on computing puiseux series for multiple imaginary characteristic roots of lti systems with commensurate delays obtaining the puiseux series of multiple imaginary characteristic roots mirs is a fundamental issue in the stability analysis of time delay systems however to the best of the authors knowledge this issue has not been fully investigated up to date this note focuses on the puiseux series expansion of mirs of linear time invariant systems including commensurate delays for an mir of any multiplicity we propose an algorithm for defining the structure of the puiseux series as well as the explicit computation of the corresponding coefficients by using the proposed method we can find all the puiseux series corresponding to all the root loci

attractivity and stability in the competitive systems of pdes of kolmogorov type abstract in this paper we consider n species nonautonomous competitive systems of partial differential equations of kolmogorov type under the neumann boundary conditions we give a sufficient condition for the system to be uniform stable and globally attractive

uniform persistence and existence of strictly positive solutions in nonautonomous lotka volterra competitive systems with delays abstract in this paper we establish some new sufficient conditions for uniform persistence and existence of strictly positive solutions of the general nonautonomous n species competitive lotka volterra systems with delays these results are different to those in 1 4

global attractivity for discrete models of nonautonomous logistic equations consider the following discrete model of a nonautonomous logistic equation n n 1 n n exp c n j 0mb j n n n j n 0 n 0 n 0 0andn j n j 0 1 j m where c n and b j n 0 j m n 0 are bounded and c n 0 b 0 n 0 b j n 0 1 j m n 0 in this paper using some kind of iterative method to the above equation we establish sufficient conditions that ensure the global attractivity for solutions the result is an extension of the former work k uesugi y muroya e ishiwata on the global attractivity for a logistic equation with piecewise constant arguments j math anal appl 294 2004 560 580 to the nonautonomous case

global attractivity of positive periodic solution to periodic lotka volterra competition systems with pure delay abstract we consider a periodic lotka volterra competition system without instantaneous negative feedbacks i e pure delay systems x i t x i t r i t j 1 n a i j t x j t i j t i 1 2 n we establish some 3 2 type criteria for global attractivity of a positive periodic solution of the system which generalize the well known wright s 3 2 criteria for the autonomous delay logistic equation and thereby address the open problem proposed by both kuang y kuang global stability in delayed nonautonomous lotka volterra type systems without saturated equilibria differential integral equations 9 1996 557 567 and teng z teng nonautonomous lotka volterra systems with delays j differential equations 179 2002 538 561

balancing survival and extinction in nonautonomous competitive lotka volterra systems abstract we generalise and unify some recent results about extinction in n th order nonautonomous competitive lotka volterra systems for each r n we show that if the coefficients are continuous bounded by strictly positive constants and satisfy certain inequalities then any solution with strictly positive initial values has the property that n r of its components vanish whilst the remaining r components asymptotically approach a canonical solution of an r dimensional restricted system in other words r of the species being modeled survive whilst the remaining n r are driven to extinction

dynamics of kolmogorov systems of competitive type under the telegraph noise abstract this paper studies the dynamics of kolmogorov systems of competitive type under the telegraph noise the telegraph noise switches at random two kolmogorov competition type deterministic models the aim of this work is to describe the omega limit set of the system and investigates properties of stationary density

asymptotically periodic solutions of n competing species problem with time delays abstract a general nonautonomous lotka volterra system of integro differential equations with infinite delay is considered and sufficient conditions for uniform stability and asymptotic stability of solutions are investigated these limiting equations are used to obtain the existence of asymptotically periodic solutions of the corresponding system of equations where lower limit in the integration is zero

quadratic stability and stabilization of uncertain linear discrete time systems with state delay abstract this paper deals with the problem of quadratic stability analysis and quadratic stabilization for uncertain linear discrete time systems with state delay the system under consideration involves state time delay and time varying norm bounded parameter uncertainties appearing in all the matrices of the state space model necessary and sufficient conditions for quadratic stability and quadratic stabilization are presented in terms of certain matrix inequalities respectively a robustly stabilizing state feedback controller can be constructed by using the corresponding feasible solution of the matrix inequalities two examples are presented to demonstrate the effectiveness of the proposed approach

