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

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

on the periodic solutions of periodic multi species kolmogorov type competitive system with delays and feedback controls abstract in this paper we consider a periodic multi species kolmogorov type competitive system with delays and feedback controls applying schauder s fixed point theorem a criterion on the existence of the positive periodic solution of the system are obtained as application the existence of the positive periodic solution of a kind of nonlinear competitive model with delays and feedback controls is discussed

a high order spectral method for nonlinear water waves over moving bottom topography we present a numerical method for simulations of nonlinear surface water waves over variable bathymetry it is applicable to either two or three dimensional flows as well as to either static or moving bottom topography the method is based on the reduction of the problem to a lower dimensional hamiltonian system involving boundary quantities alone a key component of this formulation is the dirichlet neumann operator which in light of its joint analyticity properties with respect to surface and bottom deformations is computed using its taylor series representation we present new stabilized forms for the taylor terms each of which is efficiently computed by a pseudospectral method using the fast fourier transform physically relevant applications are displayed to illustrate the performance of the method comparisons with analytical solutions and laboratory experiments are provided

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

rational and transcendental growth series for the higher heisenberg groups this paper considers growth series of 2 step nilpotent groups with infinite cyclic derived subgroup every such group g has a subgroup of finite index of the form h n m where h n is the discrete heisenberg group of length 2n 1 we call n the heisenberg rank of g we show that every group of this type has some finite generating set such that the corresponding growth series is rational on the other hand we prove that if g has heisenberg rank n 2 then g possesses a finite generating set such that the corresponding growth series is a transcendental power series

complete growth functions of hyperbolic groups we study a generalization of the growth functions of finitely generated groups namely the growth functions g g gz g with coefficients in the group ring g rationality and methods of computation of such functions are discussed in particular for hyperbolic groups the complete growth functions of surface groups are explicitly computed the operator and geodesic growth functions are also studied

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

a fast and stable well balanced scheme with hydrostatic reconstruction for shallow water flows we consider the saint venant system for shallow water flows with nonflat bottom it is a hyperbolic system of conservation laws that approximately describes various geophysical flows such as rivers coastal areas and oceans when completed with a coriolis term or granular flows when completed with friction numerical approximate solutions to this system may be generated using conservative finite volume methods which are known to properly handle shocks and contact discontinuities however in general these schemes are known to be quite inaccurate for near steady states as the structure of their numerical truncation errors is generally not compatible with exact physical steady state conditions this difficulty can be overcome by using the so called well balanced schemes we describe a general strategy based on a local hydrostatic reconstruction that allows us to derive a well balanced scheme from any given numerical flux for the homogeneous problem whenever the initial solver satisfies some classical stability properties it yields a simple and fast well balanced scheme that preserves the nonnegativity of the water height and satisfies a semidiscrete entropy inequality

a family of stable numerical solvers for the shallow water equations with source terms abstract in this work we introduce a multiparametric family of stable and accurate numerical schemes for 1d shallow water equations these schemes are based upon the splitting of the discretization of the source term into centered and decentered parts these schemes are specifically designed to fulfill the enhanced consistency condition of bermudez and vazquez necessary to obtain accurate solutions when source terms arise our general family of schemes contains as particular cases the extensions already known of roe and van leer schemes and as new contributions extensions of steger warming vijayasundaram lax friedrichs and lax wendroff schemes with and without flux limiters we include some meaningful numerical tests which show the good stability and consistency properties of several of the new methods proposed we also include a linear stability analysis that sets natural sufficient conditions of stability for our general methods

a new existence theory for positive periodic solutions to functional differential equations abstract this paper deals with a new existence theory for positive periodic solutions to a kind of nonautonomous functional differential equation by employing the fixed point theorem in cones applying the general theorems established to several biomathematical models the paper improves some previous results and obtains some new results

dynamics of a class of nonautonomous semi ratio dependent predator prey systems with functional responses abstract in this paper we investigate the dynamics of a class of the so called semi ratio dependent predator prey interaction models with functional responses based on systems of nonautonomous differential equations with time dependent parameters the functional responses are classified into five types and typical examples of each type are provided then we establish sufficient criteria for the boundedness of solutions the permanence of system and the existence uniqueness and globally asymptotic stability of positive periodic solution and positive almost periodic solution some conclusive discussion is presented at the end of this paper

