geometry of exclusion principles in discrete systems abstract using an n species system of difference equations with very general density dependent growth functions we prove that weak dominance and invariance gives the exclusion of all the n 1 dominated species in the system this result is applied to very specific competition models an example of coexistence in a competition model with no invariance is studied a notion of strong dominance is developed in a general setting and shown to imply exclusion of the n 1 dominated species an example of a competition model illustrating that weak dominance plus invariance does not imply strong dominance is given

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

discrete time dynamics of a system with crowding effect and predator partially dependent on prey in the present study the stability and bifurcation analysis of discrete time predator prey system with predator partially dependent on prey and crowding effect of predator is examined global stability of the system at the fixed points has been discussed the specific conditions for existence of flip bifurcation and hopf bifurcation in the interior of r 2 have been derived by using a center manifold theorem and bifurcation theory numerical simulations have been carried out to show the complex dynamical behavior of the system and to justify our analytic results in case of flip bifurcation numerical simulations presented cascade of period doubling bifurcation in the orbits of period 2 4 8 chaotic orbits and stable window of period 9 orbit whereas in case of hopf bifurcation smooth invariant circle bifurcates from the fixed point the complexity of dynamical behavior is confirmed by computation of lyapunov exponents

the dynamics of some discrete population models in this paper we are interested in providing sufficient conditions guaranteeing the fact that all positive solutions of the discrete delay difference equation a ii 1 aa f a e converge as n 00 in e a is a constant real number with 0 0 sufficiently small thus formally equation e comes from x t h x t h yx t d x t r for small h if we set z f x ht then the preceding equation for t n and r h m becomes yh 1 1 h y n hd y n m which is of the form e where a 1 yh and f u hd u u 2 0 clearly h 0 is small if and only if a e 0 1 1069 h

permanence and global attractivity of a discrete multispecies lotka volterra competition predator prey systems in this paper we propose a discrete multispecies lotka volterra competition predator prey systems for general non autonomous case sufficient conditions which ensure the permanence and the global stability of the system are obtained for periodic case sufficient conditions which ensure the existence of a globally stable positive periodic solution of the system are obtained

global stability of discrete competition model abstract this is a study of global stability of a competition model governed by difference equations it is shown that positive equilibrium of the model is globally stable if the competition matrix is diagonally dominant and the constants defining the intraspecific competition are less than or equal to 1 in the two dimensional case a different type of sufficient conditions for the global stability is established which relaxes the restriction on the constants defining the intraspecific competition

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

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

permanence for a delayed discrete ratio dependent predator prey system with holling type functional response abstract sufficient conditions are established for the permanence in a delayed discrete predator prey model with holling type iii functional response n 1 k 1 n 1 k exp b 1 k a 1 k n 1 k 1 1 k n 1 k n 2 k n 1 2 k m 2 n 2 2 k n 2 k 1 n 2 k exp b 2 k 2 k n 1 2 k 2 n 1 2 k 2 m 2 n 2 2 k 2 our investigation confirms that when the death rate of the predator is rather small as well as the intrinsic growth rate of the prey is relatively large the species could coexist in the long run

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

the persistence and global attractivity in general nonautonomous discrete single species kolmogorov model with delays in this paper general nonautonomous discrete time single species kolmogorov model with delays is studied some sufficient conditions on the boundedness persistence permanence and global attractivity of solutions are established as application the discrete time nonautonomous delayed allee effect model is discussed the sufficient conditions on the permanence and global attractivity are obtained

dynamic behaviors of the impulsive periodic multi species predator prey system the dynamic behaviors of an impulsive periodic predator prey model with n preys and m predators are studied in this paper by constructing a suitable lyapunov function and using the comparison theorem of impulsive differential equation sufficient conditions which ensure the permanence and global attractivity of the system are obtained at the same time a set of criteria which guarantee that some species in the system are permanent and globally attractive while the remaining species are driven to extinction is obtained our results show that for the multi species predator prey community impulsivity is one of the important reasons that can change the long time behaviors of species

a generalization of volterra models with continuous time delay in population dynamics boundedness and global asymptotic stability we introduce a generalization of volterra models with continuous time delay by adding a nonnegative linear vector function of the species sufficient conditions for boundedness of solutions and global asymptotic stability of an equilibrium are provided applications from population dynamics are presented one concerns a predator prey volterra model with prey refuges and continuous time delay and another deals with a volterra system with currents of immigration for some species furthermore for this kind of model by a suitable homotopy function we provide a sufficient condition for the existence of the globally asymptotically stable equilibrium finally an example of a simple model in which two predators are competing for one prey which can take shelter is presented

