on stabilization of unstable steady states of autonomous ordinary differential equations via delayed feedback controls abstract the paper discusses stabilizing effects of some time delayed feedback controls applied to unstable steady states of an autonomous system of ordinary differential equations first we derive explicit delay dependent stability conditions that are applicable to a family of time delayed systems with simultaneously triangularizable system matrices then using this criterion and other argumentation we employ diagonal delayed feedback controls of conventional and pyragas type to stabilize unstable steady states of the studied autonomous system more precisely we formulate explicit non improvable and immediately applicable conditions on time delay and feedback strength that enable such a stabilization as an illustration we stabilize the unstable steady states of the rossler dynamical system considered under the standard choice of entry parameters when the uncontrolled system displays a chaotic behavior also we consider a non diagonal feedback control whose rotational gain matrix involving a feedback strength and phase commutes with the jacobi matrix of the uncontrolled system and show its larger stabilization potential with respect to the appropriate diagonal control the obtained results are tested by numerical experiments and confronted with the existing results as a supplement we provide matlab codes supporting theoretical conclusions

cluster method for the ashkin teller model a cluster monte carlo algorithm for the ashkin teller at model is constructed according to the guidelines of a general scheme for such algorithms its dynamical behaviour is tested for the square lattice at model we perform simulations on the line of critical points along which the exponents vary continuously and find that critical slowing down is significantly reduced we find continuous variation of the dynamical exponent z along the line following the variation of the ratio alpha nu in a manner which satisfies the li sokal bound z cluster geq alpha nu that was so far proved only for potts models

asymptotic stability of linear non autonomous difference equations with fixed delay abstract this paper studies the asymptotic stability of the linear non autonomous difference equations with fixed delay it is shown that the difference system is asymptotically stable if and only if the norm of the limit for the coefficient matrix is less than 1 under some conditions furthermore the discretization of the pantograph equation by runge kutta methods with variable stepsize is analyzed finally some numerical experiments are made to demonstrate the main conclusions

unbounded solutions of the equation asymptotic behavior of solutions of first order differential equation with deviating arguments in the email protected t email protected email protected i t y email protected i y email protected i is discussed for t a criterion for representing solutions in exponential form is proved inequalities for solution estimation are given sufficient conditions for the existence of unbounded solutions are derived a relevant illustrative example is given as well known results are discussed and compared

corrections to finite size scaling in two dimensional potts models abstract high resolution monte carlo simulations are used to examine the finite size behavior of q state potts models in two dimensions for q 3 we find that at the critical point bulk properties are subject to much larger corrections to finite size scaling than were previously realized for q 4 we find that corrections to finite size scaling are subtle and that the multiplicative logarithmic correction is insufficient to correct the dominant terms

existence of periodic solutions in a linear higher order system of difference equations in this paper we investigate the existence of nontrivial periodic solutions of a higher order system of difference equations our framework is based on an earlier periodicity condition of us we also use the theory of circulant matrices combined by a theorem of silvester on the computation the determinant of block matrices an illustrative application is given to show the effectiveness of our framework and to point out the connection between our periodicity results and some known stability conditions

improvement of efficiency intervals based on dea by adjusting inputs and outputs we improve the efficiency interval of a dmu by adjusting its given inputs and outputs the interval dea model has been formulated to obtain an efficiency interval consisting of evaluations from both the optimistic and pessimistic viewpoints dmus which are not rated as efficient in the conventional sense are improved so that their lower bounds become as large as possible under the condition that their upper bounds attain the maximum value one the adjusted inputs and outputs keep each other balanced by improving the lower bound of efficiency interval since the lower bound becomes small if all the inputs and outputs are not proportioned in order to improve the lower bound of efficiency interval different target points are defined for different dmus the target point can be regarded as a kind of benchmark for the dmu first a new approach to improvement by adjusting only outputs or inputs is proposed then the combined approach to improvement by adjusting both inputs and outputs simultaneously is proposed lastly numerical examples are shown to illustrate our proposed approaches

