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

stability crossing surfaces for linear time delay systems with three delays in this article the stability of linear systems with time delays is studied the cases where the characteristic equations of the system include three delays are investigated using the geometrical relations in a normalised polynomial plane a graphical method is presented to visualise the stability domains in the space of the time delays in this space the points at which the characteristic equation has a zero on the imaginary axis the border between stability and instability regions are identified these points form several surfaces called the stability crossing surfaces this work extends the results of the previous works on the stability crossing curves defined in the two dimensional space plane of delays to a higher dimension and provides new geometric interpretations for the stability crossing conditions

demixing can occur in binary hard sphere mixtures with negative nonadditivity a binary fluid mixture of nonadditive hard spheres characterized by a size ratio gamma sigma 2 sigma 1 infinity a demixing transition with a critical consolute point at a packing fraction scaling as eta approximately d2 d is found even for slightly negative nonadditivity if delta 1 8 ln gamma 2 arguments concerning the stability of the demixing with respect to freezing are provided

depletion potentials in highly size asymmetric binary hard sphere mixtures comparison of simulation results with theory we report a detailed study using state of the art simulation and theoretical methods of the effective depletion potential between a pair of big hard spheres immersed in a reservoir of much smaller hard spheres the size disparity being measured by the ratio of diameters q ensuremath equiv ensuremath sigma s ensuremath sigma b small particles are treated grand canonically their influence being parameterized in terms of their packing fraction in the reservoir ensuremath eta s r two monte carlo simulation schemes the geometrical cluster algorithm and staged particle insertion are deployed to obtain accurate depletion potentials for a number of combinations of q ensuremath leqslant 0 1 and ensuremath eta s r after applying corrections for simulation finite size effects the depletion potentials are compared with the prediction of new density functional theory dft calculations based on the insertion trick using the rosenfeld functional and several subsequent modifications while agreement between the dft and simulation is generally good significant discrepancies are evident at the largest reservoir packing fraction accessible to our simulation methods namely ensuremath eta s r 0 35 these discrepancies are however small compared to those between simulation and the much poorer predictions of the derjaguin approximation at this ensuremath eta s r the recently proposed morphometric approximation performs better than derjaguin but is somewhat poorer than dft for the size ratios and small sphere packing fractions that we consider the effective potentials from simulation dft and the morphometric approximation were used to compute the second virial coefficient b 2 as a function of ensuremath eta s r comparison of the results enables an assessment of the extent to which dft can be expected to correctly predict the propensity toward fluid fluid phase separation in additive binary hard sphere mixtures with q ensuremath leqslant 0 1 in all the new simulation results provide a fully quantitative benchmark for assessing the relative accuracy of theoretical approaches for calculating depletion potentials in highly size asymmetric mixtures

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

synchronized hopf bifurcation analysis in a neural network model with delays we consider the synchronized periodic oscillation in a ring neural network model with two different delays in self connection and nearest neighbor coupling employing the center manifold theorem and normal form method introduced by hassard et al we give an algorithm for determining the hopf bifurcation properties using the global hopf bifurcation theorem for fde due to wu and bendixson s criterion for high dimensional ode due to li and muldowney we obtain several groups of conditions that guarantee the model have multiple synchronized periodic solutions when the transfer coefficient or time delay is sufficiently large

asymptotic stability for a linear difference equation with variable delay we shall obtain sufficient conditions for the uniform stability and the global asymptotic stability of the linear difference equation with variable delay xn 1 xn pnxn kn 0 n n where pn is a sequence of nonnegative real numbers kn is a sequence of nonnegative integers and there exists a nonnegative integer k such that kn k for n n

depletion interactions in colloidal fluids statistical mechanics of derjaguin s analysis abstract the statistical mechanics of hard body models of colloidal fluids is reviewed for specific comparison with the well known analysis of derjaguin predicting the nature of solvent mediated colloidal interactions special attention is focussed on the so called depletion interaction for which derjaguin s analysis predicts dramatic effects at medium to high solvent density not supported by standard integral equation approximations liquid state density functional theory nor available simulation data nevertheless the derjaguin approximation limit can be expressed in terms of an exact statistical mechanical sum rule whose nature makes it difficult to argue for a qualitative breakdown of the derjaguin prediction for depletion forces i focus attention on the remarkable structural consequences implied by the derjaguin sum rule analysis including a possible physical interpretation in terms of the difficulty of squeezing out the final layer of solvent adsorbed between colloids or a colloid and a wall i conclude that the statistical mechanics of colloidal depletion is extremely interesting in that either current standard approximations in liquid state physics qualitatively fail to describe the phenomena or our understanding of the physics of colloidal interactions is seriously defective