global asymptotic stability beyond 3 2 type stability for a logistic equation with piecewise constant arguments abstract in this paper a logistic equation with multiple piecewise constant arguments is investigated in detail we generalize the approach in two papers k uesugi y muroya e ishiwata on the global attractivity for a logistic equation with piecewise constant arguments j math anal appl 294 2 2004 560 580 and y muroya e ishiwata n guglielmi global stability for nonlinear difference equations with variable coefficients j math anal appl 334 1 2007 232 247 and establish a new condition for the global stability of the equation their results are given as one of the special cases moreover we improve the 3 2 type stability condition under several dominance assumptions on the coefficients of the equation some examples and numerical simulations are also presented all of these examples show that there are several conditions for the global stability of the equation depending on the coefficients on the delay terms of the equation beyond the 3 2 type stability condition

the divisor periodic point of escape time n of the mandelbrot set this paper offers a rendering method based on the escape time method to draw the mandelbrot set in different colors the rendering method chooses different colors according to the distance and the escape time n so it can effectively render the mandelbrot set which can show us the 3 d view of the mandelbrot set according to amplify the part of the mandelbrot set drawn by the rendering method we will find some cirques with one heart like the equipotential lines the center point c 0 of the cirques with one heart whose color will be rendered by black has a period and only those center points c 0 whose periods are the divisors of the escape time n will show us the cirques with one heart like the equipotential lines around them we call those center points c 0 the divisor periodic points of the escape time n

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

on the stability and uniform persistence of a discrete model of nicholson s blowflies abstract consider the delay difference equation n n 1 nn n n pn n k e an n k n 0 1 2 1 which is a discrete analogue of the delay differential equation n t n t pn t e an t t 0 cf 8 we show that when p the zero solution of 1 is uniformly asymptotically stable and every non negative solution of 1 tends to zero as n while for p 1 is uniformly persistent moreover if in addition to p we also have 1 k 1 1 ln p 1 then every positive solution of 1 tends to the positive equilibrium n 1 a ln p

the generalized mandelbrot set perturbed by composing noise of additive and multiplicative adopting the experimental mathematics method combining complex variable function theory with computer aided drawing this paper researches on the structural characteristic and the fission evolution law of the generalized mandelbrot set generalized m set in short perturbed by composing noise of additive and multiplicative analyzes the effect of random perturbation to the generalized m set

almost periodic solutions of a discrete almost periodic logistic equation with delay abstract in this paper we consider an almost periodic discrete logistic equation with delay by constructing suitable lyapunov functional and almost periodic functional hull theory a sufficient condition is obtained for the existence of a unique almost periodic solution which is globally attractive an example together with its numerical simulation shows the feasibility of our main result

physical meaning for mandelbrot and julia sets abstract we consider the dynamics of a kicked charged particle moving in a double well potential and a time dependent magnetic field in certain cases the stroboscopic dynamics reduces to the complex logistic map thus providing physical meaning for the mandelbrot set in other cases we obtain iterated function systems consisting of the inverse complex logistic map thus providing physical meaning for julia sets our approach can be generalized to complex mappings with a maximum of order q

on a topological closeness of perturbed mandelbrot sets in the present work we propose a numerical and visual tool for the study of the deformation of the mandelbrot sets of perturbed mandelbrot maps by noise in comparison with the original mandelbrot set further by employing these numerical tools we support the invariance of the mandelbrot set of a noise perturbed mandelbrot map under different noise realizations finally we provide evidence for the non fractal structure of the mandelbrot set of a noise perturbed mandelbrot map

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

the area of the mandelbrot set we obtain upper bounds for the area of the mandelbrot set an effective procedure is given for computing the coefficients of the conformal mapping from the exterior of the unit circle onto the exterior of the mandelbrot set the upper bound is obtained by computing finitely many of these coefficient and applying green s theorem the error in such calculations is estimated by deriving explicit formulas for infinitely many of the coefficients and comparing

uniform persistence and periodic solutions for a discrete predator prey system with delays abstract in this paper we deal with a discrete predator prey system with delay we first give a sufficient condition for the uniform persistence of the system assuming that the coefficients in the system are periodic by generalizing the yoshizawa s theorem on the existence of periodic solution for ordinary differential equations to the difference equations with delays we obtain the existence of a periodic solution basing on the uniform persistence result