effects of time delayed feedback on chaotic oscillators we study the effects of time delayed feedback on chaotic systems where the delay time is both fixed static case and varying dynamic case in time for the static case typical phase coherent and incoherent chaotic oscillators are investigated detailed phase diagrams are investigated in the parameter space of feedback gain k and delay time tau linear stability analysis by assuming the time delayed perturbation varies as e lambdat where lambda is the eigenvalue gives the boundaries of the stability islands and critical feedback gains k c for both rossler oscillators and lorenz oscillators we also found that the stability island are found when the delay time is about tau n 1 2 t where n is an integer and t is the average period of the chaotic oscillator it is shown that these analytical predictions agree well with the numerical results for the dynamic case we investigate rossler oscillator with periodically modulated delay time stability regimes are found for parameter space of feedback gain and modulation frequency in which it was impossible to be stabilized for a fixed delay time we also trace the detailed routes to the stability near the island boundaries for both cases by investigating bifurcation diagrams

analysis and optimization of feedback control algorithms for data transfers in high speed networks two linear feedback control algorithms for handling and preventing congestion in high speed networks are proposed and analyzed the fluid approximation model is described with a continuous time system of delay differential equations the algorithms are asymptotically stable and the transient processes are nonoscillatory the control parameters are locally optimal optimality is based on the asymptotic rate of convergence the results of numerical experiments suggest that these parameters are globally optimal as well the dependence of the quality of service on the duration of the control intervals is analyzed and the performance of algorithms in a nonstationary environment is addressed

global attractivity in nonlinear difference equations of higher order with a forcing term consider the following nonlinear difference equation of order k 1 with a forcing term 0 1 x n 1 a n x n b n f x n k r n n 0 1 where an is a positive sequence in 0 1 bn is a positive sequence rn is a real sequence k is a nonnegative integer and f is a continuous function with 0 we establish a sufficient condition for every solution of eq 0 1 to converge to zero as n several new global attractivity results are obtained for some special cases of eq 0 1 which have been studied widely in the literature our results can be applied to some difference equations derived from mathematical biology

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

stability and bifurcation analysis for a discrete time model of lotka volterra type with delay a discrete model of lotka volterra type with delay is considered and a bifurcation analysis is undertaken for the model we derive the precise conditions ensuring the asymptotic stability of the positive equilibrium with respect to two characteristic parameters of the system it is shown that for certain values of these parameters fold or neimark sacker bifurcations occur but codimension 2 fold neimark sacker double neimark sacker and resonance 1 1 bifurcations may also be present the direction and the stability of the neimark sacker bifurcations are investigated by applying the center manifold theorem and the normal form theory

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

analytical calculation of two leading exponents of the dilute potts model a potts model on a square lattice with two and four spin interaction and site and bond dilution is shown to be dual to itself the model is mapped onto a vertex problem which in turn is equivalent to a solid on solid model by means of these mappings the dilute potts model can be written as a gaussian like model with staggered and direct periodic fields the leading and next to leading exponents of the potts model are calculated subject to the validity of certain assumptions

a sufficient condition for the stability of discrete time systems with state dependent coefficient matrices there is no systematic method of checking the stability of general nonlinear systems in this study we focus on discrete time autonomous systems with state dependent coefficient matrices sufficient conditions for local and global asymptotic stabilities are given for upper triangularizable systems the transformation matrix for triangularization is not required explicitly for checking such conditions moreover the system may have nondifferentiability at the origin which is an advantage of our approach over lyapunov s indirect method

discrete halanay type inequalities and applications in this paper we derive new discrete halanay type inequalities and show some applications in the investigation of the asymptotic behavior of nonlinear di4erence equations in particular di4erence equations involving the maximum functional are considered 2003 elsevier ltd all rights reserved

control of unstable steady states by long delay feedback we present an asymptotic analysis of time delayed feedback control of steady states for large delay time by scaling arguments and a detailed comparison with exact solutions we establish the parameter ranges for successful stabilization of an unstable fixed point of focus type insight into the control mechanism is gained by analyzing the eigenvalue spectrum which consists of a pseudocontinuous spectrum and up to two strongly unstable eigenvalues although the standard control scheme generally fails for large delay we find that if the uncontrolled system is sufficiently close to its instability threshold control does work even for relatively large delay times

