continuous pole placement for delay equations in this paper we describe a stabilization method for linear time delay systems which extends the classical pole placement method for ordinary differential equations unlike methods based on finite spectrum assignment our method does not render the closed loop system finite dimensional but consists of controlling the rightmost eigenvalues because these are moved to the left half plane in a quasi continuous way we refer to our method as continuous pole placement we explain the method by means of the stabilization of a linear finite dimensional system in the presence of an input delay and illustrate its applicability to more general stabilization problems

stability and bifurcation in delay differential equations with two delays abstract the purpose of this paper is to study a class of differential difference equations with two delays first we investigate the local stability of the zero solution of the equation by analyzing the corresponding characteristic equation of the linearized equation general stability criteria involving the delays and the parameters are obtained second by choosing one of the delays as a bifurcation parameter we show that the equation exhibits the hopf bifurcation the stability of the bifurcating periodic solutions are determined by using the center manifold theorem and the normal form theory finally as an example we analyze a simple motor control equation with two delays our results improve some of the existing results on this equation

delay induced instabilities in gyroscopic systems it is shown that stable linear gyroscopic systems of the form mx tx kx 0 m 0 always become unstable when an arbitrarily small delay is introduced in the gyroscopic term in the case where k is negative definite then the system will be unstable for all positive delays on the other hand examples are given showing that some of these systems may actually become asymptotically stable for larger values of the delay parameter

complex dynamics in a singular leslie gower predator prey bioeconomic model with time delay and stochastic fluctuations in this paper a class of singular leslie gower predator prey bioeconomic models with environment fluctuations and time delays is investigated local stability analysis of the model reveals that there is a phenomenon of singularity induced bifurcation due to variation of economic interest of harvesting by choosing the delay as a bifurcation parameter it is shown that the hopf bifurcations can occur as the delay crosses some critical values then the effect of a fluctuating environment on the singular stochastic delayed predator prey bioeconomic model is discussed finally numerical simulations demonstrate that the amplitude of oscillation for population is enhanced when compared with the oscillation observed in the deterministic environment

a sufficient condition for the asymptotic stability of certain linear processes a sufficient condition is given for the laplace transforms of some linear processes to be analytic in the closed right half plane

uniform persistence and global attractivity for nonautonomous competitive systems with nonlinear dispersion and delays in this paper we consider a nonautonomous lotka volterra competitive system with nonlinear discrete dispersion and a finite number of discrete delays the system which is consisted of two lotka volterra patches has two competitors one can disperse between two patches but the other is confined to one patch and cannot disperse our main focus is persistence i e the survival in two patches of the population and the existence of a periodic solution we also establish conditions under which the system admits a positive periodic solution which attracts all solutions

stability test and stability conditions for delay differential systems in this paper a stability test method is demonstrated and explicit stability conditions for the first order retarded delay differential system with constant coefficients in the delay interval are obtained this paper shows that under suitable conditions a class of first order delay systems can be alternately stable as the delay h

delay independent stability of a special sequence of neutral difference differential equations with one delay abstract the equations of the title for the state x t r l x d a d a n x t b d b d b n x t t 0 d d dt 1 are considered in the parameter space a b b n p where p is defined by re a a is a second real point a a for a r a is the complex conjugate to a c the same notation applies for b by a tedious but elementary analysis the set s0 p for which 1 has for all t 0 only asymptotically stable solutions in the sense of liapunov is explicitly determined in the form b n a b 1 2 the stability boundary decays exponentially with respect to the multiplicity n of the zeros of the coefficient polynomials of 1 we generalize a theorem of f brauer j differential equations 69 1987 185 191 dealing with delay independent stability for characteristic equations of the form h z a z b z exp zt t 0 3 where a z b z are holomorphic in re z 0 in such a way that the neutral case can be dealt with

modeling instability in the control system for human respiration applications to infant non rem sleep mathematical models of the human respiratory control system have been developed since 1940 to study a wide range of features of this complex system the phenomena collectively referred to as periodic breathing including cheyne stokes respiration and apneustic breathing have important medical implications the hypothesis that periodic breathing is the result of delay in the feedback signals to the respiratory control system has been studied since the work of f s grodins j gray a i norins r w jones j appl physiol 1 1954 283 308 in the early 1950s the purpose of this paper is to extend the model presented by m c k khoo r e kronauer k p strohl a s slutsky j appl physiol 53 3 1982 644 659 in 1991 to include variable delay in the feedback control loop and to study the phenomena of periodic breathing and apnea as they occur during quiet sleep in infant sleep respiration at around 4 months of age the nonlinear mathematical model consists of a feedback control system of five delay differential equations numerical simulations are performed to study instabilities in the control system and the occurrence of periodic breathing and apnea in the above case which is a time frame of high incidence of sudden infant death syndrome sids