stable periodic solution of a discrete periodic lotka volterra competition system abstract this paper discusses a discrete lotka volterra competition system we first obtain the persistence of the system assuming that the coefficients in the system are periodic we obtain the existence of a periodic solution moreover under some additional conditions this periodic solution is globally stable our results not only reduce to those for the scalar equation when there is no coupling but also improve and complement some in the literature

strongly order preserving semiflows generated by functional differential equations the aim of this paper is to apply some recently developed improvements in the theory of monotone dynamical systems due to the authors 12 13 j to certain systems of functional differential equations fde s which do not enjoy the quasimonotone property considered by one of us in 9 the present work extends our previous results in this direction for scalar equations in 111 to systems in the fundamental paper s m w hirsch establishes that most orbits of a strongly monotone scmiflow on a strongly ordered space x tend to the set e of equilibria employing ideas of hirsch and of h matano 7 the authors have extended the theory to obtain some improvements in the results of hirsch and matano under matano s weaker assumption that the semiflow is strongly order preserving recently in 13 we gave sufficient conditions for most orbits of a strongly order preserving semiflow to converge to an equilibrium these conditions require additional smoothness of the semiflow and a certain strong monotonicity condition for the linearized flow determined by the variational equation about each equilibrium p policik s has also given sufficient conditions for most orbits to converge for semilinear parabolic evolution equations possessing certain strong monotonicity properties in this paper wc apply the convergence results developed in 131 to nonquasimonotone fde s in this introduction wc briefly review the application of monotone dynamical systems theory to fde s enjoying the quasimonotone property this research appeared in 9 133 then we state one of the main results of this paper which applies when the quasimonotone property fails but when another property m holds some simple examples are given which

repelling conditions for boundary sets using liapunov like functions ii persistence and periodic solutions abstract this paper deals with repulsivity conditions for the points of the boundary of a set g with respect to the solutions of the differential system x t x which are contained in the set g applications are given to the problem of persistence i e solutions starting at the interior of a set remain asymptotically far from its boundary and to the existence of periodic solutions using the nonejective fixed point theorem

global periodic solutions of a generalized n species gilpin ayala competition model abstract in this paper we investigate a generalized n species gilpin ayala competition system with several deviating arguments in periodic environment which is more general and more realistic than the classical lotka volterra competition systems by using the method of coincidence degree a set of easily verifiable sufficient conditions are derived for the existence of at least one strictly positive componentwise periodic solution some new results are obtained as applications we also apply our main results to some special cases of the system we consider here including the classical n species lotka volterra competition systems and n species gilpin ayala competition model which have been studied extensively in the literature some known results are improved and generalized the examples show that our criteria are new general and easily verifiable

periodic solution for stochastic non autonomous multispecies lotka volterra mutualism type ecosystem we give sufficient conditions for the existence of positive periodic solution we give sufficient conditions for the global attractiveness of the periodic solution we prove that all species will be extinct if the intensity of noise is large enough the results are illustrated by computer simulations the paper characterizes some qualitative dynamic properties of a stochastic non autonomous multi species mutualism model with continuous periodic parameters using khasminskii theory of stability with suitable lyapunov functions and m matrices sufficient conditions are established to guarantee existence of positive periodic solutions to the system we also provide conditions for the global attractiveness of the latter or extinction of all species for sufficiently high volatility levels results are finally supported by numerical computations

stochastic functional kolmogorov type population dynamics abstract in this paper we stochastically perturb the functional kolmogorov type system x t diag x 1 t x n t f x t into the stochastic functional differential equation d x t diag x 1 t x n t f x t d t g x t d w t this paper studies existence and uniqueness of the global positive solution and its asymptotic bound properties and moment average in time these properties are natural requirements from the biological point of view as the special cases we discuss the various stochastic lotka volterra systems

persistence attractivity and delay in facultative mutualism abstract relations between persistence and ultimate boundedness of the solutions of the lotka volterra system dx t dt x t r 1 a 11 x t a 22 y t dy t dt y t r 2 a 21 x t a 22 y t modelling facultative mutualism with delayed responses are established and sufficient conditions are obtained for the global attractivity of the positive equilibrium of the delay system

