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

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

approximate controllability of fractional nonlocal delay semilinear systems in hilbert spaces we study the existence and approximate controllability of a class of fractional nonlocal delay semilinear differential systems in a hilbert space the results are obtained by using semigroup theory fractional calculus and schauder s fixed point theorem multi delay controls and a fractional nonlocal condition are introduced furthermore we present an appropriate set of sufficient conditions for the considered fractional nonlocal multi delay control system to be approximately controllable an example to illustrate the abstract results is given

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

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

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

invariance of the reachable set under nonlinear perturbations for the abstract controlled volterra equation qquad x t bar x t int 0 t boldsymbol psi t s phi s x s bf b s v s ds on 0 t we consider the reachable set mathcal k phi x t text for some v in mathfrak b viewing phi cdot cdot as a nonlinear perturbation of an otherwise linear control problem conditions are obtained under which mathcal k phi mathcal k 0 for a suitable class mathfrak f of such nonlinear perturbations phi whenever the linear problem is known to have a reachable set invariant under affine perturbations phi cdot cdot g in mathfrak z the results generalize those obtained by naito 7 for control of the heat equation

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

nonlocal cauchy problems governed by compact operator families abstract we study the existence of mild solutions for the nonlocal cauchy problem u t au t f t u t t t 0 t 0 t u t 0 g u u 0 and give new criterions which extend some existing results in this area

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 conditions for a class of delay differential systems in this paper necessary and sufficient conditions of asymptotic stability independent of delay of a certain class of both the retarded and neutral types of delay differential systems are obtained the stability conditions reduce to positivity of a quartic equation conditions for the latter in explicit form are given by the authors in an earlier publication in addition sufficient conditions for stability for a general order delay differential system independent of delay are also obtained such conditions are ascertained from the fact that a sufficient condition for any algebraic equation to have no positive real roots is that all its coefficients be positive

on concepts of controllability for deterministic and stochastic systems the new necessary and sufficient conditions which are formulated in terms of convergence of a certain sequence of operators involving the resolvent of the negative of the controllability operator are found for deterministic linear stationary control systems to be completely and approximately controllable respectively these conditions are applied to study the s controllability a property of attaining an arbitrarily small neighborhood of each point in the state space with a probability arbitrarily close to one and c controllability the s controllability fortified with some uniformity of stochastic systems it is shown that the s controllability the c controllability of a partially observable linear stationary control system with an additive gaussian white noise disturbance on all the intervals 0 t for t 0 is equivalent to the approximate complete controllability of its deterministic part on all the intervals 0 t for t 0

lf spaces quasi baire spaces and the strongest locally convex topology on e coarser than r n 1 2 if e 0 e and is the finest locally convex n l topology on e which induces on each e a topology coarser than then e is said to be the inductive limit of the sequence e z ithe family e z 1 is a definin9 sequence for the inductive limit space e z note that we are using a narrow definition of the notion of an inductive limit that befits our needs if each e r is a fr6chet banach space e e 1 and z is hausdorff then the inductive limit e z is said to be an lf space lb space and we write

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

linear systems with commensurate time delays stability and stabilization independent of delay notions of exponential stability independent of delay and stabilizability independent of delay are developed for the class of delay differential systems of the retarded type with commensurate time delays various criteria for exponential stability independent of delay with a given order are specified in terms of matrices whose entries are functions of a single real parameter and polynomials in one variable whose coefficients are functions of a single real parameter sufficient conditions and a necessary condition based on local stabilizability are given for stabilizability independent of delay using state feedback with commensurate time delays constructive methods for determining a stabilizing feedback are also presented the last part of the paper deals with a standard type of observer and regulator with the requirement that the closed loop system be stable independent of delay

partial approximate controllability of nonlocal fractional evolution equations via approximating method abstract in this paper we study partial approximate controllability of semilinear nonlocal fractional evolution equations in hilbert spaces by using fractional calculus variational approach and approximating technique we give the approximate problem of the control system and get the compactness of approximate solution set then new sufficient conditions for the partial approximate controllability of the control system are obtained when the compactness conditions or lipschitz conditions for the nonlocal function are not required finally we apply our abstract results to the partial approximate controllability of the semilinear heat equation and delay equation