dynamics of second order in time evolution equations with state dependent delay abstract we deal with a class of second order in time nonlinear evolution equations with state dependent delay this class covers several important pde models arising in the theory of nonlinear plates we first prove well posedness in a certain space of functions which are c 1 in time in contrast with the first order models with discrete state dependent delay this result does not require any compatibility conditions the solutions constructed generate a dynamical system in a c 1 type space over delay time interval our main result shows that this dynamical system possesses compact global and exponential attractors of finite fractal dimension to obtain this result we adapt the recently developed method of quasi stability estimates

critical delays and polynomial eigenvalue problems in this work we present a new method to compute the delays of delay differential equations ddes such that the dde has a purely imaginary eigenvalue for delay differential equations with multiple delays the critical curves or critical surfaces in delay space that is the set of delays where the dde has a purely imaginary eigenvalue are parameterized we show how the method is related to other works in the field by treating the case where the delays are integer multiples of some delay value i e commensurate delays the parameterization is done by solving a quadratic eigenvalue problem which is constructed from the vectorization of a matrix equation and hence typically of large size for commensurate delay differential equations the corresponding equation is a polynomial eigenvalue problem as a special case of the proposed method we find a closed form for a parameterization of the critical surface for the scalar case we provide several examples with visualizations where the computation is done with some exploitation of the structure of eigenvalue problems

harmless delays for uniform persistence abstract this paper studies a two dimensional predator prey system with a finite number of discrete delays our purpose is to demonstrate that the time delays are harmless for uniform persistence of the solutions of the system the results are obtained by constructing suitable persistence functionals

the effects of harvesting and time delay on predator prey systems with holling type ii functional response in this paper the effects of harvesting and time delay on two different types of predator prey systems with delayed predator specific growth and holling type ii functional response are studied by applying the normal form theory of retarded functional differential equations developed by faria and magalhaes j differential equations 122 1995 pp 181 200 j differential equations 122 1995 pp 201 224 hopf bifurcations are demonstrated in models with harvesting of the prey at a constant rate by taking the delay as a bifurcation parameter and numerical examples supporting our theoretical prediction are also given furthermore bifurcation analysis indicates that delayed predator prey systems with predator harvesting exhibit bogdanov takens bifurcation the versal unfoldings of the models at the bogdanov takens singularity are obtained and numerical simulations and bifurcation diagrams are given to illustrate the obtained results

dynamical analysis of a delayed ratio dependent prey predator model within fluctuating environment abstract in this paper we consider a two dimensional ratio dependent prey predator model involving discrete time delay within fluctuating environment firstly we discuss basic dynamical properties of non delayed and delayed model system in brief within deterministic environment next we construct the stochastic differential equation model and stochastic delay differential equation model to study the effect of environmental driving forces on the dynamical behaviour stochastic models are extension of deterministic models by perturbing two demographic parameters namely birth rate of prey population and death rate of predator population with white noise terms characterized by gaussian distribution having zero mean and unit spectral density we calculate population fluctuation intensity variance for prey and predator species by laplace transform methods for stochastic differential equation model and fourier transforms method for stochastic delay differential equation model numerical simulations are carried out to substantiate the analytical findings significant outcomes of our analytical findings and their interpretations from ecological point of view are provided in concluding section

a dynamic is lm business cycle model with two time delays in capital accumulation equation in this paper we analyze a augmented is lm business cycle model with the capital accumulation equation that two time delays are considered in investment processes according to kalecki s idea applying stability switch criteria and hopf bifurcation theory we prove that time delays cause the equilibrium to lose or gain stability and hopf bifurcation occurs

power spectra and dynamical invariants for delay differential and difference equations abstract the mackey glass and ikeda delay differential equations ddes are models of feedback systems in which attractor dimension is proportional to the delay power spectra from these models are investigated analytically and numerically as the delay increases much beyond the system response time an exponentially decaying spectrum with a near periodic superimposed modulation appears it is shown that each peak in this modulation is associated with a mode of oscillation predicted by linear stability analysis around the fixed point the number of such modes within a characteristic autocorrelation time of the solution agrees with the lyapunov dimension of the attractor the disappearance of this modulation at higher delay values is also explained the decay rate of the spectrum in the mid to high frequency range is found to agree with the sum of the positive lyapunov exponents i e with the metric entropy realistic models with a distribution of delays display similar spectra as their memory kernel narrows into a delta function for very large delay the dde approaches an infinite dimensional continuous time difference equation ctde with each point on a delay interval evolving independently and according to a chaotic discrete time map ctde spectra which have many features of finite delay dde spectra can be computed analytically if the spectrum of this map is known for constant initial functions they have a 1 f 2 form at low frequencies our analysis suggests that the spectrum of the chaotic map is at the origin of the peak shapes in dde spectra at low frequency our findings highlight the relevance of the linear prrperties of ddes to the characterization of their nonlinear properties

empirical shrinkage estimator for consistency assessment of treatment effects in multi regional clinical trials multi regional clinical trials have been widely used for efficient global new drug developments both a fixed effect model and a random effect model can be used for trial design and data analysis of a multi regional clinical trial in this paper we first compare these two models in terms of the required sample size type i error rate control and the interpretability of trial results we then apply the empirical shrinkage estimation approach based on the random effect model to two criteria of consistency assessment of treatment effects across regions as demonstrated in our computations compared with the sample estimator the shrinkage estimator of the treatment effect of an individual region borrowing information from the other regions is much closer to the estimator of the overall treatment effect has smaller variability and therefore provides much higher probability for demonstrating consistency we use a multinational trial example with time to event endpoint to illustrate the application of the method copyright 2012 john wiley sons ltd