finite spectrum assignment of unstable time delay systems with a safe implementation the instability mechanisms related to the implementation of distributed delay controllers in the context of finite spectrum assignment were studied in detail in the past few years in this note we introduce a distributed delay control law that assigns a finite closed loop spectrum and whose implementation with a sum of point wise delays is safe this property is obtained by implicitly including a low pass filter in the control loop this leads to a closed loop characteristic quasipolynomial of retarded type and not one of neutral type which was shown to be a cause of instability in previous schemes

stability analysis for continuous systems with two additive time varying delay components this paper presents a new result of stability analysis for continuous systems with two additive time varying delay components which represent a general class of delay systems with strong application background in network based control systems this criterion is expressed as a set of linear matrix inequalities which can be readily tested by using standard numerical software a numerical example is provided to show the effectiveness and advantage of the proposed stability condition

the lyapunov functionals for delay lotka volterra type models by means of lyapunov functionals we have succeeded in establishing the global attractivity of the positive equilibrium of n species lotka volterra systems modeled by equations of the pure delay type with both finite and infinite delays involved as a corollary we show that if the delay system is dissipative and the coefficient matrix is vl stable then the global attractivity of the unique positive equilibrium is maintained provided the delays are small estimates on the allowable sizes of delays are indicated applications to 2 species prey predator models and n species food chains and competition models are included

global stability for infinite delay lotka volterra type systems abstract in this paper sufficient conditions are established for the global stability of the saturated equilibrium of an infinite delay nonautonomous lotka volterra type system the present work is distinguished from previous work principally be allowing the system to be nonautonomous and relaxing the traditional requirement that the undelayed intraspecific competition dominates both the delayed intraspecific competition as well as the interspecific interactions we require the undelayed intraspecific competition to dominate the latter but not the former

an eigenvalue perturbation approach to stability analysis part ii when will zeros of time delay systems cross imaginary axis this paper presents an application of the eigenvalue series developed in part i j chen et al siam j control optim 48 2010 pp 5564 5582 to the study of linear time invariant delay systems focusing on the asymptotic behavior of critical characteristic zeros on the imaginary axis we consider systems given in state space form and as quasi polynomials and we develop an eigenvalue perturbation analysis approach which appears to be both conceptually appealing and computationally efficient our results reveal that the zero asymptotic behavior of time delay systems can in general be characterized by solving a simple eigenvalue problem and additionally when described by a quasi polynomial by computing the derivatives of the quasipolynomial

brief paper stabilization of linear strict feedback systems with delayed integrators the problem of compensation of input delays for unstable linear systems was solved in the late 1970s systems with simultaneous input and state delay have remained a challenge although exponential stabilization has been solved for systems that are not exponentially unstable such as chains of delayed integrators and systems in the feedforward form we consider a general system in strict feedback form with delayed integrators which is an example of a particularly challenging class of exponentially unstable systems with simultaneous input and state delays and design a predictor feedback controller for this class of systems exponential stability is proven with the aid of a lyapunov krasovskii functional that we construct using the pde backstepping approach

new contractivity condition in a population model with piecewise constant arguments abstract in this paper we improve contractivity conditions of solutions for the positive equilibrium n 1 a i 0 m b i of the following differential equation with piecewise constant arguments d n t d t n t r t 1 a n t i 0 m b i n n i n t n 1 n 0 1 2 n 0 n 0 0 and n j n j 0 j 1 2 m where r t is a nonnegative continuous function on 0 r t 0 i 0 m b i 0 b i 0 i 0 1 2 m and a b 0 i 1 m b i in particular for the case a 0 and m 1 we really improve the known three type conditions of the contractivity for solutions of this model see for example y muroya a sufficient condition on global stability in a logistic equation with piecewise constant arguments hokkaido math j 32 2003 75 83 for the other case a 0 and m 1 under the condition j 1 m b j 2 b 0 a j 1 m b j 1 b 0 j 0 m b j the obtained result partially improves the known results on the contractivity of solutions for the positive equilibrium of this model given by the author y muroya persistence contractivity and global stability in logistic equations with piecewise constant delays j math anal appl 270 2002 602 635 and others

