solving boundary value problems for delay differential equations by a fixed point method a general linear boundary value problem for a nonlinear system of delay differential equations dde in short is reduced to a fixed point problem v a v with a properly chosen generally nonlinear operator a the unknown fixed point v is approximated by piecewise linear function v h defined by its values v i v h t i at grid points t i i 0 1 n where n is a given positive integer and h max 1 i n t i t i 1 under suitable assumptions the existence of a fixed point of a is equivalent to existence of so called e h approximate fixed points of v h a v h which can be found by minimization of l 2 n norm of residuum v h a v h with respect to the variables v i these e h approximate fixed points are used for obtaining approximate solutions of the original boundary value problem for a system of dde numerical experiments with the boundary value problem for a system of delay differential equations of population dynamics as well as with two periodic boundary value problems one for the periodic distributed delay lotka volterra competition system and the second one modeling two coupled identical neurons with time delayed connections show an efficiency of this kind of approach

radial discrete pde splines on lipschitz domains abstract in the framework of an elliptic partial differential equation pde certain boundary conditions and a set of points to approximate in a lipschitz domain and arbitrary dimension we use radial basis function rbf techniques for the construction and characterization of discrete pde splines we also show convergence and derive error estimates

periodic solutions of a periodic lotka volterra system with delays a lotka volterra periodic delay model with m predators and n preys is studied in this paper sufficient conditions for the global existence of a positive periodic solutions of this delay model are obtained by means of topological degree finally a suitable example is given to illustrate that the conditions of the main theorem are feasible

permanence and extinction in nonlinear single and multiple species system with diffusion in this paper we consider the effect of diffusion on the permanence and extinction of single and multiple endangered species that live in changing patch environments average conditions are obtained for the permanence and extinction of the systems considered the results obtained in this paper generalize the main results of cui and chen the effect of diffusion on the time varying logistic population growth comput math appl 36 3 1998 1 9 permanence and extinction in logistic and lotka volterra systems with diffusion j math anal appl 258 2 2001 512 535

periodic solutions of a predator prey system with stage structures for predator and prey abstract by using the continuation theorem of coincidence degree theory the existence of a positive periodic solution for the predator prey system with stage structures for predator and prey is established

periodic solution and global stability for a nonautonomous competitive lotka volterra diffusion system the periodic solution and global stability for a nonautonomous competitive lotka volterra diffusion system is considered in this paper by using of brouwer fixed point theorem and constructing a suitable liapunov function under some appropriate conditions the system has a unique periodic solution which is globally stable

global stability of a delay differential equations model of plankton allelopathy abstract in this paper we consider a delay differential equations model of plankton allelopathy using an iterative method the global stability of the interior equilibrium point of the system is investigated which shows that toxic substances are harmless for the stability of the interior equilibrium point the results we obtained improve and complement those of chattopadhyay j chattopadhyay effect of toxic substances on a two species competitive system ecol model 84 1996 287 289 samanta g p samanta a two species competitive system under the influence of toxic substances appl math comput 216 2010 291 299 and mukhopadhyay et al a mukhopadhyay j chattopadhyay p k tapaswi a delay differential equations model of plankton allelopathy math biosci 149 1998 167 189 we also present some examples to verify our main result

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

positive periodic solution of a general discrete non autonomous difference system of plankton allelopathy with delays the main purpose of this paper is to investigate a discrete time non autonomous difference system of plankton allelopathy with delays by employing continuous theorem proposed by gains and mawhin and some new techniques a set of verifiable sufficient criteria are established for the existence of at least one strictly positive componentwise periodic solution and as an application we also examine some special case showing that these conditions are similar to those of continuous differential system it is also shown that the time delays are harmless for the existence of positive periodic solutions of system

periodic solutions of periodic delay lotka volterra equations and 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 both periodic lotka volterra equations and systems with distributed or state dependent delays our results substantially extend and improve existing results