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

technical communique on stability of second order quasi polynomials with a single delay in this note the stability of a second order quasi polynomial with a single delay is studied although there is a vast literature on this problem most available solutions are limited to some particular cases moreover some published results on this subject appear to contain imprecise or even wrong conditions the purpose of this note is to show that by accurate application of known theories a complete explicit characterization of stability regions can be derived in a most general case as a byproduct of the proposed analysis we show that in the high order case the quasi polynomial is delay independent unstable whenever its delay free version has an odd number of unstable roots or equivalently a negative static gain

stability and bifurcation analysis in van der pol s oscillator with delayed feedback abstract the classical van der pol equation with delayed feedback and a modified equation where a delayed term provides the damping are considered linear stability of the equations is investigated by analyzing the associated characteristic equations it is found that there exist the stability switches when delay varies and the hopf bifurcation occurs when the delay passes through a sequence of critical values the bifurcation diagram is drawn in e k plane and the stability and direction of the hopf bifurcation are determined by applying the normal form theory and the center manifold theorem

stability of a competition model with two stage structure a population model with stage structure which describes the competition of two species for space is considered the model is established under the assumptions that reproductive rates of two species are affected by competition and that the space occupied by one type of juveniles cannot be neglected estimates on the length of delays for which positive equilibrium of the model remains stable are given sufficient conditions are also derived that ensure global stability of positive equilibrium

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

stability and bifurcations of equilibria in a multiple delayed differential equation the influence of multiple negative delayed feedback loops on the stability of a single action mechanism are considered a characteristic equation for the linearized stability of the equilibrium is completely analyzed as a function of two parameters describing a delay in one loop and a ratio of the gains in the two feedback loops the bifurcations occurring as the linear stability is lost are analyzed by the construction of a centre manifold in particular the nature of hopf and more degenerate higher codimension bifurcations are explicitly determined

sdes with oblique reflection on nonsmooth domains in this paper we consider stochastic differential equations with reflecting boundary conditions for domains that might have corners and for which the allowed directions of reflection at a point on the boundary of the domain are possibly oblique the main results are strong existence and uniqueness for solutions of such equations a key ingredient is a family of relatively regular functions appropriate to the given domain and directions of reflection two cases are treated in the paper in the first case the direction of reflection is single valued and varies smoothly and the main new feature is that the boundary of the domain may be nonsmooth in the second case the domain is taken to be the intersection of a finite number of domains with relatively smooth boundary and at the resulting corner points more than one oblique direction is allowed

brief paper delay dependent stability for discrete systems with large delay sequence based on switching techniques this paper considers the exponential stability problem for a class of discrete time varying delay systems with large delay sequences ldss a new method based on a switching technique is presented to solve this problem a switched delay system in which one of the discrete subsystems may be unstable is firstly employed to describe such a system and then some new concepts about ldss are introduced next using a novel piecewise lyapunov functional explicit delay dependent conditions are developed to show how long and how frequent the ldss can be and still maintain the system exponentially stable without ldss the criterion obtained in this paper includes the established one as a special case two numerical examples are given to show the effectiveness of the proposed method

stability conditions for the general linear difference differential equation with constant coefficients and one constant delay abstract for the application low degree cases of the equations of the title are of special interest lag independent stability conditions are derived for all systems up to degree two inclusive some necessary stability conditions for large lags are expounded in the non neutral case left half planes depending on the lag and containing all zeros of the characteristic function are obtained a sufficient lag independent condition for the whole class considered is found special attention is devoted to the neutral case for that case a collection of disks covering all zeros of the characteristic function is given the result is illustrated by the example of the general neutral characteristic function with coalescing zeros finally zero free regions around the zeros of the coefficient polynomials are derived to derive the results conformal mappings are studied

boundedness of solutions of a nonlinear nonautonomous neutral delay equation abstract sufficient conditions are obtained for the boundedness of solutions of the non linear nonautonomous neutral equation x t r t x t a t x t 1 c t x t 1 which arise in a food limited population model this partially answers a recent open question proposed by k gopalsamy and b g zhang

dynamics of the density dependent predator prey system with beddington deangelis functional response abstract two models of a density dependent predator prey system with beddington deangelis functional response are systematically considered one includes the time delay in the functional response and the other does not the explorations involve the permanence local asymptotic stability and global asymptotic stability of the positive equilibrium for the models by using stability theory of differential equations and lyapunov functions for the permanence the density dependence for predators is shown to give some negative effect for the two models further the permanence implies the local asymptotic stability for a positive equilibrium point of the model without delay also the global asymptotic stability condition which can be easily checked for the model is obtained for the model with time delay local and global asymptotic stability conditions are obtained