permanence criteria for general delayed discrete nonautonomous n species kolmogorov systems and its applications in this paper the permanence for the general nonautonomous n species discrete kolmogorov systems with delays is studied by using the method of multiple discrete lyapunov like functionals a quite general sufficient condition is established as application of this result new sufficient conditions are obtained to ensure the permanence of all species for the discrete nonautonomous pure delayed n species lotka volterra competitive systems and food chain systems particularly as special cases a series of new sufficient conditions on the permanence for the discrete nonautonomous pure delayed lotka volterra two species competitive systems predator prey systems and three species food chain systems and the discrete autonomous pure delayed lotka volterra competition systems and food chain systems are obtained

analysis of a stochastic autonomous mutualism model abstract an autonomous lotka volterra mutualism system with random perturbations is investigated under some simple conditions it is shown that there is a decreasing sequence k which has the property that if 1 1 then all the populations go to extinction i e lim t x i t 0 1 i n if k 1 k 1 then lim t x j t 0 j k 1 n whilst the remaining k populations are stable in the mean i e lim t t 1 0 t x i s d s a positive constant i 1 k if n 1 then all the species are stable in the mean sufficient conditions for stochastic permanence and global asymptotic stability are also established

delay dependent stabilization of linear systems with time varying state and input delays the integral inequality method is a new way of tackling the delay dependent stabilization problem for a linear system with time varying state and input delays email protected t ax t a 1x t h 1 t b 1u t b 2u t h 2 t in this paper a new integral inequality for quadratic terms is first established then it is used to obtain a new state and input delay dependent criterion that ensures the stability of the closed loop system with a memoryless state feedback controller finally some numerical examples are presented to demonstrate that control systems designed based on the criterion are effective even though neither a b 1 nor a a 1 b 1 is stabilizable

recursive predictor design for state and output feedback controllers for linear time delay systems this paper presents a recursive method to design state and output feedback controllers for mimo block feedforward linear systems with delays in the inputs outputs and interconnections between the blocks the resulting controller is of predictor type which means that it contains finite integrals over past state and input values the method is a generalization of the well known model reduction approach for systems with input delay a recursive procedure replaces delay terms with non delay ones step by step from the top of the cascade structure down controller gains are computed for the proxy system without delays while the construction guarantees the same closed loop poles for the delay system and the proxy one the observer is designed by applying the duality argument and the separation principle is also shown to apply

permanence and extinction of a periodic predator prey delay system with functional response and stage structure for prey abstract in this paper we consider a periodic coefficients predator prey system with functional response and infinite delay in which the prey has a history that takes them through two stages immature and mature sufficient conditions which guarantee the permanence and extinction of the system are obtained finally we give an example

positive solution and its asymptotic behaviour of stochastic functional kolmogorov type system abstract in general population systems are often subject to environmental noise this paper considers the stochastic functional kolmogorov type system d x t diag x 1 t x n t f x t d t g x t d w t under the traditionally diagonally dominant condition we study existence and uniqueness of the global positive solution of this stochastic system and its asymptotic bound properties and moment average boundedness in time these properties are natural requirements from the biological point of view as the special cases we also discuss some stochastic lotka volterra systems

uniform persistence in functional differential equations abstract in this paper we investigate the question of uniform persistence for retarded functional differential equations by utilizing liapunov like functions razumikhin techniques and differential inequalities we are able to establish criteria for uniform persistence analogous to those obtained by others for ordinary differential equations difference equations and reaction diffusion equations we apply these criteria to some well known biological models with delay our results indicate that the conditions which guarantee the existence of an interior equilibrium are enough to ensure uniform persistence moreover these conditions are equivalent to uniform persistence for the cases without delay as well

persistence criteria for a chemostat with variable nutrient input abstract the standard single species chemostat model is modified to include a variable nutrient input which is assumed only to be nonnegative bounded and continuous we obtain necessary and sufficient conditions for persistence and show that all solutions of any given chemostat system have the same long time behavior independent of the initial conditions counterexamples shed light on the results obtained