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

permanence and global stability of nonautonomous lotka volterra system with predator prey and deviating arguments by using comparison theorem and constructing suitable lyapunov functional some sufficient conditions for the permanence and global asymptotic stability of the general nonautonomous lotka volterra system with predator prey and deviating arguments are obtained

derivation of continuous explicit two step runge kutta methods of order three we describe a construction of continuous extensions to a new representation of two step runge kutta methods for ordinary differential equations this representation makes possible the accurate and reliable estimation of local discretization error facilitates the efficient implementation of these methods in variable stepsize environment and adapts readily to the numerical solution of a class of delay differential equations a number of numerical tests carried out on the obtained methods of order 3 with quadratic interpolants show their efficiency and robust performance which allow them to compete with the state of the art dde23 code from matlab

periodicity in a logistic type system with several delays with the help of a continuation theorem based on gaines and mawhin s coincidence degree easily verifiable criteria are established for the global existence of positive periodic solutions of the following several delays logistic type system du t dt u t a t j 1mb j t u t t j t q j where a t b j t are positive periodic continuous functions with periodic w 0 t j t are nonnegative continuous periodic functions with periodic w 0 after that by constructing a suitable lyapunov functional some sufficient conditions which guarantee the stability of the positive periodic solutions are obtained

interpolated finite impulse response filters a new approach to implement computationally efficient finite impulse response fir digital filters is presented the filter structure is a cascade of two sections the first section generates a sparse set of impulse response samples and the other section generates the remaining samples by using interpolation the method can be used to implement most practical fir filters with significant savings in the number of arithmetic operations typically 1 2 to 1 8 of the number of multipliers and adders of conventional fir filters are required in the implementation the saving is achieved both in the linear phase and the non linear phase cases in addition the new implementation gives smaller coefficient sensitivities and better roundoff noise properties than conventional implementations

an abstract existence theorem at resonance and its applications abstract by using brouwer degree theory and a continuation theorem based on mawhin s coincidence degree an abstract existence theorem at resonance for operator equations is developed as applications of this result some sufficient conditions are given for the existence of periodic solutions of semilinear equations at resonance where the kernel of the linear part has dimension n n 2 the results due to nagle and sinkala are generalized improved and unified

periodic solutions for delay differential equations model of plankton allelopathy abstract in this paper we propose a modified delay differential equation model of the growth of two species of plankton having competitive and allelopathic effects on each other by using the continuation theorem of coincidence degree theory a set of easily verifiable sufficient conditions are obtained for the existence of positive periodic solutions for this model

periodicity in a food limited population model with toxicants and state dependent delays abstract with the help of a continuation theorem based on gaines and mawhin s coincidence degree easily verifiable criteria are established for the global existence of positive periodic solutions of a food limited population model with toxicant and state dependent delays that is du t dt u t r t a t u t j 1 m b j t u t j t u t k t c t u t j 1 m d j t u t j t u t where r t k t a t bj t dj t j 1 2 m are continuous real valued periodic functions with period 0 and r t k t a t 0 bj t dj t 0 j 1 2 m are periodic continuous functions with period 0 j j are periodic with respect to their first arguments some new results are obtained

periodic solution for a two species nonautonomous competition lotka volterra patch system with time delay abstract by using the continuation theorem of coincidence degree theory the existence of a positive periodic solution for a two species nonautonomous competition lotka volterra patch system with time delay x 1 t x 1 t r 1 t a 1 t x 1 t b 1 t y t d 1 t x 2 t x 1 t x 2 t x 2 t r 2 t a 2 t x 2 t d 2 t x 1 t x 2 t y t y t r 3 t a 3 t x 1 t b 3 t y t t 0 k s y t s ds is established where ri t ai t i 1 2 3 di t i 1 2 bi t i 1 3 and t are all positive periodic continuous functions with period w 0 is a nonnegative constant and k s is a continuous nonnegative function on 0

meshless galerkin methods using radial basis functions we combine the theory of radial basis functions with the field of galerkin methods to solve partial differential equations after a general description of the method we show convergence and derive error estimates for smooth problems in arbitrary dimensions

new results on positive periodic solutions of a periodic integro differential competition system considered is the periodic integro differential competition system with infinite delays recently studied by fan and wang z angew math mech 81 2001 197 using the method of coincidence degree we present another set of sufficient conditions for the existence of positive componentwise periodic solutions of the system our results improve and supplement those obtained by fan and wang z angew math mech 81 2001 197