neurocomputing with time delay analysis for solving convex quadratic programming problems this paper presents a neural network computational scheme with time delay consideration for solving convex quadratic programming problems based on some known results a delay margin is explicitly determined for the stability of the neural dynamics under which the states of the neural network does not oscillate the configuration of the proposed neural network is provided operational characteristics of the neural network are demonstrated via numerical examples

harmless delays and global attractivity for nonautonomous predator prey system with dispersion abstract in this paper we consider a nonautonomous predator prey model with dispersion and a finite number of discrete delays the system consists of two lotka volterra patches and has two species one can disperse between two patches but the other is confined to one patch and cannot disperse our purpose is to demonstrate that the time delays are harmless for uniform persistence of the solutions of the system furthermore we establish conditions under which the system admits a positive periodic solution which attracts all solutions

mathematical analysis of coral reef models abstract it is acknowledged that coral reefs are globally threatened p j mumby et al 10 constructed a mathematical model with ordinary differential equations to investigate the dynamics of coral reefs in this paper we first provide a detailed global analysis of the coral reef ode model in 10 next we incorporate the inherent time delay to obtain a mathematical model with delay differential equations we consider the grazing intensity and the time delay as focused parameters and perform local stability analysis for the coral reef dde model if the time delay is sufficiently small the stability results remain the same however if the time delay is large enough macroalgae only state and coral only state are both unstable while they are both stable in the ode model meanwhile if the grazing intensity and the time delay are endowed some suitable values the dde model possesses a nontrivial periodic solution whereas the ode model has no nontrivial periodic solutions for any grazing rate we study the existence and property of the hopf bifurcation points and the corresponding stability switching directions

parametric empirical bayes inference theory and applications abstract this article reviews the state of multiparameter shrinkage estimators with emphasis on the empirical bayes viewpoint particularly in the case of parametric prior distributions some successful applications of major importance are considered recent results concerning estimates of error and confidence intervals are described and illustrated with data

multi regional clinical trial design and consistency assessment of treatment effects we can apply both fixed and random effects models to multi regional clinical trial mrct design and data analysis thoroughly understanding the features of these models in an mrct setting will help assessing their applicability to an mrct in this paper we discuss the interpretations of trial results from these models we also evaluate the impact of the number of regions and the sample size configuration across the regions on the required total sample size for the overall treatment effect assessment for quantifying treatment effects of individual regions the empirical shrinkage estimator and the james stein type shrinkage estimator associate with smaller variability compared with the regular sample estimator we conduct computation and simulation to compare the performance of these estimators when they are applied to assess consistency of treatment effects across regions we use a multinational trial example to illustrate the application of these methods copyright 2014 john wiley sons ltd

stability analysis and stability conditions in the delay intervals for second order delay systems abstract in tills paper the stability and the stability conditions of a number of second order retarded delay linear differential systems are discussed the paper shows especially that the system which has stationary oscillation when without delay can become asymptotically stable in the large in certain suitable delay intervals

stability in a scalar differential equation with multiple distributed time delays abstract we consider a linear scalar delay differential equation dde consisting of two arbitrary distributed time delays we formulate necessary conditions for stability of the trivial solution which are independent of the distributions for the case of one discrete and one gamma distributed delay we give an explicit description of the region of stability of the trivial solution and discuss how this depends on the model parameters

hopf bifurcation analysis of a system of coupled delayed differential equations in this paper we have considered a system of delay differential equations the system without delayed arises in the lengyel epstein model its dynamics are studied in terms of local analysis and hopf bifurcation analysis linear stability is investigated and existence of hopf bifurcation is demonstrated via analyzing the associated characteristic equation for the hopf bifurcation analysis the delay parameter is chosen as a bifurcation parameter the stability of the bifurcating periodic solutions is determined by using the center manifold theorem and the normal form theory introduced by hassard et al 1981 7 furthermore the direction of the bifurcation the stability and the period of periodic solutions are given finally the theoretical results are supported by some numerical simulations

period to delay ratio near stability boundaries for systems with delayed feedback we show how with a suitable choice of a free parameter period to delay ratios near stability boundaries may be found for delay differential systems with a single delay and with a characteristic equation of the form f g e 0 when f and g do not depend on the delay itself is a natural choice for the free parameter and the the period to delay ratio can be easily found for given values of the parameters of f and g it is shown that if more than one stability switch occurs for such a system as is increased then the period to delay ratio will become progressively smaller with each stable unstable change by considering a model with a variable delay we demonstrate how to determine period to delay ratios when the characteristic equation is such that f and g themselves depend on and show that for the model considered the period must always lie between and 2 an appendix considers the appearance of zero eigenvalues in such characteristic equations

