existence of multiple positive periodic solutions for differential equation with state dependent delays by utilizing a fixed point theorem in cones we present some sufficient conditions which guarantee the existence of multiple positive periodic solutions for a class of differential equations with state dependent delays our results extend and improve some previous results

runge kutta methods for the multi pantograph delay equation this paper deals with the properties of the numeric solution of the multi pantograph equationu t email protected t email protected 1u q 1t email protected 2u q 2t email protected lu q lt u 0 u 0 where 0

superstability and rigorous asymptotics in singularly perturbed state dependent delay differential equations abstract we study the singularly perturbed state dependent delay differential equation e x t x t k x t r r r x t 1 x t which is a special case of the equation e x t g x t x t r r r x t one knows that for every sufficiently small e 0 eq possesses at least one so called slowly oscillating periodic solution and moreover the graph of every such solution approaches a specific sawtooth like shape as e 0 in this paper we obtain higher order asymptotics of the sawtooth including the location of the minimum and maximum of the solution with the form of the solution near these turning points and as well an asymptotic formula for the period using these and other asymptotic formulas we further show that the solution enjoys the property of superstability namely the nontrivial characteristic multipliers are of size o e for small e this stability property implies that this solution is unique among all slowly oscillating periodic solutions again for small e

quasi fuchsian seifert surfaces let k subset s 3 be a non fibered knot with hyperbolic complement given a seifert surface of minimal genus for k we prove that it corresponds to a quasi fuchsian group by showing it has no accidental parabolics in particular this shows that any lift of the seifert surface to the universal cover is a quasi disk and its limit set is a quasi circle in the sphere at infinity

global dynamics of a state dependent delay model with unimodal feedback abstract we obtain the global attractivity of nonnegative stationary states for a parameterized state dependent delay equation with unimodal feedback under certain mild conditions we show that the equation with unimodal type nonlinearity can generate rich dynamics as the parameter varies to be specific global attractivity of the positive stationary state is obtained in a set of nonnegative bounded continuous functions when the stationary state is less than a value implicitly determined by a condition on the unimodal feedback the general results of global attractivity are illustrated through two examples arising from population dynamics moreover hopf bifurcations are demonstrated in the examples when the positive stationary states lose global attractivity

global attractivity of a positive periodic solution for a nonautonomous stage structured population dynamics with time delay and diffusion by employing the continuation theorem of coincidence degree theory the existence of a positive periodic solution for a nonautonomous stage structured population dynamics with time delay and diffusion is established further by constructing a lyapunov functional and using the result of the existence of positive periodic solution the attractivity of a positive periodic solution for above system is obtained

exponential stability for a class of state dependent delay equations via the crandall liggett approach abstract in this paper we are concerned with the exponential asymptotic stability of the solution of a class of differential equations with state dependent delays our approach is based on the crandall liggett approximation and the properties of semigroups

hopf bifurcation of a predator prey system with stage structure and harvesting abstract in this paper a two species predator prey system with stage structure and harvesting is investigated the existence of hopf bifurcations of the system is given and the stability and directions of hopf bifurcations are determined by applying the normal form theory and the center manifold theorem

a periodic solution of a differential equation with state dependent delay we study a differential equation for delayed negative feedback which models a situation where the delay depends on the present state and becomes effective in the future the main result is existence of a periodic solution in case the equilibrium is linearly unstable the proof employs the ejective fixed point principle on a compact convex set k0 c h 0 r of lipschitz continuous functions and uses that the equation generates a smooth semiflow on an infinite dimensional submanifold of the space c1 h 0 r

recursive block coding a new approach to transform coding the concept of fast kl transform coding introduced earlier 7 8 for first order markov processes and certain random fields has been extended to higher order autoregressive ar sequences and practical images yielding what we call recursive block coding rbc algorithms in general the rate distortion performance for these algorithms is significantly superior to that of the conventional block kl transform algorithm moreover these algorithms permit the use of small size transforms thereby removing the need for fast transforms and making the hardware implementation of such coders more appealing this improved performance has been verified for practical image data and results in suppression of the block boundary effect commonly observed in traditional transform coding techniques this is illustrated by comparing rbc with cosine transform coding using both one and twodimensional algorithms examples of rbc encoded images at various rates are given