permanence of a delayed non autonomous gilpin ayala competition model abstract in this paper we consider a delayed non autonomous n species gilpin ayala competitive system which is more general and more realistic then classical lotka volterra competition model by means of ahmad and lazer s definitions of lower and upper averages of a function we give the average conditions for the permanence of the system it is shown that our result is the generalization of those of zhao et al j d zhao j f jiang a c lazer the permanence and global attractivity in a nonautonomous lotka volterra system nonlinear analysis real world applications 5 4 2004 265 276 our results also supplement the results of fan and wang m fan k wang global periodic solutions of a generalized n species gilpin ayala competition model computer and mathematics with applications 40 2000 1141 1151

global attractivity of an almost periodic n species nonlinear ecological competitive model abstract by using comparison theorem and constructing suitable lyapunov functional we study the following almost periodic nonlinear n species competitive lotka volterra model x i t x i t r i t j 1 n a i j t x j i j t j 1 n b i j t x j i j t i j t j 1 n c i j t x i i i t x j i j t a set of sufficient conditions is obtained for the existence and global attractivity of a unique positive almost periodic solution of the above model as applications some special competition models are studied again our new results improve and generalize former results examples and their simulations show the feasibility of our main results

positive periodic solution of a kind of nonlinear food chain system a nonlinear periodic food chain predator prey model is proposed in this paper which can be seen as the modification of the traditional lotka volterra food chain system sufficient conditions which guarantee the existence of the positive periodic solution of the system are obtained

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

automatic structures rational growth and geometrically finite hyperbolic groups we show that the set s mathfrak a g of equivalence classes of synchronously automatic structures on a geometrically finite hyperbolic groupg is dense in the product of the sets s mathfrak a p over all maximal parabolic subgroupsp the set bs mathfrak a g of equivalence classes of biautomatic structures ong is isomorphic to the product of the sets bs mathfrak a p over the cusps conjugacy classes of maximal parabolic subgroups ofg each maximal parabolicp is a virtually abelian group so s mathfrak a p and bs mathfrak a p were computed in ns1

boundary element free method befm and its application to two dimensional elasticity problems in this study we first discuss the moving least square approximation mls method in some cases the mls may form an ill conditioned system of equations so that the solution cannot be correctly obtained hence in this paper we propose an improved moving least square approximation imls method in the imls method the orthogonal function system with a weight function is used as the basis function the imls has higher computational efficiency and precision than the mls and will not lead to an ill conditioned system of equations combining the boundary integral equation bie method and the imls approximation method a direct meshless bie method the boundary element free method befm for two dimensional elasticity is presented compared to other meshless bie methods befm is a direct numerical method in which the basic unknown quantity is the real solution of the nodal variables and the boundary conditions can be applied easily hence it has higher computational precision for demonstration purpose selected numerical examples are given

positive periodic solutions of nonautonomous functional differential systems abstract considered is the periodic functional differential system with a parameter x t a t x t x t f t x t using the eigenvalue problems of completely continuous operators we establish some criteria on the existence of positive periodic solutions moreover we apply the results to a couple of population models and obtain sufficient conditions for the existence of positive periodic solutions which are compared with existing ones

periodic solutions for a non monotone family of delayed differential equations with applications to nicholson systems for a family of n dimensional periodic delay differential equations which encompasses a broad set of models used in structured population dynamics the existence of a positive periodic solution is obtained under very mild conditions the proof uses the schauder fixed point theorem and relies on the permanence of the system a general criterion for the existence of a positive periodic solution for nicholson s blowflies periodic systems with both distributed and discrete time varying delays is derived as a simple application of our main result generalizing the few existing results concerning multi dimensional nicholson models in the case of a nicholson system with discrete delays all multiples of the period the global attractivity of the positive periodic solution is further analyzed improving results in recent literature