permanence in nonautonomous multi species predator prey system with feedback controls a nonautonomous multi species predator prey system with feedback controls is proposed in this paper where the competition among the predator species and among the prey species is considered also some important factors such as the effect of toxins and the age structure are also considered average conditions are obtained for permanence and global attractivity in the system the results obtained here generalized the main results of zhao and jiang j d zhao j f jiang permanence in nonautonomous lotka volterra system with predator prey appl math computat 152 2004 99 109

on a periodic multi species ecological model a periodic predator prey model with m predators and n preys is proposed in this paper which can be seen as the modification of the traditional lotka volterra model by using comparison theorem the ultimately bounded region of the system is obtained by using comparison theorem and brouwer fixed point theorem sufficient conditions with guarantee the existence of a positive periodic solution of the system is obtained finally by constructing a suitable lyapunov function some sufficient conditions are obtained for the existence of a unique globally attractive periodic solution of system the results obtained here generalized the main results of j d zhao w c chen global asymptotic stability of a periodic ecological model applied mathematics and computation 147 3 2004 881 892

on a boundary value problem for delay differential equations of population dynamics and chebyshev approximation in this paper a boundary value problem for delay differential equations of population dynamics is considered we obtain approximate solutions by using chebyshev polynomial series and newton raphson s procedure and give the error estimation the method of the error estimation has been obtained in an existence theorem proved by a part of the authors we carry out some numerical experiments by a computer language matlab

multivariate approximation by pde splines this work deals with an approximation method for multivariate functions from data constituted by a given data point set and a partial differential equation pde the solution of our problem is called a pde spline we establish a variational characterization of the pde spline and a convergence result of it to the function which the data are obtained we estimate the order of the approximation error and finally we present an example to illustrate the fitting method

global dynamics behaviors for a nonautonomous lotka volterra almost periodic dispersal system with delays abstract a nonautonomous lotka volterra dispersal system with continuous delays and discrete delays is considered by using a comparison theorem and delay differential equation basic theory we obtain sufficient conditions for the permanence of the population in every patch by constructing a suitable lyapunov functional we prove that the system is globally asymptotically stable under some appropriate conditions using almost periodic functional hull theory we get sufficient conditions for the existence uniqueness and globally asymptotical stability for an almost periodic solution this implies that the population in every patch exhibits stable almost periodic fluctuation furthermore the results show that the permanence and global stability of system and the existence and uniqueness of a positive almost periodic solution depend on the delay then we call it profitless

extinction in two dimensional nonautonomous lotka volterra systems with the effect of toxic substances in this paper we consider a nonautonomous competitive lotka volterra system of two species with the effect of toxic substances it is shown that toxic substances play an important role in the extinction of species we prove that one of components will be driven to extinction while the other will stabilize at a certain solution of a logistic equation under some conditions

a subdivision approach to the construction of approximate solutions of boundary value problems with deviating arguments abstract using the ideas employed in the construction of subdivision algorithms we offer here a high accuracy algorithm to compute numerical solutions for two point boundary value problems of differential equations with deviating arguments numerical examples are included to demonstrate the fast convergence and high accuracy of the algorithm this paper is a further development to our previous works for solving various types of boundary value problems

periodic solution and almost periodic solution for a nonautonomous lotka volterra dispersal system with infinite delay abstract this paper studies a nonautonomous lotka volterra dispersal systems with infinite time delay which models the diffusion of a single species into n patches by discrete dispersal our results show that the system is uniformly persistent under an appropriate condition the sufficient condition for the global asymptotical stability of the system is also given by using mawhin continuation theorem of coincidence degree we prove that the periodic system has at least one positive periodic solution further obtain the uniqueness and globally asymptotical stability for periodic system by using functional hull theory and directly analyzing the right functional of almost periodic system we show that the almost periodic system has a unique globally asymptotical stable positive almost periodic solution we also show that the delays have very important effects on the dynamic behaviors of the system