differentiability of solutions with respect to parameters in neutral differential equations with state dependent delays in this paper we consider a class of nonlinear neutral differential equations with state dependent delays in both the neutral and the retarded terms we study well posedness and continuous dependence issues and differentiability of the parameter map with respect to the initial function and other possibly infinite dimensional parameters in a pointwise sense and also in the c norm

jointly optimized spatial prediction and block transform for video and image coding this paper proposes a novel approach to jointly optimize spatial prediction and the choice of the subsequent transform in video and image compression under the assumption of a separable first order gauss markov model for the image signal it is shown that the optimal karhunen loeve transform given available partial boundary information is well approximated by a close relative of the discrete sine transform dst with basis vectors that tend to vanish at the known boundary and maximize energy at the unknown boundary the overall intraframe coding scheme thus switches between this variant of the dst named asymmetric dst adst and traditional discrete cosine transform dct depending on prediction direction and boundary information the adst is first compared with dct in terms of coding gain under ideal model conditions and is demonstrated to provide significantly improved compression efficiency the proposed adaptive prediction and transform scheme is then implemented within the h 264 avc intra mode framework and is experimentally shown to significantly outperform the standard intra coding mode as an added benefit it achieves substantial reduction in blocking artifacts due to the fact that the transform now adapts to the statistics of block edges an integer version of this adst is also proposed

dynamics in a periodic competitive model with stage structure in this paper we consider a time delayed periodic system which describes the competition among mature populations by appealing to theories of monotone dynamical systems periodic semiflows and uniform persistence we analyze the evolutionary behavior of the system and establish sufficient conditions for competitive coexistence and exclusion

the existence of nonoscillatory solutions to a generalized nonautonomous delay logistic equation sufficient conditions for the existence of nonoscillatory solutions to the delay logistic equation x t r t x t 1 x g t k are obtained where 1

an approximate solution for a neutral functional differential equation with proportional delays in this paper a novel algorithm based on reproducing kernel theory for neutral functional differential equation with proportional delays is proposed the advantages of the presented method are the establishment of complete approximate solution theory and high precision of absolute error some examples are given to demonstrate the validity and applicability of the new method and some comparisons are made with the existing results

semigroup properties and the crandall liggett approximation for a class of differential equations with state dependent delays abstract we present an approach for the resolution of a class of differential equations with state dependent delays by the theory of strongly continuous nonlinear semigroups we show that this class determines a strongly continuous semigroup in a closed subset of c 0 1 we characterize the infinitesimal generator of this semigroup through its domain finally an approximation of the crandall liggett type for the semigroup is obtained in a dense subset of c as far as we know this approach is new in the context of state dependent delay equations while it is classical in the case of constant delay differential equations

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

global hopf bifurcation for differential equations with state dependent delay abstract we develop a global hopf bifurcation theory for a system of functional differential equations with state dependent delay the theory is based on an application of the homotopy invariance of s 1 equivariant degree using the formal linearization of the system at a stationary state our results show that under a set of mild conditions the information about the characteristic equation of the formal linearization with frozen delay can be utilized to detect the local hopf bifurcation and to describe the global continuation of periodic solutions for such a system with state dependent delay

optimal harvesting policy for single population with stage structure it is the purpose of this paper to analyze the exploitation of the stage structured singleautonomous population model we analyze the harvesting population equation and obtain existence local and global geometric properties of nonnegative equilibria explicit expressions are obtained for the optimal harvesting effort the maximum sustainable yield and the corresponding population level

global attractivity of nonautonomous stage structured population models with dispersal and harvest the nonautonomous stage structured single species dispersal model with harvesting of mature individuals in an n patch environment is considered in which the individual members of the population have a life history that takes them through two stages immature and mature by using the theory of monotone and concave operators to functional differential equations we establish conditions under which this population dynamical system admits a positive periodic solution which attracts all positive solutions