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

finite size scaling for correlations of quantum spin chains at criticality we study the finite size scaling behavior of two point correlation functions of translationally invariant many body systems at criticality we propose an efficient method for calculating the two point correlation functions in the thermodynamic limit from numerical data of finite systems our method is most effective when applied to a two dimensional classical system which possesses a conformal invariance by using this method with numerical data obtained from exact diagonalizations and monte carlo simulations we study the spin spin correlations of the quantum spin 1 2 and 3 2 antifierromagnetic chains in particular the logarithmic corrections to power law decay of the correlation of the spin 1 2 isotropic heisenberg antiferromagnetic chain are studied thoroughly we clarify the cause of the discrepancy in previous calculations for the logarithmic corrections our result strongly supports the field theoretic prediction based on the mappings to the wess zumino witten nonlinear model or the sine gordon model we also treat logarithmic corrections and crossover phenomena in the spin spin correlation of the spin 3 2 isotropic heisenberg antiferromagnetic chain our results are consistent with the affleck haldane prediction that the correlation of the spin 3 2 chain exhibits a crossover to the same asymptotic behavior as in the spin 1 2 chain

simple uniform exponential stability conditions for a system of linear delay differential equations abstract uniform exponential stability of linear systems with time varying coefficients x i t j 1 m k 1 r ij a ij k t x j h ij k t i 1 m is studied where t 0 m and r ij i j 1 m are natural numbers a ij k 0 r and h ij k 0 r are measurable functions new explicit result is derived with the proof based on bohl perron theorem the resulting criterion has advantages over some previous ones in that e g it involves no m matrix to establish stability several useful and easily verifiable corollaries are deduced and examples are provided to demonstrate the advantage of the stability result over known results

universality of the crossing probability for the potts model for q 1 2 3 4 the universality of the crossing probability pi hs of a system to percolate only in the horizontal direction was investigated numerically by a cluster monte carlo algorithm for the q state potts model for q 2 3 4 and for percolation q 1 we check the percolation through fortuin kasteleyn clusters near the critical point on the square lattice by using representation of the potts model as the correlated site bond percolation model it was shown that probability of a system to percolate only in the horizontal direction pi hs has the universal form pi hs a q q z for q 1 2 3 4 as a function of the scaling variable z b q l 1 nu q p p c q l zeta q here p 1 exp beta is the probability of a bond to be closed a q is the nonuniversal crossing amplitude b q is the nonuniversal metric factor nu q is the correlation length index and zeta q is the additional scaling index the universal function q x approximately equal exp z the nonuniversal scaling factors were found numerically

an improvement to the cost efficiency interval a dea based approach the purpose of this paper is to improve the cost efficiency interval of a decision making unit by adjusting its observed inputs and outputs we first propose a dea based model with an interval efficiency in which the lower bound and upper bound of this interval are respectively the efficiency obtained from optimistic and pessimistic viewpoints then units which are not prevail as cost efficient are improved so that their lower bounds of cost efficiency become as large as possible and their upper bound attain the maximum value 1 the particular application area investigated is that involving the gas companies of iran

asymptotic convergence criteria of solutions of delayed functional differential equations abstract the convergence of all solutions of the scalar equation x f t x t is studied under the main assumption that every constant is its solution the criterion and the sufficient conditions for convergence are proved for the considered classes of equations it is among others proved that all solutions are convergent if and only if there exists at least one increasing and convergent solution as applications criteria for some classes of linear equations as well as for nonlinear equations are obtained some comparisons with already known results are given too

