract the paper addresses for retarded functional differential equations fdes with parameters the computation of normal forms associated with the flow on a finite dimensional invariant manifold tangent to an invariant space for the infinitesimal generator of the linearized equation at a singularity the analysis is based on the theory previously developed for fdes without parameters by considering an extension of a phase space appropriate to the computation of these normal forms as an application the generic hopf bifurcation for scalar retarded fdes is considered

classification of linearly compact simple jordan and generalized poisson superalgebras abstract we classify all linearly compact simple jordan superalgebras over an algebraically closed field of characteristic zero as a corollary we deduce the classification of all linearly compact unital simple generalized poisson superalgebras

global asymptotic stability of a class of nonautonomous integro differential systems and applications abstract in this paper we study the global asymptotic stability of a class of nonautonomous integro differential systems by constructing suitable lyapunov functionals we establish new and explicit criteria for the global asymptotic stability in the sense of definition 2 1 in the autonomous case we discuss the global asymptotic stability of a unique equilibrium of the system and in the case of periodic system we establish sufficient criteria for existence uniqueness and global asymptotic stability of a periodic solution also explored are applications of our main results to some biological and neural network models the examples show that our criteria are more general and easily applicable and improve and generalize some existing results

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

chaotic attractors of an infinite dimensional dynamical system abstract we study the chaotic attractors of a delay differential equation the dimension of several attractors computed directly from the definition agrees to experimental resolution with the dimension computed from the spectrum of lyapunov exponents according to a conjecture of kaplan and yorke assuming this conjecture to be valid as the delay parameter is varied from computations of the spectrum of lyapunov exponents we observe a roughly linear increase from two to twenty in the dimension while the metric entropy remains roughly constant these results are compared to a linear analysis and the asymptotic behavior of the lyapunov exponents is derived

hopf bifurcations in time delay systems with band limited feedback abstract we investigate the steady state solution and its bifurcations in time delay systems with band limited feedback this is a first step in a rigorous study concerning the effects of ac coupled components in nonlinear devices with time delayed feedback we show that the steady state is globally stable for small feedback gain and that local stability is lost generically through a hopf bifurcation for larger feedback gain we provide simple criteria that determine whether the hopf bifurcation is supercritical or subcritical based on the knowledge of the first three terms in the taylor expansion of the nonlinearity furthermore the presence of double hopf bifurcations of the steady state is shown which indicates possible quasiperiodic and chaotic dynamics in these systems as a result of this investigation we find that ac coupling introduces fundamental differences to systems of ikeda type k ikeda k matsumoto high dimensional chaotic behavior in systems with time delayed feedback physica d 29 1987 223 235 already at the level of steady state bifurcations e g bifurcations exist in which limit cycles are created with periods other than the fundamental period 2 mode found in ikeda type systems

calculus structure on the lie conformal algebra complex and the variational complex we construct a calculus structure on the lie conformal algebra cochain complex by restricting to degree one chains we recover the structure of a g complex introduced in a de sole and v g kac

on the tits kantor koecher construction of unital jordan bimodules abstract in this paper we explore relationship between representations of a jordan algebra j and the lie algebra g obtained from j by the tits kantor koecher construction more precisely we construct two adjoint functors l i e j mod 1 g mod 1 and j o r g mod 1 j mod 1 where j mod 1 is the category of unital j bimodules and g mod 1 is the category of g modules admitting a short grading using these functors we classify j such that the semisimple part is of clifford type and the category j mod 1 is tame

on the existence and global bifurcation of periodic solutions to planar differential delay equations abstract this paper is concerned with periodic solutions to one parameter families of planar differential delay equations the concept of slowly oscillating periodic solution is extended to this setting and we state the existence of an unbounded continuum of such solutions

structurable superalgebras of cartan type abstract we describe the simple lie superalgebras arising from the unital structurable superalgebras of characteristic 0 and construct four series of the unital simple structurable superalgebras of cartan type we give a classification of simple structurable superalgebras of cartan type over an algebraically closed field f of characteristic 0 together with the faulkner theorem on the classification of classical such superalgebras it gives a classification of the simple structurable superalgebras over f

existence and global exponential stability of periodic solution of cellular neural networks with time varying delays by using the continuation theorem of mawhin s coincidence degree theory and gronwall s inequality some new sufficient conditions are obtained ensuring existence and global exponential stability of periodic solution of cellular neural networks with periodic coefficients and delays these results are helpful to design globally exponentially stable and oscillatory cellular neural networks

convergence dynamics and pseudo almost periodicity of a class of nonautonomous rfdes with applications this paper studies the dynamics of a system of retarded functional differential equations i e rfdes which generalize the hopfield neural network models the bidirectional associative memory neural networks the hybrid network models of the cellular neural network type and some population growth model sufficient criteria are established for the globally exponential stability and the existence and uniqueness of pseudo almost periodic solution the approaches are based on constructing suitable lyapunov functionals and the well known banach contraction mapping principle the paper ends with some applications of the main results to some neural network models and population growth models and numerical simulations

the stability chart for the linearized cushing equation with a discrete delay and with gamma distributed delays in a proper setting the problem of the title amounts to the determination of all pairs d t for which the function z z 1 exp zt d and the functions fn z z 1 1 ztn n d n n d t 0 have all their zeros in re z 0 of the complex z plane correct versions of results and proofs found in papers of k l cooke and j m grossman j math anal appl 86 1982 592 627 and s p blythe r m nisbeth w s c gurney and n macdonald j math anal appl 109 1985 388 396 are given the argumentation in the proofs of the present paper differs from that of the studies mentioned in contrast to blythe et al the stability behaviours of both models are seen as similar stability charts and stability conditions for some other classes of systems are also given in addition to the gamma distribution for the lags other distributions which are similar in shape but differ greatly in their stability behaviour are also considered

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

representations of simple jordan superalgebras abstract this paper completes description of categories of representations of finite dimensional simple unital jordan superalgebras over algebraically closed field of characteristic zero

systems of differential delay equations floquet multipliers and discrete lyapunov functions abstract we define a discrete integer valued lyapunov function v for cyclic nearest neighbor systems of differential delay equations possessing a feedback condition this extends analogous definitions for cyclic systems of ode s and for scalar differential delay equations we relate the values of v to the real parts of the floquet multipliers for such linear periodic systems and thereby prove all floquet subspaces are at most two dimensional

the behaviour of eigenstates of arithmetic hyperbolic manifolds in this paper we study some problems arising from the theory of quantum chaos in the context of arithmetic hyperbolic manifolds we show that there is no strong localization scarring onto totally geodesic submanifolds arithmetic examples are given which show that the random wave model for eigenstates does not apply universally in 3 degrees of freedom