permanence and global attractivity of a delayed periodic logistic equation in this paper we consider the delayed periodic logistic equation n t n t a t b t np t t c t nq t t which describes the evolution of a single species sufficient conditions which guarantee the permanence and the globally attractivity of the system are obtained

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

on the existence and uniqueness of almost periodic solutions for delay logistic equations by using lyapunov functional the conditions of existence and uniqueness of almost periodic solutions for delay logistic equations are obtained

permanence of periodic holling type predator prey system with stage structure for prey abstract in this paper we study the permanence of the following periodic holling type predator prey system with stage structure for prey x 1 t a t x 2 t b t x 1 t d t x 1 2 t e t x 1 t p t x 1 t y t x 2 t c t x 1 t f t x 2 2 t y t y t g t h t x 1 t p t x 1 t q t y t sufficient and necessary condition which guarantee the predator and the prey species to be permanent is obtained some new results are obtained

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

stability of group relations under small hilbert schmidt perturbations abstract if matrices almost satisfying a group relation are close to matrices exactly satisfying the relation then we say that a group is matricially stable here almost and close are in terms of the hilbert schmidt norm using tracial 2 norm on i i 1 factors we similarly define i i 1 factor stability for groups our main result is that all 1 relator groups with non trivial center are i i 1 factor stable many of them are also matricially stable and rfd for amenable groups we give a complete characterization of matricial stability in terms of the following approximation property for characters each character must be a pointwise limit of traces of finite dimensional representations this allows us to prove matricial stability for the discrete heisenberg group h 3 and for all virtually abelian groups for non amenable groups the same approximation property is a necessary condition for being matricially stable we study this approximation property and show that rf groups with character rigidity have it

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

orbit inequivalent actions for groups containing a copy of mathbb f _ 2 we prove that if a countable group contains a copy of mathbb f 2 then it admits uncountably many non orbit equivalent actions

bifurcation analysis of modified leslie gower predator prey model with michaelis menten type prey harvesting abstract in the present paper we discuss bifurcation analysis of a modified leslie gower prey predator model in the presence of nonlinear harvesting in prey we give a detailed mathematical analysis of the model to describe some significant results that may arise from the interaction of biological resources the model displays a complex dynamics in the prey predator plane the permanence stability and bifurcation saddle node bifurcation transcritical hopf andronov and bogdanov takens of this model are discussed we have analyzed the effect of prey harvesting and growth rate of predator on the proposed model by considering them as bifurcation parameters as they are important from the ecological point of view the local existence and stability of the limit cycle emerging through hopf bifurcation is given the emergence of homoclinic loops has been shown through simulation when the limit cycle arising though hopf bifurcation collides with a saddle point this work reflects that the feasible upper bound of the rate of harvesting for the coexistence of the species can be guaranteed numerical simulations using matlab are carried out to demonstrate the results obtained

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

detecting large groups let g be a finitely presented group and let p be a prime then g is large respectively p large if some normal subgroup with finite index respectively index a power of p admits a non abelian free quotient this paper provides a variety of new methods for detecting whether g is large or p large these relate to the group s profinite and pro p completions to its first l2 betti number and to the existence of certain finite index subgroups with rapid descent the paper draws on new topological and geometric techniques together with a result on error correcting codes

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

constraint metric approximations and equations in groups abstract we introduce notions of a constraint metric approximation and of a constraint stability of a metric approximation this is done in the language of group equations with coefficients we give an example of a group which is not constraintly sofic in building it we find a sofic representation of free group with trivial commutant among extreme points of the convex structure on the space of sofic representations we consider the centralizer equation in permutations as an instance of this new general setting we characterize permutations p s k whose centralizer is stable in permutations with respect to the normalized hamming distance that is a permutation which almost centralizes p is near a centralizing permutation this answers a question of gorenstein sandler mills 1962

persistence and global stability for nonautonomous predator prey system with diffusion and time delay abstract in this paper a nonautonomous predator prey model with diffusion and continuous time delay is studied where all parameters are time dependent the system which is composed of two lotka volterra patches has two species one can diffuse between two patches but the other is confined to one patch and cannot diffuse it is proved that the system is uniformly persistent under appropriate conditions furthermore sufficient conditions are established for global stability of the system