multistability and stable asynchronous periodic oscillations in a multiple delayed neural system abstract we consider a network of three identical neurons with multiple discrete signal transmission delays the model for such a network is a system of nonlinear delay differential equations after some consideration of the absolute synchronization of the system and the global attractivity of the zero solution we present a detailed discussion about the boundaries of the stability region of the trivial solution this allows us to determine the possible codimension one bifurcations which occur in the system in particular we show the existence of standard hopf bifurcations giving rise to synchronized periodic solutions and of d 3 equivariant hopf bifurcations giving rise to three types of periodic solutions phase locked mirror reflecting and standing waves hopf hopf and hopf steady state bifurcations interactions are shown to exist and give rise to coexistence of stable synchronized and desynchronized solutions perturbation techniques coupled with the floquet theory are used to determine the stability of the phase locked oscillations

exact stability sets for a linear difference system with diagonal delay abstract this paper is devoted to the stability analysis of a delay difference system of the form x n 1 a x n k b y n y n 1 c x n a y n k where a b and c are real numbers and k is a positive integer we establish some exact conditions for the zero solution of the system to be asymptotically stable

fundamental measure density functional theory for nonadditive hard core mixtures the one dimensional case we treat a one dimensional binary mixture of hard core particles that possess nonadditive diameters for this model a density functional theory is constructed following similar principles as an earlier extension of rosenfeld s fundamental measure theory to three dimensional nonadditive hard sphere mixtures the theory applies to arbitrary positive and moderate negative nonadditivity and reduces to percus exact functional in the additive case bulk direct correlation functions are obtained as functional derivatives of the excess free energy functional results for the partial pair correlation functions in bulk as calculated via the ornstein zernike route and using the direct correlation functions as input show very good agreement with results from our monte carlo computer simulations of the mixture

dynamics of a higher order rational difference equation abstract our aim in this paper is to investigate the dynamics of difference equation y n 1 p qy n 1 y n k n 0 1 2 where the initial conditions y k y 1 y0 are non negative k 1 2 3 and the parameters p and q are non negative we study characteristics such as the global stability the boundedness of positive solutions and the character of semicycles of the above mentioned difference equation in particular our results solve the open problem introduced by kulenovic and ladas in their monograph m r s kulenovic g ladas dynamics of second order rational difference equations with open problems and conjectures chapman and hall crc boca raton 2002

a spectral element approach for the stability of delay systems we describe a spectral element approach to study the stability and equilibria solutions of delay differential equations ddes in contrast to the prototypical temporal finite element analysis tfea the described spectral element approach admits spectral rates of convergence and allows exploiting hp convergence schemes the described approach also avoids the limitations of analytical integrations in tfea by using highly accurate numerical quadratures enabling the study of more complicated ddes the effectiveness of this new approach is compared with well established methods in the literature using various case studies specifically the stability results are compared with the conventional tfea and legendre collocation methods whereas the equilibria solutions are compared with the numerical simulations and the homotopy perturbation method hpm solutions our results reveal that the presented approach can have higher rates of convergence than both collocation methods and the hpm copyright 2011 john wiley sons ltd

well posedness for semidiscrete fractional cauchy problems with finite delay abstract we address the study of well posedness on lebesgue spaces of sequences for the following fractional semidiscrete model with finite delay 0 1 u n t u n u n f n n n 0 1 r n 0 where t is a bounded linear operator defined on a banach space x typically a space of functions like l p 1 p and corresponds to the time discretization of the continuous riemann liouville fractional derivative by means of the poisson distribution we characterize the existence and uniqueness of solutions in vector valued lebesgue spaces of sequences of the model 0 1 in terms of boundedness of the operator valued symbol z 1 z 1 i z t 1 z 1 z 1 whenever 0 1 and x satisfies a geometrical condition for this purpose we use methods from operator valued fourier multipliers and resolvent operator families associated to the homogeneous problem we apply this result to show a practical and computational criterion in the context of hilbert spaces