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

time delay identifiability and estimation for the delayed linear system with incomplete measurement abstract when the excitation and the response of a multiple degree of freedom dof active system is incompletely measurable the identifiability of delay parameter turns into vague it instantly brings confidence problems on health monitoring and fault diagnosing for the control loop to fix this problem this paper inspects the difference between the system s frequency responses before and after control and thereby gives practical criteria on parameter identifiability it shows that when the active control only connects points within measurable ones the delay parameters are all identifiable in other words if someone wants to identify all of the delay parameters in the control loop only the frequency responses that are relative with the control connected points need to be measured based on this conclusion a parameter identification algorithm based on newton raphson method is proposed numerical simulation results show that this algorithm not only gives accurate parameters but also possesses a good quality of noise resistance

limitation of generalized delayed feedback control abstract it had been proved that the delayed feedback control dfc of chaos has a limitation as follows if the linear variational equation about the target hyperbolic unstable periodic orbit upo has an odd number of real characteristic multipliers greater than unity the upo can never be stabilized by the dfc with any value of feedback gain we show that this limitation also holds for generalized dfcs based on the feedback of the difference between the current state and delayed states which include the extended time delay auto synchronization etdas and an exponential dfc

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

convergence of the solutions of the equation y t β t y t δ y t τ in the critical case we study the asymptotic behavior of the solutions of the first order differential equation containing two delays y t t y t y t with t0 r 0 the convergence of all solutions is characterized by the existence of a strictly increasing bounded solution a critical case is found for the coefficient function for coefficients below the critical function a strictly increasing and bounded solution is constructed and thus the convergence of all solutions is shown relations with known results are discussed too

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

unbounded increasing solutions of a system of difference equations with delays we consider a homogeneous system of difference equations with deviating arguments in the form y n k 1 q k n y n p k y n r k where n n 0 n 0 z p k r k are integers r k p k 0 q is a positive integer y y 1 y s t y n 0 r n 0 r 1 r s is an unknown discrete vector function s 1 is an integer r max r 1 r q y n y n 1 y n and k n ij k n i j 1 s are real matrices such that ij k n 0 n 0 1 0 and k 1 q j 1 s ij k n 0 for each admissible i and all n n 0 the behavior of solutions of this system is discussed for n the existence of unbounded increasing solutions in an exponential form is proved and estimates of solutions are given the scalar case is discussed as well

sharp algebraic periodicity conditions for linear higher order difference equations in this paper we give easily verifiable but sharp in most cases necessary and sufficient algebraic conditions for the solutions of systems of higher order linear difference equations to be periodic the main tool in our investigation is a transformation recently introduced by the authors which formulates a given higher order recursion as a first order difference equation in the phase space the periodicity conditions are formulated in terms of the so called companion matrices and the coefficients of the given higher order equation as well

global asymptotic stability in a perturbed higher order linear difference equation abstract in this note we give a sufficient condition for the global asymptotic stability of the zero solution of the difference equation n 1 i 0 k p 1 n n i f n n n 1 n 1 n 0 1 where k and l are nonnegative integers the coefficients pi n are real numbers and the nonlinearity f satisfies the growth condition f n 0 1 l q 0 i lmax i for n 0 1 and i r 0 i where q is a constant the stability condition is formulated in terms of the fundamental solution of the unperturbed equation y n 1 i 0 k p i n y n 1

on the rational difference equation y n 1 a y n y n k we find conditions for the global asymptotic stability of the unique negative equilibrium y 1 a of the equation yn 1 a yn yn k where y k y k 1 y0 a r and k 1 2 3 4