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

a converse to dye s theorem every non amenable countable group induces orbit inequivalent ergodic equivalence relations on standard borel probability spaces not every free ergodic measure preserving action of f 2 on a standard borel probability space is orbit equivalent to an action of a countable group on an inverse limit of finite spaces there is a treeable non hyperfinite borel equivalence relation which is not universal for treeable in the b ordering

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

expansion in sl d z q z q arbitrary let s be a fixed finite symmetric subset of sl d z and assume that it generates a zariski dense subgroup g we show that the cayley graphs of q g with respect to the generating set q s form a family of expanders where q is the projection map z z q z

bibo stabilization for system with multiple mixed delays and nonlinear perturbations the problem of bibo stabilization for multiple mixed time delayed control system with nonlinear perturbations is studied in this paper the new delay dependent bibo stabilization criteria are derived by the lyapunov functional and given in terms of existence of a positive definite solution to an auxiliary algebraic riccati matrix equation the robust quadratic stability for such system is also discussed the work of this paper will extend the results of some references

the dynamic behavior of n species cooperation system with continuous time delays and feedback controls in this paper we consider a n species cooperation system with continuous time delays and feedback controls for general nonautonomous case by using differential inequality theory and constructing a suitable lyapunov functional we obtain sufficient conditions which guarantee the permanence and the global attractivity of the system for the periodic case we obtain sufficient conditions which guarantee the existence uniqueness and stability of a positive periodic solution for the almost periodic case by using the razumikhin type theorem we obtain the sufficient conditions which guarantee the existence of a positive almost periodic solution of the system

stability for product groups and property τ abstract we study the notion of permutation stability or p stability for countable groups our main result provides a wide class of non amenable product groups which are not p stable this class includes the product group whenever admits a non abelian free quotient and admits an infinite cyclic quotient in particular we obtain that the groups f m z d and f m f n are not p stable for any integers m n 2 and d 1 this implies that p stability is not closed under the direct product construction which answers a question of becker lubotzky and thom the proof of our main result relies on a construction of asymptotic homomorphisms from to finite symmetric groups starting from sequences of finite index subgroups in and with and without property our method is sufficiently robust to show that the groups covered are not even flexibly p stable thus giving the first such non amenable residually finite examples

on permanence and global stability in a general gilpin ayala competition predator prey discrete system abstract in this paper we propose a discrete multispecies general gilpin ayala competition predator prey model by using new difference inequality and developing the analysis technique of chen and zhou y chen z zhou stable periodic solution of a discrete periodic lotka volterra competition system j math anal appl 277 2003 358 366 sufficient conditions are established for the permanence and the global stability an example shows the feasibility of our results

on the chern gauss bonnet integral for conformal metrics on r4 where m is the euler number ofm later huber hu extended this inequality to metrics with much weaker regularity more importantly he proved that such a surface m is conformally equivalent to a closed surface with finitely many punctures the deficit in formula 1 1 has an interpretation as an isoperimetric constant on a complete and open surface with gaussian curvature absolutely integrable one may represent each end conformally as r2 k for some compact set k we consider the isoperimetric ratio

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

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

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

on the nonlinear stability of nonautonomous binary systems abstract nonlinear nonautonomous binary systems of o d es are considered in the framework of the liapunov direct method stability instability criteria are obtained via a sharp liapunov function cfr sect 1 applications either to the celebrated equation of nonlinear mechanics x p t x x x q t x x x 0 in particular to the hill mathieu hill and nonautonomous duffing equations or to the nonautonomous lotka volterra system are furnished

stability and bifurcation analysis of a delayed predator prey model of prey dispersal in two patch environments abstract in this paper a class of delayed predator prey model of prey dispersal in two patch environments is considered by analyzing the associated characteristic transcendental equation its linear stability is investigated and hopf bifurcation is demonstrated some explicit formulae determining the stability and the direction of the hopf bifurcation periodic solutions bifurcating from hopf bifurcations are obtained by using the normal form theory and center manifold theory some numerical simulation for justifying the theoretical analysis are also provided finally biological explanations and main conclusions are given

symmetric groups and expander graphs we construct explicit generating sets sn and tilde s n of the alternating and the symmetric groups which turn the cayley graphs mathcal c text alt n s n and mathcal c text sym n tilde s n into a family of bounded degree expanders for all n

the compact and crank nicolson adi schemes for two dimensional semilinear multidelay parabolic equations this paper deals with numerical solutions of initial boundary value problems of the two dimensional semilinear multidelay parabolic equations two types of alternating direction implicit adi schemes are suggested the unique solvability convergence and unconditional stability of the schemes are analyzed and hence the corresponding criteria are established especially by using the discrete energy method it is proven that the compact adi scheme can attain second order accuracy in time and fourth order accuracy in space and the crank nicolson adi scheme has second order accuracy in both time and space numerical experiments are performed to verify the efficiency and accuracy of the both schemes