a halfspace theorem for mean curvature h 12 surfaces in h2 r abstract we prove a vertical halfspace theorem for surfaces with constant mean curvature h 1 2 properly immersed in the product space h 2 r where h 2 is the hyperbolic plane and r is the set of real numbers the proof is a geometric application of the classical maximum principle for second order elliptic pde using the family of noncompact rotational h 1 2 surfaces in h 2 r

feedback stabilization of linear autonomous time lag systems a stabilization theory which employs well established finite dimensional control system tools is developed for the stabilization of linear autonomous time lag systems the main ideas include 1 a set whose elements are matrices each of which is a left zero of the system characteristic quasi polynomial matrix and 2 a linear transformation which reduces the delay system to a delay free system whose state matrix is a direct sum of n elements of the matrix set where n is some positive integer from the definition of this matrix set it is shown that each of its elements inherits its spectrum from that of the delay system so that by design the system unstable poles may be embedded in the spectrum of the delay free system under the assumption of spectral stabilizability it is then shown how to obtain a stabilizing feedback control law on the basis of the delay free system numerical examples are presented to confirm the theory

a different consideraton about the globally asymptotically stable solution of the periodic n competing species problem abstract we consider the volterra lotka equations for n competing species n 2 in which the right hand sides are periodic in time we show that conditions given by k gopalsamy j austral math soc ser b 27 1985 66 72 which imply the existence of a periodic solution with positive components also imply the uniqueness and asymptotic stability of the solution

persistence and global stability in discrete models of lotka volterra type abstract in this paper we establish new sufficient conditions for global asymptotic stability of the positive equilibrium in the following discrete models of lotka volterra type n i p 1 n i p exp c i a i n i p j 1 n a i j n j p k i j p 0 1 i n n i p n i p 0 p 0 and n i 0 0 1 i n where each n i p for p 0 each c i a i and a i j are finite and a i 0 a i a i i 0 1 i n and k i j 0 1 i j n applying the former results y muroya persistence and global stability for discrete models of nonautonomous lotka volterra type j math anal appl 273 2002 492 511 on sufficient conditions for the persistence of nonautonomous discrete lotka volterra systems we first obtain conditions for the persistence of the above autonomous system and extending a similar technique to use a nonnegative lyapunov like function offered by y saito t hara and w ma y saito t hara w ma necessary and sufficient conditions for permanence and global stability of a lotka volterra system with two delays j math anal appl 236 1999 534 556 for n 2 to the above system for n 2 we establish new conditions for global asymptotic stability of the positive equilibrium in some special cases that k i j k j j 1 i j n and j 1 n a j i a j k 0 i k these conditions become a i j 1 n a j i 2 1 i n and improve the well known stability conditions a i j 1 n a j i 1 i n obtained by k gopalsamy k gopalsamy global asymptotic stability in volterra s population systems j math biol 19 1984 157 168

input delay compensation of linear systems with both state and input delays by nested prediction abstract in this paper we consider the input delay compensation of linear systems with both state and input delays under the condition that the open loop time delay systems in the absence of input delay can be stabilized by delayed state feedback a nested predictor based approach is established to predict the future states so that the delays in the input are compensated it is shown that the compensated closed loop system in the presence of input delay possesses the same characteristic equation as the closed loop system in the absence of input delay the proposed approach can be generalized to general linear systems having multiple state delays and or multiple input delays to implement the nested predictor based controllers by applying numerical integration approaches an augmented nested predictor based approach by adding input filters is proposed two numerical examples are worked out to show the effectiveness of the proposed approach

on distributed delay in linear control laws part i discrete delay implementations this note proposes two approaches to approximate distributed delay in linear control laws and furthermore to implement it in the z domain and in the s domain the h sup spl infin norm of the approximation error converges to 0 when the number n of approximation steps approaches spl infin hence the instability problem due to the approximation error which has been widely studied in recent years does not exist provided that n is large enough moreover the static gain is guaranteed so that no extra efforts are needed to retain the steady state performance as by products two new formulas for the forward and backward rectangular rules are obtained these formulas are more accurate than the conventional ones when the integrand has an exponential term