approximate controllability of semilinear evolution equations of fractional order with nonlocal and impulsive conditions via an approximating technique abstract this paper is concerned with the approximate controllability of the semilinear fractional evolution equations with nonlocal and impulsive conditions our main results are obtained by utilizing the technique of approximate solution and the theory of fixed point in addition the impulsive functions in this paper are supposed to be continuous and the nonlocal item is divided into two cases lipschitz continuous and only continuous which generalizes the previous contributions finally two examples are worked out to illustrate our obtained results

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

approximate controllability of semilinear functional equations in hilbert spaces in this paper approximate and complete controllability for semilinear functional differential systems is studied in hilbert spaces sufficient conditions are established for each of these types of controllability the results address the limitation that linear systems in infinite dimensional spaces with compact semigroup cannot be completely controllable the conditions are obtained by using the schauder fixed point theorem when the semigroup is compact and the banach fixed point theorem when the semigroup is not compact

approximate controllability of evolution systems with nonlocal conditions we study the approximate controllability for the abstract evolution equations with nonlocal conditions in hilbert spaces assuming the approximate controllability of the corresponding linearized equation we obtain sufficient conditions for the approximate controllability of the semilinear evolution equation the results we obtained are a generalization and continuation of the recent results on this issue at the end an example is given to show the application of our result

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

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

approximate controllability of a delayed semilinear control system with growing nonlinear term abstract this paper deals with the approximate controllability of a semilinear control system with delay where the nonlinear term satisfies the linear growth condition sufficient conditions for the approximate controllability of a semilinear control system have been established by assuming that the corresponding linear control system with delay is approximately controllable to prove our results the schauder fixed point theorem is applied and instead of a co semigroup associated with the mild solution of the system we use the so called fundamental solution

partial controllability concepts the main results in theory of controllability are formulated for deterministic or stochastic control systems given in a standard form i e given as a first order differential equation driven by an infinitesimal generator of strongly continuous semigroup in an abstract hilbert or banach space and disturbed by a deterministic function or by a white noise process at the same time some deterministic or stochastic linear systems can be written in a standard form if the state space is enlarged respectively the ordinary controllability conditions for them are too strong since they assume extended state space it is reasonable to introduce partial controllability concepts which assume original state space in this paper we study necessary and sufficient conditions of partial controllability for deterministic and stochastic linear control systems given in a standard form and their implications to particular cases

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

on the approximate controllability of semilinear fractional differential systems fractional differential equations have wide applications in science and engineering in this paper we consider a class of control systems governed by the semilinear fractional differential equations in hilbert spaces by using the semigroup theory the fractional power theory and fixed point strategy a new set of sufficient conditions are formulated which guarantees the approximate controllability of semilinear fractional differential systems the results are established under the assumption that the associated linear system is approximately controllable further we extend the result to study the approximate controllability of fractional systems with nonlocal conditions an example is provided to illustrate the application of the obtained theory

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

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

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 with respect to the delay on a paper of k l cooke and p van den driessche a proposal for the correction of the main result of the title s paper is made some accompanying comments on other points are given so a simpler central result is derived an explicit representation of the set of stable delays is achieved

approximate controllability of fractional delay dynamic inclusions with nonlocal control conditions we introduce a nonlocal control condition and the notion of approximate controllability for fractional order quasilinear control inclusions approximate controllability of a fractional control nonlocal delay quasilinear functional differential inclusion in a hilbert space is studied the results are obtained by using the fractional power of operators multi valued analysis and sadovskii s fixed point theorem main result gives an appropriate set of sufficient conditions for the considered system to be approximately controllable as an example a fractional partial nonlocal control functional differential inclusion is considered