non maximally decimated analysis synthesis filter banks applications in wideband digital filtering we present a new class of highly effective and low complexity digital filters for processing very wideband signals digital filtering for wideband signals is often limited by the number of arithmetic operations that has to be performed per input sampling interval we will show the new architecture permits filtering to be performed on partitioned spectral segments of the input signal at significantly reduced sample rate the digital filtering will be shown to include various tasks such as linear non linear phase finite impulse response fir filtering fractional delay filter among others the proposed technique utilizes the framework of non maximally decimated filter banks nmdfbs with perfect reconstruction pr property which makes the filter bank design simpler and more flexible compact representation for the generalized dft based nmdfbs as well as its efficient polyphase implementation will be provided the digital filtering is made possible by incorporating the desired intermediate processing elements in between the analysis and synthesis filter banks we will show this embedded intermediate processing elements can achieve spectral shaping signal manipulation task which is a generalization of the concept of manipulating a digital filter in the frequency domain we also analyze both analytically and experimentally the spectral shaping accuracy based on different design strategies

a new approach to numerical solution of fixed point problems and its application to delay differential equations in this paper we consider a certain approximation of fixed points of a continuous operator a mapping the metric space into itself by means of finite dimensional e h fixed points of a these finite dimensional functions are obtained from functions defined on discrete space grid points related to a parameter h 0 by applying suitably chosen extension operators p h a theorem specifying necessary and sufficient conditions for existence of fixed points of a in terms of e h fixed points of a is given a corollary which follows the theorem yields an approximate method for a fixed point problem and determines conditions for its convergence an example of application of the obtained general results to numerical solving of boundary value problems for delay differential equations is provided numerical experiments carried out on three examples of boundary value problems for second order delay differential equations show that the proposed approach produces much more accurate results than many other numerical methods when applied to the same examples

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

existence uniqueness and stability analysis of allelopathic stimulatory phytoplankton model in this paper we consider the two species competitive delay plankton allelopathy stimulatory model system we show the existence and uniqueness of the solution of the deterministic model moreover we study the persistence of the model and the stability properties of its equilibrium points we illustrate the theoretical results by some numerical simulations

four periodic solutions of a generalized delayed predator prey system by using the continuation theorem of coincidence degree theory the existence conditions of four periodic solutions for the delayed predator prey system is established

on the synthesis of very sharp decimators and interpolators using the frequency response masking technique decimation and interpolation are very common multirate signal processing operations conventional decimation or interpolation technique using polyphase filters has the advantage that for a given transition band sharpness the filter s computational complexity decreases with increasing interpolation or decimation factor nevertheless if the transition band of the decimation or interpolation filter is very sharp the complexity of the filter may still be very high the complexity of a very sharp filter may be reduced using the frequency response masking frm technique however as shown in this paper for a given transition band sharpness the computational complexity of the classical frm method does not reduce as rapidly as the increase in decimation or interpolation factor in this paper we present a novel variant of the frm technique for interpolation or decimation application in this new variant the computational complexity reduces as rapidly as the interpolation or decimation factor increases the reduction in computational complexity increases with decreasing transition width over an order of magnitude reduction in computational complexity is achieved when compared with conventional polyphase approach in a particular example presented in this paper

a periodic predator prey chain system with impulsive perturbation a periodic predator prey chain system with impulsive effects is considered by using the global results of rabinowitz and standard techniques of bifurcation theory the existence of its trivial semi trivial and nontrivial positive periodic solutions is obtained it is shown that the nontrivial positive periodic solution for such a system may be bifurcated from an unstable semi trivial periodic solution furthermore the stability of these periodic solutions is studied

extinction in periodic competitive stage structured lotka volterra model with the effects of toxic substances in this paper we consider a periodic competitive stage structured lotka volterra model with the effects of toxic substances it is shown that toxic substances play an important role in the extinction of species we obtain a set of sufficient conditions which guarantee that one of the components is driven to extinction while the other is globally attractive the numerical simulation of an example verifies our main results

permanence and extinction analysis for a delayed periodic predator prey system with holling type ii response function and diffusion abstract in this paper it is studied that two species predator prey lotka volterra type dispersal system with delay and holling type ii response function in which the prey species can disperse among n patches while the density independent predator species is confined to one of the patches and cannot disperse sufficient conditions of integrable form for the boundedness permanence extinction and the existence of positive periodic solution are established respectively