the solution manifold and c1 smoothness for differential equations with state dependent delay abstract let h 0 u c 1 h 0 r n open and f u r n continuously differentiable if f satisfies two mild additional smoothness conditions then the set x u 0 f is a c1 submanifold of codimension n in c 1 h 0 r n the maximal solutions x of the initial value problems x t f x t x 0 x define a continuous semiflow f on x and all operators f t are continuously differentiable their derivatives d2f t are given in the usual way by solutions v to the variational equation along x with segments vt in the tangent spaces tf t x the additional conditions on f are motivated by properties of differential equations with state dependent delay and are verified for an example

on state dependent delay partial neutral functional integro differential equations in this paper the existence of mild solutions for a class of abstract neutral integro differential equations with state dependent delay is studied

existence of periodic solutions for delay differential equations with state dependent delay abstract in this paper we study the existence of periodic solutions of a delay differential equation with delay depending indirectly on the state a fixed point problem related to a poincare operator is constructed and solved using an ejective fixed point theorem

wavefronts and global stability in a time delayed population model with stage structure we formulate and study a one dimensional single species diffusive delay population model the time delay is the time taken from birth to maturity without diffusion the delay differential model extends the well known logistic differential equation by allowing delayed constant birth processes and instantaneous quadratically regulated death processes this delayed model is known to have simple global dynamics similar to that of the logistic equation through the use of a sub supersolution pair method we show that the diffusive delay model continues to generate simple global dynamics this has the important biological implication that quadratically regulated death processes dramatically simplify the growth dynamics we also consider the possibility of travelling wavefront solutions of the scalar equation for the mature population connecting the zero solution of that equation with the positive steady state our main finding here is that our fronts appear to be all monotone regardless of the size of the delay this is in sharp contrast to the frequently reported findings that delay causes a loss of monotonicity with the front developing a prominent hump in some other delay models

stability of nonlinear differential systems with state dependent delayed impulses we consider nonlinear differential systems with state dependent delayed impulses impulses which involve the delayed state of the system for which the delay is state dependent such systems arise naturally from a number of applications and the stability issue is complex due to the state dependence of the delay we establish general and applicable results for uniform stability uniform asymptotic stability and exponential stability of the systems by using the impulsive control theory and some comparison arguments we show how restrictions on the change rates of states and impulses should be imposed to achieve system s stability in comparison with general impulsive delay differential systems with state dependent delay in the nonlinearity or the differential systems with constant delays in our approach the boundedness of the state dependent delay is not required but derives from the stability result obtained examples are given to demonstrate the sharpness and applicability of our general results and the proposed approach

metastable periodic patterns in singularly perturbed state dependent delayed equations abstract we consider the scalar delayed differential equation x t x t f x t r where 0 r r x 1 r x and f represents either a monotone positive feedback d f d x 0 or a monotone negative feedback d f d x 0 plus some other hypotheses when the delay is a constant i e r x 1 this equation can support metastable rapidly oscillating solutions that are transients whose duration is of order exp c for some c 0 in this paper combining analytic and numerical techniques we investigate whether this metastable behavior persists when the delay r x depends non trivially on the state variable x more precisely we proceed in three steps first we explore theoretically and numerically the existence of branches of rapid periodic solutions for these equations then to predict conditions for metastability we introduce transition layer equations that depict the asymptotic shape of transient oscillations when tends to zero and finally these predictions are validated by numerical simulations numerical explorations are also performed for other scalings of with our conclusions are i when 0 0 there are no metastable transients ii when 0 0 and 0 is finite for monotone negative feedback the metastable oscillations exist irrespective of choices of f and r iii for monotone positive feedback they require that the feedback f and the delay r satisfy extra conditions such as f being an odd function and the delay r x an even function one novel result is that state dependent delays may lead to metastable dynamics in equations that cannot support such regimes when the delay is constant

hyperbolic knots spanning accidental seifert surfaces of arbitrarily high genus a method for constructing hyperbolic knots each of which bounds accidental incompressible seifert surfaces of arbitrarily high genus is given