hopf bifurcation in differential equations with delay for tumor immune system competition model this paper deals with the qualitative analysis of the solutions to a model that refers to the competition between the immune system and an aggressive host such as a tumor the model which describes this competition is governed by a system of differential equations with one delay it is shown that the dynamics depends crucially on the time delay parameter by using the time delay as a parameter of bifurcation the analysis is focused on the hopf bifurcation problem to predict the occurrence of a limit cycle bifurcating from the nontrivial steady state the obtained results depict the oscillations given by simulations see m galach int j appl math comput sci 13 2003 pp 395 406 which are observed in reality see d kirschner and j c panetta j math biol 37 1998 pp 235 252 it is suggested to examine by laboratory experiments how to employ these results for control of tumor growth

exact versus discretized stability regions for a linear delay differential equation abstract the paper introduces a system of necessary and sufficient stability conditions for a four term linear delay difference equation with complex coefficients these conditions are derived explicitly with respect to the time lag and can be viewed as a direct discrete counterpart to the existing stability results for the underlying delay differential equation as a main proof tool the boundary locus technique combined with some special results of the polynomial theory is employed since the studied difference equation serves as a method discretization of its continuous pattern several problems of numerical stability are discussed as well

qualitative analysis in a delayed van der pol oscillator abstract the main purpose of this manuscript is to introduce and compare two methods for discussing the nature of hopf bifurcation namely a research method combining the normal form theory and the center manifold theorem and the other method of multiple scales taking a delayed van der pol oscillator as an example the local stability as well as the occurrence of hopf bifurcation are explored via choosing time delay as the bifurcation parameter on the basis of two different methods respectively the characters of hopf bifurcation which includes the direction of hopf bifurcation as well as the stability of bifurcating periodic solutions are analyzed finally numerical simulations supporting the theoretical findings are given and it is observed that the results of two methods are consistent

on approximate continuity and the support of reflected stochastic differential equations in this paper we prove an approximate continuity result for stochastic differential equations with normal reflections in domains satisfying saisho s conditions which together with the wong zakai approximation result completes the support theorem for such diffusions in the uniform convergence topology also by adapting millet and sanz sole s idea we characterize in holder norm the support of diffusions reflected in domains satisfying the lions sznitman conditions by proving limit theorems of adapted interpolations finally we apply the support theorem to establish a boundary interior maximum principle for subharmonic functions

delay enhanced coherent chaotic oscillations in networks with large disorders we study the effect of coupling delay in a regular network with a ring topology and in a more complex network with an all to all global topology in the presence of impurities disorder we find that the coupling delay is capable of inducing phase coherent chaotic oscillations in both types of networks thereby enhancing the spatiotemporal complexity even in the presence of 50 of symmetric disorders of both fixed and random types furthermore the coupling delay increases the robustness of the networks up to 70 of disorders thereby preventing the network from acquiring periodic oscillations to foster disorder induced spatiotemporal order we also confirm the enhancement of coherent chaotic oscillations using snapshots of the phases and values of the associated kuramoto order parameter we also explain a possible mechanism for the phenomenon of delay induced coherent chaotic oscillations despite the presence of large disorders and discuss its applications

stability bifurcation and multistability in a system of two coupled neurons with multiple time delays a system of delay differential equations representing a model for a pair of neurons with time delayed connections between the neurons and time delayed feedback from each neuron to itself is studied conditions for the linear stability of the trivial solution of this system are represented in a parameter space consisting of the sum of the time delays between the elements and the product of the strengths of the connections between the elements it is shown that the trivial fixed point may lose stability via a pitchfork bifurcation a hopf bifurcation or one of three types of codimension two bifurcations multistability near these latter bifurcations is predicted using center manifold analysis and confirmed using numerical simulations

quantifying heterogeneity in a meta analysis the extent of heterogeneity in a meta analysis partly determines the difficulty in drawing overall conclusions this extent may be measured by estimating a between study variance but interpretation is then specific to a particular treatment effect metric a test for the existence of heterogeneity exists but depends on the number of studies in the meta analysis we develop measures of the impact of heterogeneity on a meta analysis from mathematical criteria that are independent of the number of studies and the treatment effect metric we derive and propose three suitable statistics h is the square root of the chi2 heterogeneity statistic divided by its degrees of freedom r is the ratio of the standard error of the underlying mean from a random effects meta analysis to the standard error of a fixed effect meta analytic estimate and i2 is a transformation of h that describes the proportion of total variation in study estimates that is due to heterogeneity we discuss interpretation interval estimates and other properties of these measures and examine them in five example data sets showing different amounts of heterogeneity we conclude that h and i2 which can usually be calculated for published meta analyses are particularly useful summaries of the impact of heterogeneity one or both should be presented in published meta analyses in preference to the test for heterogeneity