permanence of a discrete nonlinear n species cooperation system with time delays and feedback controls a discrete nonlinear n species cooperation system with time delays and feedback controls is considered in this paper sufficient conditions which ensure the permanence of the system are obtained it is shown that these conditions are weaker than those of chen f d chen permanence of a discrete n species cooperation system with time delays and feedback controls appl math comput 186 2007 23 29 that is our investigation shows that the additional condition in chen s paper is not necessary

global behavior of a three dimensional linear fractional system of difference equations we investigate the global asymptotic behavior of solutions of the system of difference equations xn 1 a xnb yn yn 1 c ynd zn zn 1 e znf xn n 0 1 where the parameters a b c d e and f are in 0 and the initial conditions x0 y0 and z0 are arbitrary non negative numbers we obtain some global attractivity results for the positive equilibrium of this system for different values of the parameters

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

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

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

research on fractal structure of generalized m j sets utilized lyapunov exponents and periodic scanning techniques abstract in order to show details of fractal structure of mandelbrot set precisely lyapunov exponents and periodic scanning techniques have been brought forward by shirriff and welstead this paper generalizes these two techniques and puts forward periodicity orbit search and comparison technique which can be used to discuss the relationship of the generalized mandelbrot julia sets the generalized m j sets adopting the techniques mentioned above and the experimental mathematics method of combining the theory of analytic function of one complex variable with computer aided drawing this paper researches on the structure topological inflexibility and the discontinuity evolution law of the generalized m j sets generated from the complex mapping z z c r and explores structure and distributing of periodicity petal and topological law of periodicity orbits of the generalized m sets and finds that the generalized m set contains abundant information of structure of the generalized j sets by founding the whole portray of the generalized j sets based on the generalized m set qualitatively furthermore the physical meaning of the generalized m j sets have been expounded

global attractivity in a nonlinear difference equation abstract we consider the nonlinear difference equation x n a k 1 m b k x n k n 0 1 2 where a and bk k 1 2 m are nonnegative numbers with b mk 1bk 0 and we are interested in whether all positive solutions are attracted by the positive equilibrium l a 2 a 2 2 b

global attractivity of the periodic lotka volterra system a lotka volterra periodic model withm predators andn preys is studied in this paper a set of easily verifiable sufficient conditions that guarantee the existence uniqueness and global attractivity of the positive periodic solutions is obtained finally a suitable example is given to illustrate that the conditions of the main theorem are feasible

permanence of species in nonautonomous discrete lotka volterra competitive system with delays and feedback controls a nonautonomous n species discrete lotka volterra competitive system of difference equations with delays and feedback controls is considered new sufficient conditions are obtained for the permanence of this discrete system the results indicate that one can choose suitable controls to make the species coexistence in the long run moreover we give some examples to illustrate the feasibility of our result which can be well suited for computational purposes

stable periodic solution of a discrete periodic lotka volterra competition system with a feedback control this paper discusses a discrete lotka volterra competition system with feedback controls 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

periodic solutions of a discrete time lotka volterra type food chain model with delays a periodic discrete time three trophic level lotka volterra type food chain model is investigated by using gaines and mawhin s continuation theorem of coincidence degree theory sufficient conditions are derived for the existence of positive periodic solutions of the model

uniform persistence for a discrete predator prey system with delays abstract in this paper we deal with a discrete predator prey model with monotonic functional responses and give a sufficient condition of uniform persistence for the system

the qualitative analysis of n species nonlinear prey competition systems in this paper we consider an n species nonlinear prey competition system using the differential inequality theorem and the v function method we obtain some sufficient conditions for the permanence and global asymptotic stability of the system

global attractivity of periodic solutions of population models abstract this paper studies periodic solutions of two types of population models with time delays and periodic coefficients the first represents one species growth with delayed recruitments and the second models a single species despersal among the n patches by developing the theory of monotone and concave operators to functional differential equations we establish conditions under which each model admits a positive periodic solution which attracts all positive solutions

permanence and stability of equilibrium for a two prey one predator discrete model in this letter a predator prey system of two prey one predator discrete model is investigated it is proved that the system is permanence under some appropriate conditions by jacobian matrix method a sufficient and necessary condition is derived for the local asymptotic stability of a equilibrium of the system meanwhile we give a suitable example for supporting our theoretical result