hard sphere fluids in contact with curved substrates the properties of a hard sphere fluid in contact with hard spherical and cylindrical walls are studied rosenfeld s density functional theory dft is applied to determine the density profile and surface tension gamma for wide ranges of radii of the curved walls and densities of the hard sphere fluid particular attention is paid to investigate the curvature dependence and the possible existence of a contribution to gamma which is proportional to the logarithm of the radius of curvature moreover by treating the curved wall as a second component at infinite dilution we provide an analytical expression for the surface tension of a hard sphere fluid close to arbitrary hard convex walls the agreement between the analytical expression and dft is good our results show no signs for the existence of a logarithmic term in the curvature dependence of gamma

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

asymptotic properties of the positive equilibrium of a discrete survival model this paper is concerned with the discrete wazewska and lasota model x n 1 x email protected n pe n x n k where email protected 0 1 n email protected 0 and email protected 0 1 2 we show that every positive solution of is persistent and then we provide sufficient conditions for oscillation of all solutions about x finally we give sufficient conditions for x to be stable or attractive

the freezing method for abstract nonlinear difference equations the freezing method for ordinary differential systems is extended to a class of semilinear difference equations in a hilbert space whose linear parts have slowly varying coefficients and nonlinearities satisfying local lipschitz conditions the main methodology is based on a combined use of recent norm estimates for operator valued functions with the freezing method as well as the multiplicative representation of solutions thus explicit stability and boundedness conditions are derived applications to infinite dimensional delay difference systems are discussed

on explicit conditions for the asymptotic stability of linear higher order difference equations we derive some explicit sufficient conditions for the asymptotic stability of the zero solution in a general linear higher order difference equation and compare our estimations with other related results in the literature our main result also applies to some nonlinear perturbations satisfying a kind of sublinearity condition

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

periodic solutions and stability for a singularly perturbed linear delay differential equation abstract we describe the bifurcation hypersurfaces for periodic solutions of a singularly perturbed linear differential difference equation in the space of the coefficients of the equation for low dimension we show that the locus of stability of that equation approaches the locus of stability of a limit difference equation

complete stability robustness of third order lti multiple time delay systems a unique procedure is presented in this paper for a complete stability robustness of the third order lti multiple time delay systems lti mtds the uniqueness of the treatment is simply due to the fact that there is no comparable methodology presently in the literature the end result of this procedure is an exhaustive and precise determination of the stable regions in the domain of time delays the backbone of the method is a novel framework called the cluster treatment of characteristic roots ctcr ctcr is constructed over two fundamental propositions the first proposition claims the existence of a bounded number of so called kernel curves where the only imaginary characteristic roots occur the second proposition is on an interesting directional invariance property of the crossing tendencies of these imaginary roots for simplicity of conveyance and without loss of generality the number of time delays is taken as two in this document the new methodology is expandable to higher order dynamics with more time delays than two as the authors intend to demonstrate in future publications publications

a note on delay independent stability of a predator prey model abstract this paper analyzes the delay independent stability of a predator prey model with the assistance of the delay independent stability criteria for a class of retarded dynamical systems an interesting result is obtained that the delay independent stability condition is equivalent to the zero delay stability condition in this model the physical meaning of this result is also given

convergence and periodicity of solutions for a class of delay difference equations we derive a class of delay difference equations with piecewise constant nonlinearity the convergence of solutions and the existence of asymptotically stable periodic solutions are investigated for such a class of difference equations

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

positive solutions to a type of multi point boundary value problem with delay and one dimensional p laplacian abstract this paper deals with a type of multi point boundary value problem with delay and one dimensional p laplacian by using guo krasnosel skii fixed point theorem and generalization of the leggett williams fixed point theorem due to avery and peterson we obtain that bvp 1 1 has at least one positive solution or three positive solutions

qualitative analysis of a discrete logistic equation with several delays in this paper we study the qualitative behavior of solutions of the discrete delay logistic equation with several delaysx n 1 x email protected i 1 mr i1 x n k ik n 0 1 2 where r email protected 0 for i 1 m k i i 1 2 m are positive integers and email protected 0 we obtain sufficient conditions for the global attractivity of all positive solutions about the positive equilibrium furthermore we show that such model is uniformly persistent and that all its eventually positive solutions are bounded the oscillation about the positive equilibrium is also discussed