an eigenvalue based approach for the robust stabilization of linear time delay systems we present a new numerical procedure for the robust stabilization of linear delay differential equations based on the position of the eigenvalues in the complex plane we assume static perturbations on the system matrices and express the robustness of the stability in terms of complex stability radii in the numerical procedure these stability radii are maximized as a function of the controller parameters this corresponds to a synthesis problem which is solved by a quasi continuous shaping of some frequency response plots the structure of the algorithm is analogous to the continuous pole placement algorithm for the non robust stabilization of linear delay differential equations

stability and bifurcation analysis on a logistic model with discrete and distributed delays in this paper a logistic model with discrete and distributed delays is investigated we first consider the stability of the positive equilibrium and the existence of local hopf bifurcations in succession using the normal form theory and center manifold argument we derive the explicit formulas which determine the stability direction and other properties of bifurcating periodic solutions a numerical simulation for supporting the theoretical analysis is also given

competition in the chemostat a distributed delay model and its global asymptotic behavior in this paper we propose a two species competition model in a chemostat that uses a distributed delay to model the lag in the process of nutrient conversion and study the global asymptotic behavio

theoretical analysis of destabilization resonances in time delayed stochastic second order dynamical systems and some implications for human motor control a linear stochastic delay differential equation of second order is studied that can be regarded as a kramers model with time delay an analytical expression for the stationary probability density is derived in terms of a gaussian distribution in particular the variance as a function of the time delay is computed analytically for several parameter regimes strikingly in the parameter regime close to the parameter regime in which the deterministic system exhibits hopf bifurcations we find that the variance as a function of the time delay exhibits a sequence of pronounced peaks these peaks are interpreted as delay induced destabilization resonances arising from oscillatory ghost instabilities on the basis of the obtained theoretical findings reinterpretations of previous human motor control studies and predictions for future human motor control studies are provided 2006 the american physical society

technical communique invariance properties in the root sensitivity of time delay systems with double imaginary roots if i w ir is an eigenvalue of a time delay system for the delay t 0 then i w is also an eigenvalue for the delays t k t 0 k2 p w for any k z we investigate the sensitivity periodicity and invariance properties of the root i w for the case that i w is a double eigenvalue for some t k it turns out that under natural conditions the condition that the root exhibits the completely regular splitting property if the delay is perturbed the presence of a double imaginary root i w for some delay t 0 implies that i w is a simple root for the other delays t k k 0 moreover we show how to characterize the root locus around i w the entire local root locus picture can be completely determined from the square root splitting of the double root we separate the general picture into two cases depending on the sign of a single scalar constant the imaginary part of the first coefficient in the square root expansion of the double eigenvalue

stochasticity and non locality of time abstract we present simple classical dynamical models to illustrate the idea of introducing a stochasticity with non locality into the time variable for stochasticity in time these models include noise in the time variable but not in the space variable which is opposite to the normal description of stochastic dynamics similarly with respect to non locality we discuss the delayed and predictive dynamics which involve two points separated on the time axis with certain combinations of fluctuations and non locality in time we observe a resonance effect this is an effect similar to stochastic resonance which has been discussed within the normal context of stochastic dynamics but with different mechanisms we discuss how these models may be developed to fit a broader context of generalized dynamical systems where fluctuations and non locality are present in both space and time

existence of strong solutions for ito s stochastic equations via approximations given strong uniqueness for an ito s stochastic equation with discontinuous coefficients we prove that its solution can be constructed on any probability space by using for example euler s polygonal approximations stochastic equations in d and in domains in d are considered

stability and bifurcation in a delayed predator prey system with beddington deangelis functional response we consider a delayed predator prey system with beddington deangelis functional response the stability of the interior equilibrium will be studied by analyzing the associated characteristic transcendental equation by choosing the delay as a bifurcation parameter we show that hopf bifurcation can occur as the delay crosses some critical values the direction and stability of the hopf bifurcation are investigated by following the procedure of deriving normal form given by faria and magalhaes an example is given and numerical simulations are performed to illustrate the obtained results

limit theorems and the support of sdes with oblique reflections on nonsmooth domains abstract in this paper we consider the wong zakai type approximation and the support problem of stochastic differential equations with oblique reflections in nonsmooth domains satisfying conditions introduced by dupuis and ishii 4 we first establish the limit theorem for reflected diffusions by proving that the sequence of solutions of approximating equations converge uniformly in l p to the unique solution of the reflected stochastic differential equation we also prove the approximate continuity and thus characterize the support of diffusions described by reflected sdes

stability and bifurcations for the chronic state in marchuk s model of an immune system in the paper we present known and new results concerning stability and the hopf bifurcation for the positive steady state describing a chronic disease in marchuk s model of an immune system we describe conditions guaranteeing local stability or instability of this state in a general case and for very strong immune system we compare these results with the results known in the literature we show that the positive steady state can be stable only for very specific parameter values stability analysis is illustrated by mikhailov s hodographs and numerical simulations conditions for the hopf bifurcation and stability of arising periodic orbit are also studied these conditions are checked for arbitrary chosen realistic parameter values numerical examples of arising due to the hopf bifurcation periodic solutions are presented