on numerical approximations of the area of the generalized mandelbrot sets in the present work the area of the generalized mandelbrot sets is defined as the double limit of the areas of the plotted generalized mandelbrot sets in a given square lattice using the finite escape algorithm while the lattice resolution and the number of iteration counts used to plot them tends to infinity the asymptotic behavior of the areas of the generalized mandelbrot sets in terms of their degree growth is investigated finally numerical approximations of the area of the mandelbrot set are proposed by using tools from regression analysis

global asymptotic behavior of a two dimensional difference equation modelling competition we investigate the global asymptotic behavior of solutions of the system of difference equations xn 1 xn a cyn yn 1 yn b dxn n 0 1 where the parameters a and b are in 0 1 c and d are arbitrary positive numbers and the initial conditions x0 and y0 are arbitrary nonnegative numbers we show that the stable manifold of this system separates the positive quadrant into basins of attraction of two types of asymptotic behavior in the case where a b we find an explicit equation for the stable manifold

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

global asymptotic stability of lotka volterra diffusion models with continuous time delay we consider the global asymptotic stability of diffusion models with multiple species heterogeneous patches and incorporate the effect of continuous time delays for species in each patch for two different patches connected by diffusion with multiple species and with patch dynamics governed by lotka volterra models with continuous time delays and constant influxes we give sufficient conditions for boundedness of solutions and the existence of a nonnegative equilibrium point providing also a candidate for a lyapunov function by applying the homotopy function technique for different symbiotic patches with time delays we provide a sufficient condition for the existence of a positive globally asymptotically stable equilibrium point further we discuss the global asymptotic stability for the prey predator model where the prey has its shelter from predation and only the predator can diffuse between patches we consider also the existence condition for the globally asymptotically stable equilibrium for t

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

global attractivity in an almost periodic multi species nonlinear ecological model abstract a nonlinear almost periodic predator prey model with n preys and m predators is studied in this paper which can be seen as the modification of the traditional multi species lotka volterra predator prey model for general nonautonomous case by using the differential inequality theory we obtain the sufficient conditions which guarantee the uniform persistence and nonpersistence of the system after that by constructing a suitable lyapunov function some sufficient conditions are obtained which ensure the global attractivity of the system for almost periodic case by constructing a suitable lyapunov function sufficient conditions which guarantee the existence of an unique globally attractive positive almost periodic solution of the system are obtained examples together with their numeric simulations show the feasibility of our main results

the problem of scattering by a partially coated crack abstract in this paper we consider the scattering of an electromagnetic time harmonic plane wave by an infinite cylinder having an open arc in r 2 as the cross section we assume that the arc is divided into two parts and one of the two parts is possibly coated on one side by a material with surface impedance applying potential theory the problem can be reformulated as a boundary integral system we obtain the existence and uniqueness of a solution to the system by using fredholm theory

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

asymptotic behavior of a predator prey system with diffusion and delays abstract in this paper the asymptotic behavior of solutions of a predator prey system is determined the model incorporates time delays due to gestation and assumes that the prey disperses between two patches of a heterogeneous environment with barriers between patches and that the predator disperses between the patches with no barrier conditions are established for the permanence of the populations and the global attractivity of a positive equilibrium

global asymptotic stability of a periodic ecological model the periodic lotka volterra model with m predators and n preys is considered in this paper under the suppose that the intrinsic growth rate of the prey species may be negative while the total intrinsic growth rate in a period are positive sufficient conditions are obtained for existence and global asymptotic stability of the periodic solution of this model

numeric characteristics of generalized m set with its asymptote the mandelbrot set m set formulated by f c z z 2 c is important in chaos theory it has been extended into generalized m set k m set f c z z k c by using different exponent k the escape time algorithm is used to draw fractals which need preset thresholds and a maximum iteration times as input this paper presents and proves the upper and lower bounds of generalized m set thresholds a new method is also introduced to draw k m set when k is a rational number this method uses asymptotes of k m set to approach k m set from the outside we prove that k m set is the limit of these asymptotes finally some experiments are presented to validate our methods