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

on a nonlinear nonautonomous predator prey model with diffusion and distributed delay in this paper a nonlinear nonautonomous predator prey model with diffusion and continuous distributed delay is studied where all the parameters are time dependent the system which is composed of two patches has two species the prey can diffuse between two patches but the predator is confined to one patch we first discuss the uniform persistence and global asymptotic stability of the model after that by constructing a suitable lyapunov functional some sufficient conditions for the existence of a unique almost periodic solution of the system are obtained an example shows the feasibility of our main results

on the convergence of cardinal interpolation by parameterized radial basis functions abstract we consider cardinal interpolation on gridded data by using various radial basis functions associated with one or two parameters one of which leads asymptotically to so called flat limits previously it had been shown that the classical paley wiener functions can be recovered by such cardinal interpolations as the parameter tends to infinity in this article we extend the results by relaxing the requirements on the approximand functions from several points of view the radial basis functions that we are concerned with and which are of special interest contain the celebrated multiquadrics inverse multiquadrics and shifted thin plate spline radial basis functions for instance we also generalise the classes of admitted approximands as well as the radial basis functions to generalised multiquadrics in place of the well known ordinary or for example inverse multiquadrics an interesting analytical aspect of this work is that unlike the classical whittaker shannon theorem functions approximands may be reproduced for the parameter c in the generalised multiquadrics cardinal approximands where the usual shannon series does not converge with theses approximands due to the slow decay of the sinc function which does not allow e g polynomials as approximands in contrast to the latter the generalised multiquadrics cardinal functions employed here decay sufficiently fast for each fixed parameter c that even polynomials may be admitted as approximands and are reproduced when then the parameter tends to infinity

existence and global attractivity of positive periodic solutions for delay lotka volterra competition patch systems with stocking abstract by means of mawhin s continuation theorem of coincidence degree and lyapunov functional a set of easily verifiable criteria are established for the existence and global attractivity of positive periodic solutions for delay lotka volterra competition patch system with stocking x 1 t h 1 t x 1 t a 1 t b 1 t x 1 t c 1 t y t d 1 t x 2 t 1 x 1 t s 1 t x 2 t h 2 t x 2 t a 2 t b 2 t x 2 t d 2 t x 1 t 2 x 2 t s 2 t y t h 3 t y t a 3 t b 3 t y t t 0 k s y t s ds c 3 t x 1 t s 3 t some known results are generalized and improved

positive periodic solutions of neutral lotka volterra system with feedback control with the help of a continuation theorem based on gaines and mawhin s coincidence degree easily verifiable criteria are established for the global existence of positive periodic solutions of neutral lotka volterra system with periodic delays and feedback control our results extend and improve existing results and have further applications in population dynamics

sufficient conditions for the existence positive periodic solutions of a class of neutral delay models with feedback control with the help of a continuation theorem based on gaines and mawhin s coincidence degree easily verifiable criteria are established for the global existence of positive periodic solutions of a neutral model with periodic delays and feedback controldndt n t a t email protected t n t email protected i 1nb i t n email protected i t email protected i 1nc i t n email protected i t email protected t u t email protected i 1nd i t u email protected i t dudt e t u t f t n t email protected i 1ng i t n email protected i t our results extend and improve existing results and have further applications in population dynamics