estimating stable delay intervals with a discretized lyapunov krasovskii functional formulation abstract in general a system with time delay may have multiple stable delay intervals especially a stable delay interval does not always contain zero asymptotically accurate stability conditions such as discretized lyapunov krasovskii functional dlf method and sum of square sos method are especially effective for such systems in this article a dlf based method is proposed to estimate the maximal stable delay interval accurately without using bisection when one point in this interval is given the method is formulated as a generalized eigenvalue problem gevp of linear matrix inequalities lmis and an accurate estimate may be reached by iteration either in a finite number of steps or asymptotically the coupled differential difference equation formulation is used to illustrate the method however the idea can be easily adapted to the traditional differential difference equation setting

hopf bifurcation for a differential algebraic biological economic system with time delay abstract in this paper we consider a differential algebraic biological economic system with time delay and harvesting where the dynamics is logistic with the carrying capacity proportional to prey population by considering the time delay as bifurcation parameter we analyze the stability and the hopf bifurcation of the differential algebraic biological economic system based on the normal form approach and the center manifold theory at last numerical simulations are performed to illustrate the analytical results

evaluation of local treatment effect by borrowing information from similar countries in multi regional clinical trials one key objective of a multi regional clinical trial mrct is to quantify country specific treatment effects to support local registration naive estimate of the treatment effects based on country specific subsets of data are inefficient because of relatively sparse country specific sample sizes even in large mrcts and subject to many limitations the recently developed shrinkage estimate approach improves efficiency by incorporating data from other countries but treating all other countries equally thus ignoring similarity to the country of interest ideally for the estimation of treatment effect in a country of interest it is more efficient to use all relevant data such as that from countries that are similar to the one of interest we propose a tree based approach to incorporate similarity with branches or forks used to represent the relationship of treatment effects between countries similarity in certain characteristics among countries in either continuous scale or categorical scale is used to build the tree by allowing local treatment effects for countries to be random effects and follow a gaussian process along the tree we demonstrate that countries sharing the same internal parent nodes are more correlated and a country borrows more information from the neighbors sharing the same parent node we illustrated this statistical framework using a mrct with a continuous endpoint

stabilizing fixed points of time delay systems close to the hopf bifurcation using a dynamic delayed feedback control method this paper deals with the problem of hopf bifurcation control for a class of nonlinear time delay systems a dynamic delayed feedback control method is utilized for stabilizing unstable fixed points near hopf bifurcation using a linear stability analysis we show that under certain conditions of the control parameters and without changing the operating point of the system the onset of hopf bifurcation is delayed meanwhile by applying the center manifold theorem and the normal form theory we obtain formulas for determining the direction of the hopf bifurcation and the stability of bifurcating periodic solutions of the closed loop system numerical simulations are given to justify the validity of the analytical results for the system controlled by the proposed method

stability crossing set for systems with three delays this article describes the stability crossing set for linear time delay systems of arbitrary order with three delays the crossing frequency set which consists of all frequencies where a pair of zeros of the characteristic quasipolynomial may cross the imaginary axis is partitioned to grashof sets and non grashof sets of various types it was found that the general characteristics of the stability crossing set is completely determined by the partition structure of the crossing frequency set with the exception of degenerate cases this article provides a method of explicit and complete parameterization and geometric characterization of the stability crossing set of linear systems with three delays with the well known method of finding the crossing directions this provides a powerful method of finding parameter regions of stable systems extension to systems with additional fixed delays is also discussed

a comprehensive review of stability analysis of continuous time recurrent neural networks stability problems of continuous time recurrent neural networks have been extensively studied and many papers have been published in the literature the purpose of this paper is to provide a comprehensive review of the research on stability of continuous time recurrent neural networks including hopfield neural networks cohen grossberg neural networks and related models since time delay is inevitable in practice stability results of recurrent neural networks with different classes of time delays are reviewed in detail for the case of delay dependent stability the results on how to deal with the constant variable delay in recurrent neural networks are summarized the relationship among stability results in different forms such as algebraic inequality forms m matrix forms linear matrix inequality forms and lyapunov diagonal stability forms is discussed and compared some necessary and sufficient stability conditions for recurrent neural networks without time delays are also discussed concluding remarks and future directions of stability analysis of recurrent neural networks are given

delayed stochastic resonance with a 1 d ring abstract we study here a simple one dimensional ring composed of stochastic binary elements with delayed interaction with this model we can analytically compute interspike interval histograms and show how resonance or rhythmic behaviors arise with only noise and delay

asymptotic stability of a class of neutral delay neuron system in a critical case in this brief the asymptotic stability properties of a neutral delay neuron system are studied mainly in a critical case when the exponential stability is not possible if a critical value of the coefficient in the neutral delay neuron system is considered then the difficulty for our investigation is caused by the fact that the spectrum of the linear operator is asymptotically approximated to the imaginary axis it is obvious that in such a case the equation is not exponentially stable and one needs more subtle methods in order to characterize this type of asymptotic stability hence first the local asymptotic stability for the neutral delay neuron system is studied and the main tools involved are the asymptotic expansions of characteristic roots laplace transforms and function series and a complete analysis of the stability diagram is also presented then based on the energy method the globally asymptotic stability results for the neutral delay neuron system are derived

