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

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

asymmetry of the work probability distribution we show both analytically and numerically that for a nonlinear system making a transition from one equilibrium state to another under the action of an external time dependent force the work probability distribution is in general asymmetric even if the evolution dynamics has a symmetry

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

experimental study of the fluctuation theorem in a nonequilibrium steady state the fluctuation theorem ft quantifies the probability of second law violations in small systems over short time scales while this theorem has been experimentally demonstrated for systems that are perturbed from an initial equilibrium state there are a number of studies suggesting that the theorem applies asymptotically in the long time limit to systems in a nonequilibrium steady state the asymptotic application of the ft to such nonequilibrium steady states has been referred to in the literature as the steady state fluctuation theorem or ssft in this paper we demonstrate experimentally the application of the ft to nonequilibrium steady states using a colloidal particle localized in a translating optical trap furthermore we show for this colloidal system that the ft holds under nonequilibrium steady states for all time and not just in the long time limit as in the ssft

the fractal finite element method for added mass type problems summary the fractal finite element method ffem originally developed for calculating stress intensity factors in fracture mechanics problems has been extended to analyse fluid structure interaction in the form of added mass type problems these include the free vibration of a submerged spherical shell and the interaction between a dam and a reservoir for the former problem the numerical solution from the ffem agrees well with the analytical solution and the ffem performed better than conventional finite elements and infinite elements in terms of efficiency for the latter problem the ffem predicted an added mass profile that is different from that based on westergaard s parabolic solution copyright q 2008 john wiley sons ltd

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

intrinsic parameters and stability of differential delay equations through the efforts of many authors analytic solutions and explicit stability criteria have been developed for many types of linear differentialdelay equations the treatise of bellman and cooke 3 provides a good account of work done before 1963 active research in the field continues up to the present besides the concrete results obtained for specific classes of equations there are also some rough general principles that have long guided users of differential delay equations in their efforts to understand the effects of the various kinds of time delays on stability one such principle says that instability will be present when the ratio of the time delay to the relaxation time of the system is large however the stability switching phenomenon discovered as early as 1948 by ansoff and krumhansl 2 contradicts this principle and a great variety of responses to the presence of time lags are now known in their landmark paper on the subject cooke and grossman 4 included a series of key examples illustrating the things that can happen it seems unlikely that any simple general principles will be found to serve as reliable indicators of stability instead we can reasonably hope that the development of further principles of restricted applicability will gradually fill in more of the overall picture to this end we introduce a new framework for the classification and representation of differential delay equations or dde based on the simplest notions of probability theory distributed time delays are represented as probability measures whose expectations and variances can be used to construct intrinsic parameters for the classes of ddes studied intrinsic parametrization has two advantages

steady states invariant measures and response theory using the method of computer simulation we test the predictions of nonlinear response theory for classical systems subject to dissipative external fields we provide convincing numerical evidence that kawasaki methods agree with both the transient time correlation function predictions and with a direct measurement of the nonlinear response furthermore this numerical agreement is observed over a time scale which is sufficiently long for the response to have relaxed to within ensuremath sim 1 of its nonequilibrium steady state value this is in spite of the fact that in the steady state the n particle distribution function ultimately becomes fractal we discuss the normalization of the kawasaki distribution and derive a lagrangian form of the kawasaki response function and show that it is consistent with predictions that are obtained using a natural invariant measure for nonequilibrium steady states c 1995 the american physical society

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

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

the fractal finite element method for unbounded problems the fractal finite element method previously developed for stress intensity factor calculation for crack problems in fracture mechanics is extended to analyse some unbounded problems in half space the concepts of geometrical similarity and two level finite element mesh are applied to generate an infinite number of self similar layers in the far field with a similarity ratio bigger than one that is one layer is bigger than the next in size but of the same shape only conventional finite elements are used and no new elements are generated the global interpolating functions in the form of a truncated infinite series are employed to transform the infinite number of nodal variables to a small number of unknown coefficients associated with the global interpolating functions taking the advantage of geometrical similarity transformation for one layer is enough because the relevant entries of the transformed matrix after assembling all layers are infinite geometric series of the similarity ratio and can be summed analytically accurate nodal displacements are obtained as shown in the numerical examples copyright 2004 john wiley sons ltd

jarzynski equality in van der pol and rayleigh oscillators we have studied the jarzynski equality je in van der pol and rayleigh oscillators which are typical deterministic non hamiltonian models but not expected to rigorously satisfy the je because they are not reversible our simulations that calculate the contribution to the work w of an applied ramp force with a duration show that the je approximately holds for a fairly wide range of including 0 and except for t where t denotes the period of relaxation oscillations in the limit cycle the work distribution function wdf is shown to be non gaussian with the u shaped structure for a strong damping parameter the dependence of r k b tln e w obtained by our simulations is semiquantitatively elucidated with the use of a simple expression for limit cycle oscillations where the bracket expresses an average over the wdf the result obtained in self excited oscillators is in contrast with the fact that the je holds in the nose hoover oscillator which also belongs to deterministic non hamiltonian models