a new view of the lp theory for a system of higher order difference equations it is proved under appropriate assumptions that the solutions of a linear system of higher order difference equations belong to l p that is the pth powers of the solutions are summable for some p 1 our results are based on a new transformation of the higher order system into a first step recursion where the companion matrices are well treatable from our point of view our theory is illustrated by examples including an interesting exponential stability result and a class of linear delay difference equations

absence of phase transition for antiferromagnetic potts models via the dobrushin uniqueness theorem we prove that theq state potts antiferromagnet on a lattice of maximum coordination numberr exhibits exponential decay of correlations uniformly at all temperatures including zero temperature wheneverq 2r we also prove slightly better bounds for several two dimensional lattices square lattice exponential decay forq 7 triangular lattice q 11 hexagonal lattice q 4 and kagome lattice q 6 the proofs are based on the dobrushin uniqueness theorem

global stability and asymptotics of some classes of rational difference equations in this note we prove that the positive solutions of some classes of rational difference equations are globally asymptotically stable using a berg s result we also find asymptotics of some solutions of these equations

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

asymptotic convergence of the solutions of a discrete system with delays abstract a system of s discrete equations y n n y n j y n k is considered where k and j are integers k j 0 n is a real s s square matrix defined for n n 0 k n 0 z with non negative elements ij n i j 1 s such that j 1 s ij n 0 y y 1 y 2 y s t n 0 k n 0 k 1 r s and y n y n 1 y n for n n 0 a method of auxiliary inequalities is used to prove that every solution of the given system is asymptotically convergent under some conditions i e for every solution y n defined for all sufficiently large n there exists a finite limit lim n y n moreover it is proved that the asymptotic convergence of all solutions is equivalent to the existence of one asymptotically convergent solution with increasing coordinates some discussion related to the so called critical case known for scalar equations is given as well

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

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

global attractivity of the difference equation xn 1 α xn k xn in this paper we investigate the global stability of all negative solutions of the difference equationx n email protected x n kx n n 0 1 where a 1 is an integer and the initial conditions x k x 0 are arbitrary real numbers we show that the unique negative equilibrium of the equation is a global attractor with a basin that depends on certain conditions of the coefficient

an inverse dea model for inputs outputs estimate abstract in this paper we discuss such problems if among a group of decision making units we increase certain inputs to a particular unit and assume that the dmu maintains its current efficiency level with respect to other units how much more outputs could the unit produce or if the outputs need to be increased to a certain level and the efficiency of the unit remains unchanged how much more inputs should be provided to the unit we treat them as inverse data envelopment analysis dea problems and propose a method to solve such problems the problem is transformed into a multi objective programming problem to solve though in some special cases it can be answered by solving just one single object lp problem we use two examples to illustrate our computation method

stability switches in linear delay difference equations the paper discusses necessary and sufficient conditions for the asymptotic stability of the zero solution of the linear delay difference equation y n 1 email protected n email protected n k where a b are complex numbers and k is a positive integer compared to the case when a b are real numbers the stability behavior of this equation turns out to be much richer in particular if a b 1 then as k monotonously increases the equation may switch finite times from asymptotic stability to instability and vice versa we describe an interesting structure of the set of these stability switches their explicit values and apply the obtained results to some important delay difference equations and their systems

qualitative properties of some higher order difference equations we present sufficient conditions which guarantee that all positive solutions of some higher order rational difference equations are global asymptotically stable the boundedness of the solutions and the existence of prime period two solutions of such equations 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

delayed feedback control of chaos bifurcation analysis we study the effect of time delayed feedback control in the form proposed by pyragas on deterministic chaos in the rossler system we reveal the general bifurcation diagram in the parameter plane of time delay and feedback strength k which allows one to explain the phenomena that have been discovered in some previous works we show that the bifurcation diagram has essentially a multi leaf structure that constitutes multistability the larger the time delay the larger the number of attractors that can coexist in the phase space feedback induces a large variety of regimes non existent in the original system among them tori and chaotic attractors born from them finally we estimate how the parameters of delayed feedback influence the periods of limit cycles in the system