stabilization of linear systems with both input and state delays by observer predictors this paper studies the stabilization of linear systems with both state and input delays where the input delay can be arbitrarily large yet exactly known observer predictor based controllers are designed to predict the future states so that the input delay can be properly compensated necessary and sufficient conditions guaranteeing the stability of the closed loop system are provided in terms of the stability of some simple linear time delay systems refereed to as observer error systems by which the separation principle is discovered moreover approaches in terms of linear matrix inequalities are also provided to design both the state feedback gains and observer gains finally a numerical example illustrates that the proposed approaches are more effective and safe to implement than the existing methods

existence of vertical ends of mean curvature 1 2 in ℍ ℝ we prove existence of graphs over exterior domains of h2 0 of constant mean curvature h 1 2 in h2 r and weak growth equal to the embedded rotational examples

permanence for a class of periodic time dependent competitive system with delays and dispersal in a patchy environment in this paper we study m species time delayed competitive lotka volterra type dispersal system with periodic coefficients in n patches by utilizing analytic method sufficient and realistic conditions on permanence and the existence of periodic solution are established the theoretical results are confirmed by a special example and numerical simulations

nonautonomous lotka volterra systems with delays abstract the paper studies the general nonautonomous lotka volterra multispecies systems with finite delays the ultimate boundedness permanence global attractivity and existence and uniqueness of strictly positive solutions positive periodic solutions and almost periodic solutions are obtained these results are basically an extension of the known results for nonautonomous lotka volterra multispecies systems without delay to systems with delay

existence and stability of periodic solution of a lotka volterra predator prey model with state dependent impulsive effects according to biological and chemical control strategy for pest we investigate the dynamic behavior of a lotka volterra predator prey state dependent impulsive system by releasing natural enemies and spraying pesticide at different thresholds by using poincare map and the properties of the lambert w function we prove that the sufficient conditions for the existence and stability of semi trivial solution and positive periodic solution numerical simulations are carried out to illustrate the feasibility of our main results

input delay compensation of linear systems with both state and input delays by adding integrators abstract this paper studies stabilization of linear systems with both state and input delays a dynamic input delay compensator obtained by adding integrators is established to compensate the input delays that can be arbitrarily large with the input delay compensator the original stabilization problem reduces to the problem of stabilizing an augmented linear time delay system without input delay three methods are also proposed to design stabilizing controllers for the augmented linear time delay system the first method is based on linear matrix inequalities lmis and the second method is based on model reduction the third method is based on pole placement and is built for the particular case that the original time delay system has only a pure delayed state vector on its right hand side for this method the optimal gain such that the decay rate of the closed loop system is maximized is also proposed the effectiveness of the proposed approaches is illustrated by three linear time delay systems that are open loop unstable

average conditions for kolmogorov systems in this paper we consider nonautonomous competitive kolmogorov systems which is a generalization of classical lotka volterra competition model applying ahmad and lazer s definitions of lower and upper averages of a function we give the average conditions for the persistence permanence and global attractivity of the system

persistence and global stability for discrete models of nonautonomous lotka volterra type abstract consider the following discrete models of nonautonomous lotka volterra type n i p 1 n i p exp c i p a i p n i p j 1 n l 0 m a ij l p n j p k l 1 i n p 0 1 2 n i p n ip 0 p 0 and n i0 0 1 i n where each c i p a i p and a ij l p are bounded for p 0 and inf p 0 a i p 0 a ii 0 p 0 1 i n a ij l p 0 1 i j n 0 l m k 0 0 integers k l 0 1 l m in this paper to the above discrete system we apply the techniques offered by ahmad and lazer nonlinear anal 40 2000 37 49 and establish similar conditions of the persistence and global asymptotic stability of the system

partial persistence and extinction in n dimensional competitive systems abstract in this paper we first consider an n dimensional system slightly more general than the lotka volterra system and give conditions that imply strong persistence of all species using this result we then give computable conditions on the coefficients which imply the ultimate extinction of certain species in an n dimensional lotka volterra system