a mathematical study of the hematopoiesis process with applications to chronic myelogenous leukemia this paper is devoted to the analysis of a mathematical model of blood cell production in the bone marrow hematopoiesis the model is a system of two age structured partial differential equations integrating these equations over the age we obtain a system of two nonlinear differential equations with distributed time delay corresponding to the cell cycle duration this system describes the evolution of the total cell populations by constructing a lyapunov functional it is shown that the trivial equilibrium is globally asymptotically stable if it is the only equilibrium it is also shown that the nontrivial equilibrium the most biologically meaningful one can become unstable via a hopf bifurcation numerical simulations are carried out to illustrate the analytical results the study may be helpful in understanding the connection between the relatively short cell cycle durations and the relatively long periods of peripheral cell oscillations in some periodic hematological diseases

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

reexamination of experimental tests of the fluctuation theorem the fluctuation theorem and the jarzynski equality are examined in the light of recent experimental tests for a particle dragged through a solvent it is shown that q the heat exchanged with the reservoir does not obey the jarzynski equality due to slowly decaying tails in its distribution for molecular stretching experiments substantial corrections to the jarzynski equality can result from not measuring the force at the end of the molecule that is moved we also present a proof of the fluctuation theorem for langevin dynamics that is considerably simpler than the standard proof

work distribution functions in polymer stretching experiments we compute the distribution of the work done in stretching a gaussian polymer made of n monomers at a finite rate for a one dimensional polymer undergoing rouse dynamics the work distribution is a gaussian and we explicitly compute the mean and width the two cases where the polymer is stretched either by constraining its end or by constraining the force on it are examined we discuss connections to jarzynski s equality and the fluctuation theorems

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

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

infinite elements with 1 rn type decay this paper presents a method of developing a family of 1 rn type infinite elements for the analysis of problems definite in unbounded media the proposed method is a direct extension of the conventional finite element method the resulting improper integrals are integrated exactly over the infinite element domains two numerical examples in elastic half space static problems are investigated to illustrate the applicability and accuracy of the method the use of the proposed infinite elements yields excellent results and preserves all the advantages of the finite element method

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

dynamic analysis of frames by a two level finite element method abstract a two level finite element technique of constructing a frame super element is introduced to reduce the computational efforts for solving large scale frame problems the ordinary finite element method is used first to yield matrices for the beam members then the nodal displacements of all the nodes are related to those of a small number of selected joints master nodes in the frame by means of global finite element interpolating functions thus the order of the overall matrices is greatly reduced and the frame may be considered as a super element to be connected to other elements by means of the master nodes the accuracy of solution may be improved either with finer subdivision or by taking more master nodes inside each super element

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

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

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

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

a parametric study on the fractal finite element method for two dimensional crack problems the fractal finite element method for calculating 2d stress intensity factors is modified by making the similarity ratio in the construction of the fractal mesh a variable a parametric study is then carried out to examine the effects of the similarity ratio the number of transformation terms reduced integration and the initial crack opening angle on the quality of the numerical solutions it is concluded that a large similarity ratio should be used to create the fractal mesh and that reduced integration and a small initial crack opening angle may be used without producing significant errors in the solutions copyright 2003 john wiley sons ltd

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

an ellipsoidal acoustic infinite element abstract in previous papers the authors presented new 3 d time harmonic prolate and oblate spheroidal acoustic infinite elements based on new prolate and oblate spheroidal multipole expansions for modeling acoustic fields in unbounded domains here we present the development of an ellipsoidal infinite element which is the logical generalization of those elements this development is also based on a new multipole expansion as well as a new system of ellipsoidal coordinates the element stiffness radiation damping and mass matrices are developed and presented in sufficient detail to enable their software implementation both the new coordinate system and the new element include the previous spheroidal coordinate systems and spheroidal elements as limiting cases therefore all the previously reported performance data for the spheroidal elements apply to this ellipsoidal element when used in spheroidal form since the three axes of an ellipsoid can be chosen independently an ellipsoid can circumscribe any structural shape at least as closely and generally more closely than a prolate or oblate spheroid the resulting reduction in size of the finite computational domain will result in even greater computational speeds than those already reported for the spheroidal elements the element may be used to model problems in free space 4 steradians half space 2 quarter space or eighth space 2 since this infinite element provides maximum computational efficiency for structures of all shapes software element libraries would need only this one element for all problems in unbounded domains

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