bifurcation analysis of a chemostat model with a distributed delay a chemostat model of a single species feeding on a limiting nutrient supplied at a constant rate is proposed the model incorporates a general nutrient uptake function and a distributed delay the delay indicates that the growth of the species depends on the past concentration of nutrient using the average time delay as a bifurcation parameter it is proven that the model undergoes a sequence of hopf bifurcations stability criteria for the bifurcating periodic solutions are derived it is also found that the periodic solutions become unstable if the dilution rate is increased computer simulations illustrate the results

support d un processus de reflexion let d be a regular open set in n we describe in this paper the support of d valued diffusion processes with reflecting boundary condition generalizing the results of stroock and varadhan obtained when d o

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

on stability crossing curves for general systems with two delays for the general linear scalar time delay systems of arbitrary order with two delays this article provides a detailed study on the stability crossing curves consisting of all the delays such that the characteristic quasipolynomial has at least one imaginary zero the crossing set consisting of all the frequencies corresponding to all the points in the stability crossing curves are expressed in terms of simple inequality constraints and can be easily identified from the gain response curves of the coefficient transfer functions of the delay terms this crossing set forms a finite number of intervals of finite length the corresponding stability crossing curves form a series of smooth curves except at the points corresponding to multiple zeros and a number of other degenerate cases these curves may be closed curves open ended curves and spiral like curves oriented horizontally vertically or diagonally the category of curves are determined by which constraints are violated at the two ends of the corresponding intervals of the crossing set the directions in which the zeros cross the imaginary axis are explicitly expressed an algorithm may be devised to calculate the maximum delay deviation without changing the number of right half plane zeros of the characteristic quasipolynomial and preservation of stability as a special case

stability and instability of equilibria of an equation of size structured population dynamics in this paper we consider a quasilinear equation with a nonlinear boundary condition modelling the dynamics of a biological population structured by size we suppose vital rates depending on the total population this hypothesis introduces some nonlinearities on the equation and on the boundary condition we study the existence and uniqueness of solution of the initial value problem and the existence of stationary solutions after we calculate the spectrum of the linearization at an equilibrium and we study its local stability

a generalized dynamic is lm model with delayed time in investment processes abstract in this paper we analyze a generalized dynamic is lm model with a government expenditure constraint and the capital accumulation equation that capital stock changes are caused by past investment decisions according to kalecki s idea of time delay in investment processes applying stability switch criteria we prove that the time delay causes the equilibrium point may lose or gain local stability so that the hopf bifurcation occurs

stability switches in a system of linear differential equations with diagonal delay this paper deals with the stability problem of a delay differential system of the form x t ax t t by t y t cx t ay t t where a b and c are real numbers and t is a positive number we establish some necessary and sufficient conditions for the zero solution of the system to be asymptotically stable in particular as t increases monotonously from 0 the zero solution of the system switches finite times from stability to instability to stability if 0 4a bc and from instability to stability to instability if bc 2a 0 as an application we investigate the local asymptotic stability of a positive equilibrium of delayed lotka volterra systems

degenerate lyapunov functionals of a well known prey predator model with discrete delays it is commonly believed that as far as stabilities are concerned small delays are negligible in some modelling processes however to have an affirmative answerfor this common belief is still an open problem for many nonlinear equations in this paper the classical lotka volterra prey predator equation with discrete delays is considered and by using degenerate lyapunov functionals method an affirmative answer to this open problem on both local and global stabilities of the prey predator delay equations is given it is shown that degenerate lyapunov functional method is a powerful tool for studying the stability of such nonlinear delay systems a detailed and explicit procedure of constructing such functionals is provided furthermore some explicit estimates on the allowable sizes of the delays are obtained

on the stability of some exponential polynomials abstract this paper studies elementary transcendental equations of the type z 2 pz q e z rz n 0 where p q r r p 0 q 0 r 0 n 0 1 2 we are mainly interested in the case n 0 for which a characterization of stability is accomplished that is we state a necessary and sufficient condition for all the roots to lie to the left of the imaginary axis also a characterization of stability independent of delays is given sufficient conditions for instability are stated for the cases n 1 2 the proofs are carried by elementary arguments independent of usual tools

periodic solutions and chaos in a non linear model for the delayed cellular immune response abstract we model the cellular immune response using a set of non linear delayed differential equations we observe that the stationary solution becomes unstable above a critical immune response time the exponents characterizing the approach to this bifurcation point as well as the critical slow dynamics are obtained in the periodic regime the minimum virus load is substantially reduced with respect to the stationary solution further increasing the delay time the dynamics display a series of bifurcations evolving to a chaotic regime characterized by a set of 2d portraits