boundary layer phenomena for differential delay equations with state dependent time lags i in this paper we begin a study of the differential delay equation mathtype mtef 2 1 feaafiart1ev1aaatcvaufebsjuyzl2yd9gzlbvynv2caerbulwbln hiov2dgi1btfmbaexatlxbi9gbaerbd9wdylwzybitldharqqtubsr 4rnchbgeagqivu0je9sqqrpepc0xbbl8f4rqqrffpeea0jc9yq jc9 vqaqpepm0xbba9pwe9q8fs0 yqaqpepae9pg0firpeps0he9vr0 vr 0 vqpwqaaeaabigaciaacaqabeaadaqaaqaaaoqaaiabew7aljqadi hagaqbaiaacicacawg0bgaaiykaiabg2da9iabgkhitiaadihacagg oagaamidaiaacmcacqghrawkcawgmbgaaiikaiaadihacaggoagaam idaiabgkhitiaadkhacaggpagaaiykaiaacycacaqggagaaeiiaiaa dkhacqgh9aqpcawgybgaaiikaiaadihacaggoagaamidaiaacmcaca ggpaaaaa 5192 varepsilon x t x t f x t r r r x t we prove the existence of periodic solutions for 0 0 where 0 is an optimal positive number we investigate regularity and monotonicity properties of solutions x t which are defined for all t and of associated functions like t t r x t we begin the development of a poincare bendixson theory and phase plane analysis for such equations in a companion paper these results will be used to investigate the limiting profile and corresponding boundary layer phenomena for periodic solutions as approaches zero

applications of a zp index theory to periodic solutions for a class of functional differential equations abstract by means of a new geometrical index with z p group actions multiplicity results for a certain class of nonautonomous time periodic functional differential systems are obtained

a non local pde model for population dynamics with state selective delay local theory and global attractors we propose a non local pde model for the evolution of a single species population that involves delayed feedback where the delay such as the maturation time in the delayed birth rate is selective and the selection depends on the status of the system this delay selection in contrast with the usual state dependent delay widely used in ordinary delay differential equation ensures the lipschitz continuity of the nonlinear functional in the classical phase space we also develop the local theory and the existence and upper semi continuity of the global attractor with respect to parameters

boundedness global existence and continuous dependence for nonlinear dynamical systems describing physiologically structured populations abstract the paper is aimed as a contribution to the general theory of nonlinear infinite dimensional dynamical systems describing interacting physiologically structured populations we carry out continuation of local solutions to maximal solutions in a functional analytic setting for maximal solutions we establish global existence via exponential boundedness and by a contraction argument adapted to derive uniform existence time moreover within the setting of dual banach spaces we derive results on continuous dependence with respect to time and initial state to achieve generality the paper is organized top down in the way that we first treat abstract nonlinear dynamical systems under very few but rather strong hypotheses and thereafter work our way down towards verifiable assumptions in terms of more basic biological modelling ingredients that guarantee that the high level hypotheses hold

fluctuations in a sis epidemic model with variable size population in an epidemiological model time spent in one compartment is often modeled by a delay in the model in general the presence of delay in differential equations can change the stability of an equilibrium to instability and causes the appearance of oscillatory solutions in this paper we consider a sis epidemiological model with demographic effects birth mortality and mortality caused by infection the delay is the period of infection we define the concept of oscillation in the sense that solutions of the model studied fluctuate around a steady state our goal is to show that in this model there are oscillating solutions for certain parameters values we determine a large set of initial data for which solutions of this model are slowly oscillating

numerical simulation for the space fractional diffusion equations abstract this paper presents a novel semi analytical algorithm based on the chebyshev collocation method for the solution of space fractional diffusion equations the original fractional equation is transformed into a system of ordinary differential equations odes by the chebyshev collocation method a new semi analytical method is then used to approximate the solution of the resulting system to emphasize the reliability of the new scheme a convergence analysis is presented it is shown that highly accurate solutions can be achieved with relatively few approximating terms and absolute errors are rapidly decrease as the number of approximating terms is increased by presenting some numerical examples we show that the proposed method is a powerful and reliable algorithm for solving space fractional diffusion equations and can be extended to solve another space fractional partial differential equations comparison with other methods in the literature demonstrates that the proposed method is both efficient and accurate