non baire hyperplanes in non separable baire spaces abstract given an infinite dimensional banach space e one may ask does e have 1 a properly separable quotient 2 a dense non baire hyperplane every closed hyperplane in a baire space is baire the famous separable quotient problem 1 remains unsolved and question 2 is question 13 1 1 of p perez carreras and j bonet north holland math stud vol 131 north holland amsterdam 1987 in 1966 wilansky klee conjectured the answer to 2 is always no j arias de reyna denied the conjecture math ann 249 1980 111 114 proving the answer to 2 is yes whenever the answer to 1 is yes under assumption of c additivity c a a condition weaker than martin s axiom m valdivia extended the result to e a baire 2nd category in itself topological vector space collect math 34 1983 287 296 in general 2 is non trivial only in case e is baire with e e an extension of valdivia s extension yields the complete answer for 2 in the general locally convex setting affirming question 13 1 1 of perez carreras and bonet referenced above in particular a not necessarily hausdorff locally convex space e has a dense non baire hyperplane if and only if dim e and e e even for e non locally convex dim e and e e suffices but is not necessary whereas e e is obviously always necessary in order that e have a dense non baire hyperplane whether e e suffices in the hausdorff non locally convex case and whether the assumption of c a can be omitted we do not know contrastingly any infinite dimensional e is the union of a sequence of hyperplanes and if e is baire one of the hyperplanes must be dense and baire and every hyperplane of e must be unordered baire like if e is

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

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

approximate controllability for a class of semilinear abstract equations in this paper a class of control systems governed by the semilinear abstract equation dot y ay f y bv is considered a sufficient condition for the approximate controllability is obtained which improves j henry s results on a nonlinear parabolic control systems with some more serious restrictions it is suitable not only to the infinite dimensional case but also to the finite dimensional case two examples are given to explain the applications of the theory

absolute stability in delay equations abstract an equilibrium of a delay equation is said to be absolutely stable if it is asymptotically stable for all delays this is equivalent to a certain characteristic equation s having all its roots in the left half plane for all delays we obtain a simple necessary and sufficient condition for absolute stability of a class of delay equations

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

approximate controllability of semilinear deterministic and stochastic evolution equations in abstract spaces various sufficient conditions for approximate controllability of linear evolution systems in abstract spaces have been obtained but approximate controllability of semilinear control systems usually requires some complicated and limited assumptions in this paper we show the approximate controllability of the abstract semilinear deterministic and stochastic control systems under the natural assumption that the associated linear control system is approximately controllable the results are obtained using new properties of symmetric operators which are proved in this paper compact semigroups the schauder fixed point theorem and or the contraction mapping principle

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

compact coverings for baire locally convex spaces very recently tkachuk has proved that for a completely regular hausdorff space x the space cp x of continuous real valued functions on x with the pointwise topology is metrizable complete and separable iff cp x is baire i e of the second baire category and is covered by a family k n n of compact sets such that k k if our general result which extends some results of de wilde sunyach and valdivia states that a locally convex space e is separable metrizable and complete iff e is baire and is covered by an ordered family k n n of relatively countably compact sets consequently every baire locally convex space which is quasi suslin is separable metrizable and complete

existence and controllability results for second order impulsive stochastic evolution systems with state dependent delay in this paper we discuss a kind of impulsive second order stochastic evolution systems with state dependent delay in a real separable hilbert space the results concerning the existence and controllability of mild solutions have been addressed by means of the fixed point techniques some sufficient conditions are formulated as well as an application involving partial differential equation with impulses is presented

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

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

approximate controllability of nonlocal and impulsive neutral integro differential equations using the resolvent operator theory and an approximating technique abstract our purpose in this paper is to study the approximate controllability of nonlocal and impulsive neutral integro differential equations using the resolvent operator theory the approximating technique semigroup theory and the theory of fixed point we also derive a variation of constants formula for representing a solution of the given system by resolvent operators and then study the existence of a mild solution of the system we prove the main results by taking the impulsive functions to be continuous only and taking the nonlocal initial condition function to be lipschitz continuous in the first case and continuous only in the second case finally the main results are illustrated using examples

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

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

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