permanence of a nonlinear prey competition model with delays abstract a nonlinear periodic predator prey model with m preys and n m predators and delays is studied which can be seen as the modification of the traditional lotka volterra prey competition model two sets of sufficient conditions which guarantee the permanence of the system are obtained one set is delay independent while the other set is delay dependent our results supplement those obtained by chen et al f d chen x d xie j l shi existence uniqueness and stability of positive periodic solution for a nonlinear prey competition model with delays journal of computational and applied mathematics 194 2 2006 368 387

a well balanced scheme for the numerical processing of source terms in hyperbolic equations in a variety of physical problems one encounters source terms that are balanced by internal forces and this balance supports multiple steady state solutions that are stable typical of these are gravity driven flows such as those described by the shallow water equations over a nonuniform ocean bottom 1 10 qquad h t hu x 0 text and hu t left hu 2 frac gh 2 2 right x ga x x h 0 many classic numerical schemes cannot maintain these steady solutions or achieve them in the long time limit with an acceptable level of accuracy because they do not preserve the proper balance between the source terms and internal forces we propose here a numerical scheme adapted to a scalar conservation law that preserves this balance and that can it is hoped be extended to more general hyperbolic systems the proof of convergence of this scheme toward the entropy solution is given and some numerical tests are reported

positive periodic solutions of functional differential equations abstract we consider the existence multiplicity and nonexistence of positive periodic solutions for the periodic equation x t a t g x x t b t f x t t where a b c r 0 are periodic 0 a t dt 0 0 b t dt 0 f g c 0 0 and f u 0 for u 0 g x is bounded t is a continuous periodic function define f 0 lim u 0 f u u f lim u f u u i0 number of zeros in the set f 0 f and i number of infinities in the set f 0 f we show that the equation has i0 or i positive periodic solution s for sufficiently large or small 0 respectively

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 and uniqueness of positive periodic solutions of functional differential equations abstract in this paper we consider the existence and uniqueness of positive periodic solution for the periodic equation y t a t y t h t f y t t by the eigenvalue problems of completely continuous operators and theory of concave or convex operators and its eigenvalue we establish some criteria for existence and uniqueness of positive periodic solution of above functional differential equations with parameter in particular the unique solution y t of the above equation depends continuously on the parameter finally as an application we obtain sufficient condition for the existence of positive periodic solutions of the nicholson blowflies model

diagonal riccati stability and applications abstract we consider the question of diagonal riccati stability for a pair of real matrices a b a necessary and sufficient condition for diagonal riccati stability is derived and applications of this to two distinct cases are presented we also describe some motivations for this question arising in the theory of generalised lotka volterra systems

positive periodic solutions of first order functional differential equations with parameter we prove the existence and multiplicity of positive t periodic solution s for t periodic equation x t h t x lb t f x t t t by krasnoselskii fixed point theorem where f x may be singular at x 0 our results improve some recent results in previous literature

on a delayed nonautonomous ratio dependent predator prey model with holling type functional response and diffusion abstract a two species periodic ratio dependent predator prey model with holling type functional response and diffusion is investigated three different sets of sufficient conditions one set is diffusive independent and the other two sets are diffusive dependent which ensure the permanence of the system and a set of sufficient condition which ensure the extinction of the predator species are obtained examples together with their numeric simulations show the feasibility of the main results

conjugacy growth series and languages in groups in this paper we introduce the geodesic conjugacy language and geodesic conjugacy growth series for a finitely generated group we study the effects of various group constructions on rationality of both the geodesic conjugacy growth series and spherical conjugacy growth series as well as on regularity of the geodesic conjugacy language and spherical conjugacy language in particular we show that regularity of the geodesic conjugacy language is preserved by the graph product construction and rationality of the geodesic conjugacy growth series is preserved by both direct and free products 2010 mathematics subject classification 20f65 20e45

coexistence states for periodic competitive kolmogorov systems abstract we prove the existence of positive periodic solutions for a class of nonautonomous competitive periodic kolmogorov systems which generalize the may leonard model a necessary and sufficient condition is also obtained