stability crossing set for systems with two scalar delay channels the characteristic function of a system with three scalar delay channels contains cross terms of different delays this article studies the parameterization and geometric structure of the stability crossing set the set of delay combinations with at least one characteristic root on the imaginary axis for such systems understanding the structure of this set is crucial to the identification of stable regions in the delay parameter space using the d subdivision method the presence of the cross terms significantly complicates the analysis and requires a quite different method than the case without these cross terms and it involves more numerical computation

stability of dynamic groups in distributed computing systems abstract large distributed computing systems provide the opportunity for the synergistic use of shared resources an example model is computational ecosystems however as networks continue to expand it is not obvious that all of the agents within a network should participate in one interacting set although smaller groups may forfeit potential synergy they also avoid much of the complexity and overhead of coordination the nature of the dynamics is complicated by the inherent delays in networks and the state update schemes applied by the agents large intelligent systems must provide for 1 the participation of agents in a smaller group and or 2 the participation of agents in the systemwide group only a fraction of the time both of these behaviors are modeled by a system of differential equations with a discrete distribution of time delays stability analysis determines the boundaries for damped and persistent oscillations based on the average of the discrete time delays in large systems there is a fixed ratio between these boundaries e 2 the results also show that stability improves with diversity in the delays

cohen kaplansky domains integral domains with a finite number of irreducible elements we define an integral domain r to be a cohen kaplansky domain ck domain if every element of r is a finite product of irreducible elements and r has only finitely many nonassociate irreducible elements the purpose of this paper is to investigate ck domains many conditions equivalent to r being a ck domain are given for example r is a ck domain if and only if r is a one dimensional semi local domain and for each nonprincipal maximal ideal m of r rm is finite and rm is analytically irreducible or if and only if g r the group of divisibility of r is finitely generated and rank g r max r we show that a ck domain is a certain special type of composite or pullback of a subring of a finite homomorphic image of a semilocal pid noetherian domains with g r finitely generated are also investigated

stability and exponential stability of linear discrete systems with constant coefficients and single delay this paper investigates the exponential stability and exponential estimate of the norms of solutions to a linear system of difference equations with single delay x k 1 a x k b x k m k 0 1 where a b are square constant matrices and m n sufficient conditions for exponential stability are derived using the method of lyapunov functions and its efficiency is demonstrated by examples

new explicit global asymptotic stability criteria for higher order difference equations new explicit sufficient conditions for the asymptotic stability of the zero solution of higher order difference equations are obtained these criteria can be applied to autonomous and nonautonomous equations the celebrated clark asymptotic stability criterion is improved also applications to models from mathematical biology and macroeconomics are given

geometric stability switch criteria in delay differential equations with two delays and delay dependent parameters abstract most modeling efforts involve multiple physical or biological processes all physical or biological processes take time to complete therefore multiple time delays occur naturally and shall be considered in more advanced modeling efforts carefully formulated models of such natural processes often involve multiple delays and delay dependent parameters however a general and practical theory for the stability analysis of models with more than one discrete delay and delay dependent parameters is nonexistent the main purpose of this paper is to present a practical geometric method to study the stability switching properties of a general transcendental equation which may result from a stability analysis of a model with two discrete time delays and delay dependent parameters that dependent only on one of the time delay in addition to simple and illustrative examples we present a detailed application of our method to the study of a two discrete delay sir model

on the difference equation yn 1 a ynyn k with a 0 abstract we find conditions for the global asymptotic stability of the unique negative equilibrium y 1 a of the equation 0 1 y n 1 a y n y n k where y k y k 1 y0 0 a

uniform stability of nonlinear difference systems abstract we offer sufficient conditions for the uniform stability and uniformly asymptotic stability of the zero solution of the nonlinear difference system formula where 0 1 f n s r sis the set of all functions n k 0 rfor somek n andxn sis defined byxn m x n m form n k 0