a pinned sine transform image coder the pinned sine transform pst coder described is a practical approximation to the pinned klt coder the image is partitioned into two fields a boundary field which depends only on the coded block boundaries and a pinned field which vanishes at the boundaries and is subsequently sine transformed and compressed the reconstructed image is continuous across the block boundaries and blocking effects are hardly visible simulation results are given for fixed and adaptive compression schemes with fair image quality at low bit rates down to 0 3 bits pel

role of constant prey refuge on stage structure predator prey model with ratio dependent functional response abstract a constant prey refuge has been incorporated in a stage structured predator prey model with ratio dependent functional response sufficient conditions are obtained for the uniform persistence and global asymptotic stability by constructing suitable lyapunov function our model analysis demonstrates that the constant prey refuge plays an important role on the coexistence of stage structured predator prey species

periodic solutions for differential equations with state dependent delay and positive feedback existence of a nontrivial periodic orbit and a homoclinic orbit connecting 0 to the periodic orbit is shown for the differential equation x t x t f x t r r r x t with state dependent delay and positive feedback here 0 f and r are smooth real functions with r 0 1 and f 0

stability and hopf bifurcation analysis of an eco epidemic model with a stage structure abstract in this paper an eco epidemiological model with a stage structure is considered the asymptotical stability of the five equilibria the existence of stability switches about positive equilibrium is investigated it is found that hopf bifurcation occurs when the delay passes though a critical value some explicit formulae determining the stability and the direction of the hopf bifurcation periodic solutions bifurcating from hopf bifurcations are obtained by using the normal form theory and center manifold theory some numerical simulations for justifying the theoretical analysis are also provided finally biological explanations and main conclusions are given

analysis of a model representing stage structured population growth with state dependent time delay a stage structured model of population growth is proposed where the time to ma turity is itself state dependent it is shown that under appropriate assumptions all solutions are positive and bounded criteria for the existence of positive equilibria and further conditions for the uniqueness of the equilibria are given the stability of the equilibria are also discussed in addition an attracting region is determined for solutions such that this region collapses to the unique positive equilibrium in the state independent case

on evolutionary volterra equations with state dependent delay abstract in this work we study topological properties of the solution set of abstract volterra equations with state dependent delay particularly we ensure that such a set is a nonempty compact and connected set as application we consider our abstract results in the framework of integro differential equations coming from viscoelasticity theory

on abstract differential equations with state dependent non local conditions abstract in this paper we introduce the concept of state dependent nonlocal condition and study the existence and uniqueness of solution for a general class of abstract differential equations with state dependent delay subject to this class of conditions in this type of problem the nonlocal condition can be dependent on times or time intervals determined by the unknown solution some examples on partial differential equations with state dependent delay arising in population dynamics are presented

multiple positive periodic solutions for a class of nonlinear functional differential equations abstract by employing avery henderson fixed point theorem in cones we obtain some sufficient conditions which guarantee the existence of multiple positive periodic solutions for a class of differential equations with state dependent delays

boundary layer phenomena for differential delay equations with state dependent time lags iii in this paper we begin a study of the differential delay equation varepsilon x t x t f x t r r r x t

stage structured models of intra and inter specific competition within age classes abstract in some species larvae and adults experience competition in completely different ways simple stage structured models without larval competition usually yield a single delay equation for the adults using an age structured system incorporating competition among both larvae and adults we derive a system of distributed delay equations for the numbers of larvae and adults the system is neither cooperative nor reducible to a single equation for either variable positivity boundedness and uniform strong persistence are established linear stability analysis of equilibria is difficult due to the strong coupling but results are proved for small delays using monotone systems theory and exponential ordering for small delay we prove a theorem on generic convergence to equilibria which does not directly follow from standard theory but can be proved indirectly using comparison arguments finally we consider an extension to two strain competition and prove theorems on the linear stability of the boundary equilibria

stabilization in a state dependent model of turning processes we consider a two degree of freedom model for turning processes which involves a system of differential equations with state dependent delay depending on process parameters e g spindle speed depth of cut the cutting tool can exhibit unwanted vibrations resulting in a nonsmooth surface of the workpiece in this paper we propose a feedback law to stabilize the turning process for a large range of system parameters the feedback law introduces a generic nonhyperbolic stationary point into the model which generates the main technical challenge of this work we establish the stability equivalence between the differential equations with state dependent delay and a corresponding nonlinear system with the delay fixed at its stationary value then we show the stability of that nonlinear system with constant delay by computing its normal form finally we obtain conditions on system parameters which guarantee the stability of the state dependent delay model at the nonhyperbolic stationary point