comment on existence and stability of periodic solution of a lotka volterra predator prey model with state dependent impulsive effects j comput appl math 224 2009 544 555 in this paper according to integrated pest management principles a class of lotka volterra predator prey model with state dependent impulsive effects is presented in this model the control strategies by releasing natural enemies and spraying pesticide at different thresholds are considered the sufficient conditions for the existence and stability of the positive order 1 periodic solution are given by the poincare map and the properties of the lambertw function

global attractivity of non autonomous lotka volterra competition system without instantaneous negative feedback abstract we consider a non autonomous lotka volterra competition system with distributed delays but without instantaneous negative feedbacks i e pure delay systems we establish some 3 2 type and m matrix type criteria for global attractivity of the positive equilibrium of the system which generalise and improve the existing ones

linear systems with delayed controls a reduction linear systems with delayed control action are transformed into systems without delays under an absolute continuity condition the new system is an ordinary differential control equation in the general case the new system is a measure differential control system it is shown how the controllability stabilization and various optimization problems can be analyzed via the reduced systems

global stability of discrete population models with time delays and fluctuating environment the global stability of a discrete population model of volterra type is studied the model incorporates time delays and allows for a fluctuating environment by linearization of the model at positive solutions and construction of liapunov functionals sufficient conditions are obtained to ensure a positive solution of the model is stable and attracts all positive solutions

dynamic behaviors of a delay differential equation model of plankton allelopathy in this paper we consider a modified delay differential equation model of the growth of n species of plankton having competitive and allelopathic effects on each other we first obtain the sufficient conditions which guarantee the permanence of the system as a corollary for periodic case we obtain a set of delay dependent condition which ensures the existence of at least one positive periodic solution of the system after that by means of a suitable lyapunov functional sufficient conditions are derived for the global attractivity of the system for the two dimensional case under some suitable assumptions we prove that one of the components will be driven to extinction while the other will stabilize at a certain solution of a logistic equation examples show the feasibility of the main results

on the global attractivity for a logistic equation with piecewise constant arguments in this paper we consider the following logistic equation with piecewise constant arguments dn t dt rn t 1 j 0majn t j t 0 m 1 n 0 n0 0 n j n j 0 j 1 2 m where r 0 a0 a1 am 0 j 0maj 0 and x means the maximal integer not greater than x the sequence nn n 0 where nn n n n 0 1 2 satisfies the difference equation nn 1 nnexpr1 j 0majnn j n 0 1 2 under the condition that the first term a0 dominates the other m coefficients ai 1 i m we establish new sufficient conditions of the global asymptotic stability for the positive equilibrium n 1 j 0maj

forwarding backstepping and finite spectrum assignment for time delay systems the nonlinear control ideas and results of forwarding and backstepping have been recently extended to systems with time delay in this paper we discuss how to apply these tools to design robust controls for linear delay systems we first show that the integral cross term forwarding produces a feedback law that achieves finite spectrum of the closed loop system combining it with backstepping provides a structured design method for a large class of systems with time delay robustness of the controller to uncertainties including uncertain time delay is illustrated by an example

average growth and extinction in a competitive lotka volterra system abstract in this paper we answer an earlier conjecture consider a class of nonautonomous competitive lotka volterra systems we show that certain inequalities involving the interaction coefficients and averages of the growth rates imply that the system is persistent however reversing one of these inequalities implies that the n th species goes to extinction

brief paper exponential stability of nonlinear time delay systems with delayed impulse effects the problem of exponential stability for nonlinear time delay systems with delayed impulses is addressed in this paper lyapunov based sufficient conditions for exponential stability are derived respectively for two kinds of delayed impulses i e destabilizing delayed impulses and stabilizing delayed impulses it is shown that if a nonlinear impulsive time delay system without impulse input delays is exponentially stable then under some conditions its stability is robust with respect to small impulse input delays moreover it is also shown that for a stable nonlinear impulsive time delay system if the magnitude of the delayed impulses is sufficiently small then under some conditions the delayed impulses do not destroy the stability irrespective of the sizes of the impulse input delays the efficiency of the proposed results is illustrated by three numerical examples