delay independent stability criteria for a class of retarded dynamical systems with two delays in this paper sufficient and necessary delay independent stability criteria are given for a class of retarded dynamical systems with two discrete time delays and parameters the delay independent stability problem of the system is discussed in terms of the stability of the characteristic function which is determined by checking the existence of real roots for some polynomials the criteria are also illustrated by examples

a remark on the ode with two discrete delays abstract the aim of this paper is to outline a formal framework for the analytical analysis of the hopf bifurcations in the delay differential equations with two independent time delays some results for the differential difference equations with two delays when the both of the coefficients of linearized equation are negative were obtained in x li s ruan j wei stability and bifurcation in delay differential equations with two delays j math anal appl 236 1999 254 280 in the paper we present some remarks on the case studied in x li s ruan j wei stability and bifurcation in delay differential equations with two delays j math anal appl 236 1999 254 280 and also two other cases namely when the coefficients of linearized equation have different signs and when coefficients are both positive

the asymptotic stability of xn 1 axn bxn k 0 we obtain necessary and sufficient conditions for the asymptotic stability of the difference equation xn 1 axn bxn k 0 n 0 1 2 where the coefficients a and b are real numbers and the delay k is a nonnegative integer

when is length a length function abstract we show that ideal length defines a length function on almost noetherian integral domains this length function is a sum of multiplicities and in favourable cases a linear combination on n of discrete valuations as a consequence 1 noetherian domains have length functions infra krull domains are weakly krull almost noetherian domains we characterize these integral domains and establish their properties placing emphasis on integral closures and length functions descent properties are shown applications to the computation of elasticities and factorization properties are given

theory of asymmetric nonadditive binary hard sphere mixtures it is shown that the formal procedure of integrating out the degrees of freedom of the small spheres in a binary hard sphere mixture works equally well for nonadditive as it does for additive mixtures for highly asymmetric mixtures small size ratios the resulting effective hamiltonian of the one component fluid of big spheres which consists of an infinite number of many body interactions should be accurately approximated by truncating after the term describing the effective pair interaction using a density functional treatment developed originally for additive hard sphere mixtures the zero one and two body contribution to the effective hamiltonian are determined it is demonstrated that even small degrees of positive or negative nonadditivity have significant effect on the shape of the depletion potential the second virial coefficient b2 corresponding to the effective pair interaction between two big spheres is found to be a sensitive measure of the effects of nonadditivity the variation of b2 with the density of the small spheres shows significantly different behavior for additive slightly positive and slightly negative nonadditive mixtures possible repercussions of these results for the phase behavior of binary hard sphere mixtures are discussed and it is suggested that measurements of b2 might provide a means of determining the degree of nonadditivity in real colloidal mixtures

commutative rings in which every ideal is a product of primary ideals abstract a q ring is a commutative ring in which every ideal is a product of primary ideals we show that r is a q ring if and only if r is a laskerian ring every ideal has a primary decomposition and every nonmaximal prime ideal of r is finitely generated and locally principal we also show that r x or r x is a q ring if and only if r is a finite direct product of dedekind domains and special principal ideal rings

stability analysis of nonautonomous difference systems with delaying arguments abstract we present sufficient conditions for the stability of the nonautonomous difference system x k 1 j 0 m a j k x k j k z with m 1 when the n n matrices a j are slowly varying coefficients the proposed approach is based on the generalization of the freezing method for ordinary differential equations the stability conditions are formulated in terms of the corresponding cauchy s function

what good are numerical simulations of chaotic dynamical systems abstract numerical simulations of mathematical models can suggest that the models are chaotic for example one can compute an orbit and its associated finite time lyapunov exponents and these computed exponents can be positive it is not clear how far these suggestions can be trusted because as is well known numerical methods can introduce spurious chaos or even suppress actual chaos this focused review examines the fidelity of numerical methods we look at the didactic example of the gauss map from the theory of continued fractions which allows a simple examination of backward error analysis for discrete dynamical systems and gives a clear picture of the effects of floating point arithmetic a similar use of backward error analysis in the form of defect control gives a useful understanding in the case of continuous dynamical systems finally we discuss limitations of this backward point of view