stability and hopf bifurcation for a cell population model with state dependent delay we propose a mathematical model describing the dynamics of a hematopoietic stem cell population the method of characteristics reduces the age structured model to a system of differential equations with a state dependent delay a detailed stability analysis is performed a sufficient condition for the global asymptotic stability of the trivial steady state is obtained using a lyapunov razumikhin function a unique positive steady state is shown to appear through a transcritical bifurcation of the trivial steady state the analysis of the positive steady state behavior through the study of a first order exponential polynomial characteristic equation concludes the existence of a hopf bifurcation and gives criteria for stability switches a numerical analysis confirms the results and stresses the role of each parameter involved in the system on the stability of the positive steady state

splittings of knot groups let k be a knot of genus g if k is fibered then it is well known that the knot group pi k splits only over a free group of rank 2g we show that if k is not fibered then pi k splits over non free groups of arbitrarily large rank furthermore if k is not fibered then pi k splits over every free group of rank at least 2g however pi k cannot split over a group of rank less than 2g the last statement is proved using recent results of agol przytycki wise and wise

convergence of solutions for an equation with state dependent delay abstract a result of smith and thieme shows that if a semiflow is strongly order preserving then a typical orbit converges to the set of equilibria for the equation with state dependent delay t x t f x t r x t where 0 and f and r are smooth real functions with f 0 0 and f 0 we construct a semiflow which is monotone but not strongly order preserving we prove a convergence result under a monotonicity condition different from the strong order preserving property and apply it to the above equation to obtain generic convergence

permanence and stability of a predator prey system with stage structure for predator a stage structured predator prey system with delays for prey and predator respectively is proposed and analyzed mathematical analysis of the model equations with regard to boundedness of solutions permanence and stability are analyzed some sufficient conditions which guarantee the permanence of the system and the global asymptotic stability of the boundary and positive equilibrium respectively are obtained

extinction and permanence in nonautonomous competitive system with stage structure in this paper the n species nonautonomous stage structured competitive system is constructed and considered sufficient conditions for its extinction and permanence are obtained results here generalize and unify some previous ones moreover it is concluded that stage structure in this system is one of the important factors that effect the extinction and permanence of species

dct dst alternate transform image coding an image coding method for low bit rates is proposed it is based on alternate use of the discrete cosine transform dct and the discrete sine transform dst on image blocks this procedure achieves the removal of redundancies in the correlation between neighboring blocks as well as the preservation of continuity across the block boundaries an outline of the mathematical justification of the method assuming a certain first order gauss markov model is given the resulting coding method is then adapted to nonstationary real images by locally adapting the model parameters and improving the block classification technique simulation results are shown and compared with the performance of related previous methods namely adaptive dct and fast karhunen loeve transform fklt

properties of the semigroup and the approximation of crandall liggett associated with a class of differential equations with delays depending implicitly on the state abstract in this paper we are concerned with the semigroup properties and the crandall liggett approximation associated with a class of differential equations with delays depending implicitly on the state the existence of a strongly continuous nonlinear semigroup associated with the solutions of the equations is proved various properties of this semigroup have been established such as the continuous dependence the compactness and the infinitesimal generators an approximation of crandall liggett type has also been established

the dynamics of a mutual interference age structured predator prey model with time delay and impulsive perturbations on predators in this paper we introduce a mutual interference age structured predator prey natural enemy pest model with constant maturation time delay for the prey and then propose a pest management strategy by constant periodic releasing for the predator we show that there exists a global attractive pest eradication periodic solution when the periodic releasing amount m 1 and m 2 are lager than some critical value further to obtain a more effective pest control strategy we give the conditions involving the estimate of m 1 and m 2 in which the model is uniformly permanent and the pest population is under the economic threshold level we believe that the results will provide reliable tactic basis for the practical pest management