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

profitless delays for a nonautonomous lotka volterra predator prey almost periodic system with dispersion abstract this paper studies a nonautonomous lotka volterra almost periodic predator prey dispersal system with discrete and continuous time delays which consists of two patches the prey species can disperse among two patches but the predator species is confined to one patch and cannot disperse by using comparison theorem and delay differential equation basic theory we prove the system is uniformly persistent under some appropriate conditions further by constructing suitable lyapunov functional we show that the system is globally asymptotically stable under some appropriate conditions by using a new method and almost periodic functional hull theory we show that the almost periodic system has a unique globally asymptotical stable strictly positive almost periodic solution the conditions for the permanence global stability of system and the existence uniqueness of positive almost periodic solution depend on delays so time delays are profitless finally ecological conclusions and a particular case are given these results are basically an extension of the known results for nonautonomous lotka volterra systems

a class of linear phase fir filters for decimation interpolation and narrow band filtering a new class of linear phase finite impulse response fir digital filters for decimation and interpolation is discussed the transfer function of these filters is of the form h z a zd b z where d is the decimation or interpolation ratio and a zd is realized at the lower sampling rate the polynomial a zd is adjusted so that the overall magnitude response presents an equiripple behavior in the pass band whereas b z provides an equiripple stopband response an efficient iterative procedure for the design of the filters of this type is presented and the optimal selection of the orders of a zd and b z is considered several examples show how the new decimators and interpolators require significantly fewer multiplications per second than equivalent conventional linear phase fir and elliptic designs the performance of these linear phase filters is about the same as that of the recursive filters of martinez and parks with only powers of zdin the denominator some characteristics of the new filters such as zero positions coefficient sensitivity and output noise variance due to roundoff errors are discussed and compared with conventional fir designs furthermore it is shown that by cascading multistage new decimators and interpolators we obtain efficient narrow band filters requiring considerably fewer multiplications per output sample than equivalent elliptic designs

positive periodic solutions of neutral lotka volterra system with periodic delays in this paper several sufficient conditions are investigated for the existence of positive periodic solutions of a general neutral lotka volterra system with unbounded delays by using the theory of coincidence degree our results extend and improve existing results and have further applications in population dynamics

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

periodic and almost periodic solution for a non autonomous epidemic predator prey system with time delay in this paper we studied a non autonomous predator prey system with discrete time delay where there is epidemic disease in the predator by using some techniques of the differential inequalities and delay differential inequalities we proved that the system is permanent under some appropriate conditions when all the coefficients of the system is periodic we obtained the existence and global attractivity of the positive periodic solution by mawhin s continuation theorem and constructing a suitable lyapunov functional furthermore when the coefficients of the system are not absolutely periodic but almost periodic sufficient conditions are also derived for the existence and asymptotic stability of the almost periodic solution

global stability in delay differential systems without dominating instantaneous negative feedbacks abstract most of the global stability or convergence results appearing so far for delayed lotka volterra type systems or other delay differential systems require that the instantaneous negative feedbacks dominate both delayed feedback and interspecific interactions such a requirement is rarely met in real systems since feedbacks are generally delayed this leads to the long standing question under what conditions will the global stability of a nonnegative steady state of a differential delay system persist when time delays involved in some part of the negative feedbacks are small enough this paper presents a partial answer to this open question roughly our results show that if the delay differential system remains dissipative when delays are introduced then the above open question has an affirmative answer our results also improve some recent findings

a comparative study of deterministic and stochastic dynamics for a non autonomous allelopathic phytoplankton model abstract in this paper we investigate a non autonomous competitive phytoplankton model with periodic coefficients in deterministic and stochastic environment respectively we prove the existence of at least one positive periodic solution together with it s global asymptotic stability the existence of periodic solution has been obtained by using the continuation theorem of coincidence degree theory proposed by gaines and mawhin we formulate the corresponding stochastic model by perturbing the growth rate parameters by white noise terms we prove that all the higher order moments of the solution to the stochastic system is uniformly bounded which ensure that the solution of the stochastic system is stochastically bounded we provide easily verifiable sufficient conditions for non persistence in mean extinction and stochastic permanence of the stochastic system sufficient condition for permanence shows that if the noise intensity is very low then the solution of the stochastic system persists in the periodic coexistence domain of the deterministic system we perform exhaustive numerical simulations to validate our analytical findings

existence uniqueness and stability of positive periodic solution for a nonlinear prey competition model with delays a nonlinear periodic predator prey model with m preys and n m predators and delays is proposed in this paper which can be seen as the modification of the traditional lotka volterra prey competition model sufficient conditions which guarantee the existence of a unique globally attractive positive periodic solution of the system are obtained