advanced clustering with frequency sweeping methodology for the stability analysis of multiple time delay systems a new methodology advanced clustering with frequency sweeping acfs is introduced for the stability analysis of the most general class of linear time invariant time delay systems with multiple delays acfs is a cross fertilization of algebraic geometry frequency sweeping technique and the root clustering paradigm and it can directly extract the 2 d cross sections of the stability views in any two delay domain in this domain acfs can also test the delay independent stability based on necessary and sufficient conditions and can compute for the delay dependent case the precise lower and upper bounds of the only parameter the frequency that acfs sweeps case studies that are prohibitive to analyze with the existing analytical methods are presented to demonstrate the strengths of the 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

stability robustness analysis of multiple time delayed systems using building block concept an intriguing perspective is presented in studying the stability robustness of systems with multiple independent and uncertain delays it is based on a holographic mapping which is implemented over the domain of the delays this mapping considerably alleviates the problem which is otherwise known to be notoriously complex it creates a dramatic reduction in the dimension of the problem from infinity to manageably small number ultimately the process is reduced to studying the problem within a finite dimensional cube with edges of length 2pi in the new domain what we call the building block in essence the mapping collapses the entire set of potential stability switching points onto a small upperbounded number of building hypersurfaces we further demonstrate that these building hypersurfaces can be implicitly defined and they are completely isolated within the above mentioned cube it is also shown that the exhaustive detection of these building hypersurfaces is necessary and sufficient in order to arrive at the complete stability robustness picture we seek as a consequence this concept yields a very practical and efficient procedure for the stability assessment of such systems this novel perspective serves very well for the preparatory steps of the authors earlier contribution in the area cluster treatment of characteristic roots ctcr we elaborate on this combination which forms the main contribution of the paper several example case studies are also provided

technical communique on delay robustness analysis of a simple control algorithm in high speed networks this paper focuses on the robustness analysis of a simple second order control algorithm for data transfer in high speed networks the model under consideration derived using a fluid approximation technique can be found in izmailov siam j contr optimiz 34 1996 1767 the novelty of the approach lies in characterizing the stability of the scheme in the delay parameter space where the delays correspond to the control time interval and to the round trip time respectively thus we shall compute some delay insensitive measures for the algorithm which give upper and lower bounds for the uncertainty in the knowledge of the round trip times

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

global stability of yn 1 p qyn ryn k1 yn in this paper we investigate the global stability of difference equation y n 1 p qy n ry n k1 y n n 0 1 2 where the initial conditions y k y 1 y 0 are non negative email protected 1 2 3 and the parameters p q and r are non negative we show that when rq 1 and k is odd then this equation possesses unbounded solutions

a unique methodology for the stability robustness of multiple time delay systems abstract the stability robustness is considered for linear time invariant lti systems with rationally independent multiple time delays against delay uncertainties the problem is known to be notoriously complex primarily because the systems are infinite dimensional due to delays multiplicity of the delays in this study complicates the analysis even further and rationally independent feature of the delays makes the problem prohibitively challenging as opposed to the tds with commensurate time delays where time delays are rationally related a unique framework is described for this broadly studied problem and the enabling propositions are proven we show that this procedure analytically reveals all possible stability regions exclusively in the space of the delays as an added strength it does not require the delay free system under consideration to be stable our methodology offers a resolution to this question which has been studied from variety of directions in the past four decades none of these respectable investigations can however deliver an exact and exhaustive robustness declaration from this stand point the new method has a unique contribution

dynamics of a rational difference equation in this paper we investigate the periodic character invariant intervals oscillation and global stability of all positive solutions of the equationx n 1 px n x n kq x n k n 0 1 where the parameters p and q and the initial conditions x k x 0 are nonnegative real numbers as might be expected the two cases p q give rise to different dynamic behaviors in particular our results solve the open problem proposed by kulenvic and ladas in their monograph dynamics of second order rational difference equations with open problems and conjectures chapman hall crc boca raton 2001

dynamics of a non linear difference equation abstract our aim in this paper is to investigate the dynamics of difference equation y n 1 y n py n k y n q n 0 1 2 where the initial conditions y k y 1 y0 are non negative k 1 2 3 and the parameters p and q are non negative we study characteristics such as periodicity invariant interval the character of semicycles the global stability and the boundedness of positive solutions of the above mentioned difference equation in particular our results solve the open problem introduced by kulenovic and ladas in their monograph dynamics of second order rational difference equations with open problems and conjectures chapman and hall crc boca raton 2002