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

permanence and global attractivity of the discrete gilpin ayala type population model in this paper we propose a discrete gilpin ayala competition model and a discrete gilpin ayala type multispecies competition predator model for general nonautonomous case sufficient conditions which ensure the permanence and the global stability of the system are obtained for periodic case sufficient conditions which ensure the existence of an unique globally stable positive periodic solution of the system are obtained an example together with its numeric simulations shows 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

noise perturbed generalized mandelbrot sets adopting the experimental mathematics method of combining the theory of analytic function of one complex variable with computer aided drawing in this paper on the structure characteristics and the discontinuity evolution law of the additive noise perturbed generalized mandelbrot sets m sets was studied on the influence of stochastic perturbed parameters of the structure of generalized m sets was analyzed the physical meaning of the additive noise perturbed generalized m sets was expounded

conditional stability estimation for an inverse boundary problem with non smooth boundary in ℛ in this paper we investigate an inverse problem of determining a shape of a part of the boundary of a bounded domain in r3 by a solution to a cauchy problem of the laplace equation assuming that the unknown part is a lipschitz continuous surface we give a logarithmic conditional stability estimate in determining the part of boundary under reasonably a priori information of an unknown part the keys are the complex extension and estimates for a harmonic measure

exclusion principles for density dependent discrete pioneer climax models abstract the ultimate dynamical result of an undisturbed pioneer climax model is assumed by experimental scientists to be the exclusion of the pioneer species examples that illustrate stable coexistence in a pioneer climax model with no isolated positive equilibria are given sufficient conditions are developed and used to confirm the pioneer exclusion in discrete pioneer climax models other situations are possible in such models in particular a mutual exclusion principle is established as a mathematical theorem

permanence of a discrete n species cooperation system with time delays and feedback controls in this paper a discrete n species cooperation system with time delays and feedback controls is proposed by applying the comparison theorem of difference equation sufficient conditions are obtained for the permanence of the system

the direct scattering problem for a crack buried in a piecewise homogenous medium we consider a kind of scattering problem which models the scattering of an electromagnetic time harmonic plane wave by an infinite cylinder having an open arc and a penetrable obstacle in r2 as cross section and the open arc is buried in a piecewise homogeneous medium to this end we solve a scattering problem for the helmholtz equation in r2 where the scattering object is a crack which is buried inside the bounded domain d and we have dirichlet impedance type boundary condition on and transmission boundary condition on the boundary of d applying potential theory the problem can be reformulated as a boundary integral system we establish the existence and uniqueness of a weak solution to the system by using the modified fredholm theory

regularization of a backward problem for a lotka volterra competition system abstract lotka volterra systems are used to describe the dynamics of biological systems we study the backward problem for the lotka volterra system to determine the population density of species at preceding times the problem is ill posed in the sense that if the solution exists it does not depend continuously on the given data we propose two stable regularization methods to regularize the system furthermore under some a priori assumptions on the sought solution we show that the corresponding regularized solutions converge to the exact solutions in l 2 norm numerical simulations are presented to demonstrate the theoretical results

global stability in chemostat type competition models with nutrient recycling this note corrects some typos and errors in the paper s ruan and x z he siam j appl math 58 1998 pp 170 192

searching predator and prey dominance in discrete predator prey systems with dispersion the model for this study is an extension of a discrete time predator prey model of hassell and comins that includes dispersion in a patchy habitat in a single patch system it is shown that irrespective of initial population densities a prey species with a high growth rate dominates the system with the resulting existence or extinction of the searching predator with a numerical example it is shown that if the searching predator preys exclusively on the prey species that has a high growth rate then a spectrum of dynamical behavior including predator induced coexistence exclusionary dynamics and hopf bifurcation could occur in the single patch system if the searching predator preys exclusively on the prey species that has a low growth rate then both the predator and its preferred prey species go extinct an example is given illustrating that searching predator diffusion could change a system with stable coexistence of prey to extinction of prey species in a two patch system it is shown that the

permanence of a discrete n species food chain system with time delays in this paper a discrete n species food chain system with time delays is considered by applying the comparison theorem of difference equation sufficient conditions are obtained for the permanence of the system

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

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

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

additive perturbed generalized mandelbrot julia sets abstract adopting the experimental mathematics method combining complex variable function theory with computer aided drawing this paper researches on the structural characteristic and the fission evolution law of additive perturbed generalized mandelbrot julia sets generalized m j sets in short the corresponding relationship between point coordinates in generalized m set and the general structure of generalized j sets has been founded qualitatively and the physical meaning of the generalized m j sets has been expounded the following conclusions are deduced 1 chaotic patterns of fractal structure of generalized j sets may emerge out of double periodic bifurcation which shows that brownian movement can be chaotic 2 experimental evidence of li yorke theorem is given out 3 the additive perturbed generalized m set contains abundant information on the construction of generalized j sets 4 resemble logistic map in the process of a series of double periodic bifurcation coming into chaos generalized j sets also present self similarity in parameter space

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