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

algebraic criteria for stability of linear neutral systems with a single delay abstract the stability of linear neutral delay differential systems with a single delay via routh hurwitz and schur cohn criteria is investigated some algebraic criteria for delay independent stability are presented these criteria may complement those reported in the literature finally two examples illustrate the criteria

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

asymptotic convergence of the solutions of a discrete equation with several delays abstract a discrete equation y n i 1 s i n y n j i y n k i with integer delays k i and j i k i j i 0 is considered it is assumed that i z n 0 k 0 n 0 z k max k 1 k 2 k s z p p p 1 p z i 1 s i n 0 s z 1 is a fixed integer and n z n 0 criteria of asymptotic convergence of solutions are expressed in terms of inequalities for the functions i i 1 s some general properties of solutions are derived as well it is e g proved that for the asymptotical convergence of all solutions the existence of a strictly monotone and asymptotically convergent solution is sufficient a crucial role in the analysis of convergence is played by an auxiliary inequality derived from the form of a given discrete equation

asymptotic stability condition for a class of linear delay difference equations of higher order abstract in this paper we obtain a necessary and sufficient condition for the asymptotic stability of the zero solution of the linear delay difference equation x n 1 x n p j 1 n x n k j 1 l 0 n 0 1 2 by using root analysis for the characteristic equation here p is a real number and k l and n are positive integers with k n 1 l

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

dual models of interval dea and its extension to interval data abstract the purpose of this paper is to develop a new dea with an interval efficiency an original dea model is to evaluate each dmu optimistically there is another model called inverted dea to evaluate each dmu pessimistically but there are no relations essentially between dea and inverted dea thus we formulate a dea model with an interval efficiency which consists of efficiencies obtained from the optimistic and pessimistic viewpoints thus two end points can construct an interval efficiency with the same idea we deal with the interval inefficiency model which is inverse to interval efficiency finally we extend the proposed dea model to interval data and fuzzy data

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

on asymptotic behaviour of the difference equation xn 1 α xn kxn in this paper we investigate the global stability and the periodic character of positive solutions of the difference equationx n email protected x n kx nunder specified conditions

resolving the order of phase transitions in monte carlo simulations the authors made a monte carlo simulation of the two dimensional potts model with q 3 4 and 5 to examine the question whether numerical methods can distinguish the order of a phase transition for the subtle cases that this model exemplifies they found that the finite size scaling test for susceptibilities has sufficient power for this purpose whereas the simple method of detecting metastability signals often fails

hopf bifurcation and global periodic solutions in a delayed predator prey system this paper is concerned with a delayed predator prey system with same feedback delays of predator and prey species to their growth respectively we prove that a sequence of hopf bifurcations occur at the positive equilibrium as the delay increases monotonously from zero by using the theory of normal norm and center manifold reduction an explicit algorithm for determining the direction of hopf bifurcations and the stability of bifurcating periodic solutions is derived in addition the global existence results of periodic solutions bifurcating from hopf bifurcations are established by using a global hopf bifurcation result due to wu j wu symmetric functional differential equations and neural networks with memory trans amer math soc 350 1998 4799 4838 finally a numerical example supporting our theoretical prediction is also given our findings are contrasted with recent studies on a delayed predator prey system with the feedback time delay of prey species to its growth by song and wei y song j wei local hopf bifurcation and global periodic solutions in a delayed predator prey system j math anal appl 301 2005 1 21 as the feedback time delay increases monotonously from zero the positive equilibrium of the latter switches k times from stability to instability to stability in contrast the positive equilibrium of our system appears to lose the above property

the global attractivity of difference equations of nonincreasing nonlinearities with applications abstract the global attractivity of the unique positive equilibrium of the equation x n 1 g x n k 1 x n k 2 x n k m n 0 1 2 is investigated where g is a nonincreasing continuous function in each of its arguments and the k are positive integers we are able to use our results to extract some important global attractivity criteria of the positive equilibria of the discrete clark model x n 1 x n f x n k and the rational recursive sequence x n 1 a bx n a x n 1 as well