stabilization of nonlinear systems with time varying input and state delays by approximate predictor in this paper the stabilization problem of nonlinear systems with time varying input and state delays is considered by an approximate predictor due to the introduction of state delays the nonlinear dynamic without state delays is used to predict the plant state and a new error term is introduced into the approximation error between the prediction value and the future state of the plant by lyapunov krasovskii functional and small gain argument the stability of the whole closed loop system is guaranteed provided that the sampling period the predictor accuracy and the upper bound of state delays satisfy an inequality constraint the effectiveness of the proposed results is illustrated by a numerical example

periodic solutions for delay lotka volterra competition systems abstract by using the continuation theorem of coincidence degree theory sufficient and realistic conditions are obtained for the existence of positive periodic solutions for the periodic distributed delay lotka volterra competition system du i t dt u i t r i t a ii t u i t j 1 j i n a ij t 0 t ij k ij s u j t s ds i 1 2 n and the periodic state dependent delay lotka volterra competition system du i t dt u i t r i t a ii t u i t j 1 j i n a ij t u j t j t u 1 t u n t i 1 2 n where ri aii 0 aij 0 j i i j 1 2 n are continuous periodic functions tij 0 j i i j 1 2 n kij c tij 0 0 0 tijkij s ds 1 j i i j 1 2 n i c rn 1 r and i i 1 2 n are periodic with respect to their first arguments respectively

prediction based control for systems with state and several input delays in this contribution an extension of the prediction based design scheme proposed in tsubakino etal 2015 for compensation of input delays to the case of systems with input and state delays is presented to derive safely implementable control laws we propose to apply additional input filters and obtain a closed loop system in the form of a set of retarded type differential equations an example illustrating the design scheme is given

monotone semiflows generated by functional differential equations abstract this obtains sufficient condition for an autonomous functional differential equation to generate a strongly monotone semiflow on a suitable state space this allows the application to functional differential equations of very powerful recent results on strongly monotone semiflows due to hirsch and matano in addition a very striking relationship is established between such functional differential equations and corresponding ordinary differential equations an example involving a biochemical feedback loop is considered keywords stability steady states

a necessary and sufficient condition for permanence of a lotka volterra discrete system with delays abstract in this paper we consider the permanence of the following lotka volterra discrete competition system with delays k1 k2 l1 and l2 x n 1 x n exp r1 1 x n k1 1y n k2 y n 1 y n exp r2 1 2x n l1 y n l2 we show the system is permanent for all nonnegative integers k1 k2 l1 and l2 if and only if 1

output feedback control of linear systems with input state and output delays by chains of predictors abstract in this paper we consider the control problem of linear systems with state time delays when the control signal is affected by a possibly time varying delay the problem is solved by a chain of predictors under the assumption that a stabilizing control exists for the case of no input delay this solution is then extended to the case of partial information when only delayed output is available both the input and the output delays may have arbitrary bounds with respect to previous approaches to the same problem appeared recently in the literature the method proposed here has a simpler structure and in particular it does not need the computation of distributed terms as a by product we show that it is possible to derive an observer for a system with state and output delays from an observer for the same system without output delays

persistence and global stability in discrete models of pure delay nonautonomous lotka volterra type abstract consider the persistence and the global asymptotic stability of the following discrete model of pure delay nonautonomous lotka volterra type n i p 1 n i p exp c i p j 1 n l 0 m a ij l p n j p k l p 0 1 2 1 i n n i p n i p 0 p 0 and n i 0 0 1 i n where each ci p and aijl p are bounded for p 0 and inf p 0 l 0 m a ii l p 0 a ij l p 0 i j n 1 i n and k l 0 1 l m in this paper for the above discrete system of pure delay type by improving the former work j math anal appl 273 2002 492 511 which extended the averaged condition offered by s ahmad and a c lazer nonlinear anal 40 2000 37 49 we offer conditions of persistence and considering a lyapunov like discrete function to the above discrete system we establish sufficient conditions of global asymptotic stability

on the periodic solutions of periodic multi species competitive systems with delays the paper considers general n species periodic kolmogorov competitive systems of functional differential equations with finite or infinite delays applying schauder s fixed point theorem a criterion on the existence of the positive periodic solutions is established as applications the existence and global asymptotic stability of the single species logistic periodic model and n species lotka volterra type periodic model with delays are discussed