algorithms and geometry for graph products of groups recent work of gromov epstein cannon thurston and many others has generated strong interest in the geometric and algorithmic structure of finitely generated infinite groups see 16 17 and 14 many of these structures are preserved by taking graph products the graph product of groups not to be confused with the fundamental group of a graph of groups is a product mixing direct and free products whether the product between two groups in the graph product is free or direct is determined by a simplicial graph given a simplicial graph we say that two vertices are adjacent if they are joined by a single edge

higher order functional differential systems with parameter dependence abstract in this paper we consider a class of high order functional differential systems depending on a parameter by using the fixed point index theory we prove that there exists a positive number separating 0 into two disjoint subintervals 1 and 2 such that the system has at least two positive periodic solutions for 1 one positive periodic solution for and no positive periodic solution for 2 our results extend and improve some results in the literature as an application an example is given to demonstrate our main results

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

permanence and extinction for a nonlinear diffusive predator prey system abstract in this paper we consider a non autonomous predator prey system in a poor patchy environment under the assumption that the intrinsic growth rates of the species may be negative sufficient conditions are obtained for the permanence and extinction of the system considered

almost periodic dynamics of a delayed three level food chain model abstractthis paper is concerned with the dynamics of a three level food chain model with time delays by means of mawhin s continuation theorem of coincidence degree theory we investigate the existence of positive almost periodic solutions in a three level food chain model with time delays a set of sufficient conditions for the existence of at least one positive almost periodic solution of the model is obtained in addition the global asymptotical stability of the almost periodic solution of the above model is also studied finally two examples and simulations are also given to illustrate the main results in this paper

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

positive periodic solutions of infinite delay functional differential equations depending on a parameter in this paper we employ the upper and lower solutions method to study the existence of positive periodic solutions to a system of infinite delay equations with a email protected t a t x t email protected t x t

a well balanced element free galerkin method for the nonlinear shallow water equations abstract in this paper we consider the nonlinear shallow water equations over variable bottom topography in one dimension and propose a well balanced element free galerkin method for solving this system the proposed scheme has the features of being high order accurate for general solutions and exactly preserving the still water stationary solution the main ingredient to achieve the well balanced property is to use a special decomposition to the source term and discretize the source term as the flux term numerical tests are presented to illustrate the accuracy and validity of the proposed scheme

high order well balanced cdg fe methods for shallow water waves by a green naghdi model in this paper we consider a one dimensional fully nonlinear weakly dispersive green naghdi model for shallow water waves over variable bottom topographies such model describes a large spectrum of shallow water waves and it is thus of great importance to design accurate and robust numerical methods for solving it the governing equations contain mixed spatial and temporal derivatives of the unknowns they also have still water stationary solutions which should be preserved in stable numerical simulations in our numerical approach we first reformulate the green naghdi equations into balance laws coupled with an elliptic equation we then propose a family of high order numerical methods which discretize the balance laws with well balanced central discontinuous galerkin methods and the elliptic part with continuous finite element methods linear dispersion analysis for both the reformulated green naghdi system and versions of the proposed numerical scheme is performed when the bottom topography is flat numerical tests are presented to illustrate the accuracy and stability of the proposed schemes as well as the capability of the green naghdi model to describe a wide range of shallow water wave phenomena

positive periodic solutions of nonlinear functional differential equations we apply the generalized form of leggett williams fixed point theorem to prove that the following nonlinear functional differential equationx t a t x t f t x t has at least two positive t periodic solutions where a t is a t periodic function satisfying exp 0 ta u du 1 f t x t is a nonnegative function defined on rxbc where bc denotes the banach space of bounded continuous functions

dynamic of a non autonomous predator prey system with infinite delay and diffusion in the present paper a nonlinear non autonomous predator prey dispersion model with continuous delay is studied sufficient conditions which guarantee the existence of a periodic positive solution are obtained by using gaines and mawhin s continuation theorem of coincidence degree theory moreover globally asymptotically stability of the system is also obtained by means of a suitable lyapunov functional the applications show that these criteria are easily verified

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

periodicity in a nonlinear predator prey system on time scales with 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 nonlinear state dependent delays predator prey system on time scales