dynamics of a family of two dimensional difference systems the boundedness and global asymptotic behavior of positive solutions of the nonlinear two dimensional difference systems x n f x n t 1 y n s 1 y n j y n s 2 x n t 2 where t 1 s 1 s 2 t 2 are all positive integers are investigated some sufficient conditions are established such that the positive solutions converge to the unique equilibrium finally some examples are given to illustrate our results

on exponential dichotomy bohl perron type theorems and stability of difference equations abstract for a delay difference equation x n 1 k d n a n k x k f n in a banach space the following result is proved if for any f l p the solution is x l p then the solution of the homogeneous equation f 0 is exponentially stable this result is applied to obtain new explicit conditions for exponential stability of a scalar nonautonomous delay difference equation

stability of runge kutta methods for linear delay differential equations this paper investigates the stability of runge kutta methods when they are applied to the complex linear scalar delay differential equation y prime left t right ay left t right by left t 1 right this kind of stability is called tau stability we give a characterization of tau stable runge kutta methods and then we prove that implicit euler method is tau stable

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

dynamic critical behavior of a swendsen wang type algorithm for the ashkin teller model we study the dynamic critical behavior of a swendsen wang type algorithm for the ashkin teller model we find that the li sokal bound on the autocorrelation time int const xc h holds along the self dual curve of the symmetric ashkin teller model and is almost but not quite sharp the ratio int c h appears to tend to infinity either as a logarithm or as a small power 0 05 p 0 12 in an appendix we discuss the problem of extracting estimates of the exponential autocorrelation time

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

representation of solutions of delayed difference equations with linear parts given by pairwise permutable matrices via z transform in the present paper a system of nonhomogeneous linear difference equations with any finite number of constant delays and linear parts given by pairwise permutable matrices is considered representation of its solution is derived in a form of a matrix polynomial using the z transform so the recent results for one and two delays and an inductive formula for multiple delays are unified the representation is suitable for theoretical as well as practical computations

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

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

numerical approximation of the solutions of delay differential equations on an infinite interval using piecewise constant arguments the idea of approximating the solutions of delay differential equations by equations with piecewise constant arguments epca has been suggested by gyijri l who proved convergence of the method for linear and nonlinear delay equations on compact intervals and under certain conditions also on the half line the approximating equations with piecewise constant argument can in turn be solved by use of difference equations the latter then also provide an approximation of the original delay equation the theory of epca was initiated and studied by cooke and wiener in 2 and 3 in this paper we begin to investigate the question of whether in this method of approximation the asymptotic dynamics of the delay differential equations are preserved a number of authors have dealt with the problem of showing that discretization of ordinary differential equations does not significantly alter the basic qualitative features readers may refer to the papers of kloeden and lorenz 4 and beyn 5 for some of this work for delay differential equations questions of this sort have been studied by cryer 6 barwell 7 zennaro 8 and later authors the paper of strehmel et al 9 contains an up to date list of references in our method of approximation the delay equation is first replaced by an epca and then by a difference equation and our objective is to relate the qualitative dynamics of these three equations we obtain results for autonomous and nonautonomous equations with one or many delays for autonomous equations the resulting difference algorithm is just a simple euler scheme but for nonautonomous equations it includes other possibilities in order to make the method and the nature of results as clear as possible we begin with a particular test equation k t pz t 7 p 0 7 0

convergence in asymptotically autonomous functional differential equations in this paper we consider linear and nonlinear perturbations of a linear autonomous functional differential equation which has infinitely many equilibria we give sufficient conditions under which the solutions of the perturbed equation tend to the equilibria of the unperturbed equation at infinity as a consequence we obtain sufficient conditions for systems of delay differential equations to have asymptotic equilibrium

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