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

periodic solution of a lotka volterra predator prey model with dispersion and time delays a periodic lotka volterra predator prey model with dispersion and time delays is investigated by using gaines and mawhin s continuation theorem of coincidence degree theory and by means of a suitable lyapunov functional a set of easily verifiable sufficient conditions are derived for the existence uniqueness and global stability of positive periodic solutions of the system sufficient conditions are also established for the uniform persistence of the system numerical simulations are presented to illustrate our main results

hyperlinearity essentially free actions and l2 invariants the sofic property we prove that connes embedding conjecture holds for the von neumann algebras of sofic groups that is sofic groups are hyperlinear hence we provide some new examples of hyperlinearity we also show that the determinant conjecture holds for sofic groups as well we introduce the notion of essentially free actions and amenable actions and study their properties

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 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

existence of positive periodic solution for nonautonomous predator prey system with diffusion and time delay a two species nonautonomous predator prey system with time delay and diffusion is investigated a sufficient condition of the existence of positive periodic solution is established for the system by using the continuation theorem of coincidence degree theory

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

stability of the boundary solution of a nonautonomous predator prey system with the beddington deangelis functional response abstract the dynamics of a nonautonomous predator prey system with the beddington deangelis functional response is studied from the perspective of extinction of the predator with the help of a fluctuation lemma we obtain a set of new sufficient conditions on the global asymptotic stability of the boundary solution which means the extinction of the predator the result not only improves but also complements some existing ones moreover the result indicates that the effect of the parameters is accumulative rather than pointwise

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

uniformly strong persistence of an nonlinear asymptotically periodic multispecies competition predator prey system with general functional response in this paper an nonlinear asymptotically periodic multispecies competition predator prey system with general functional response is studied and we obtain sufficient conditions for the uniformly strong persistence of the system in particular our result extend the result in f y wei k wang uniform persistence of asymptotically periodic multispecies competition predator prey systems with holling iii type of functional response appl math comput in press

permanence for an integrodifferential model of mutualism abstract sufficient conditions are obtained for the permanence of the following integrodifferential model of mutualism d n 1 t d t r 1 t n 1 t k 1 t 1 t 0 j 2 s n 2 t s d s 1 0 j 2 s n 2 t s d s n 1 t 1 t d n 2 t d t r 2 t n 2 t k 2 t 2 t 0 j 1 s n 1 t s d s 1 0 j 1 s n 1 t s d s n 2 t 2 t where r i k i i and i i 1 2 are continuous functions bounded above and below by positive constants i k i i 1 2 j i c 0 0 and 0 j i s d s 1 i 1 2

almost commuting permutations are near commuting permutations abstract we prove that the commutator is stable in permutations endowed with the hamming distance that is two permutations that almost commute are near two commuting permutations our result extends to k tuples of almost commuting permutations for any given k and allows restrictions for instance to even permutations

group stability and property t abstract in recent years there has been a considerable amount of interest in the stability of a finitely generated group with respect to a sequence of groups g n n 1 equipped with bi invariant metrics d n n 1 we consider the case g n u n resp g n sym n equipped with the normalized hilbert schmidt metric d n hs resp the normalized hamming metric d n hamming our main result is that if is infinite hyperlinear resp sofic and has property t then it is not stable with respect to u n d n hs resp sym n d n hamming this answers a question of hadwin and shulman regarding the stability of sl 3 z we also deduce that the mapping class group mcg g g 3 and aut f n n 3 are not stable with respect to sym n d n hamming our main result exhibits a difference between stability with respect to the normalized hilbert schmidt metric on u n and the unnormalized p schatten metrics since many groups with property t are stable with respect to the latter metrics as shown by de chiffre glebsky lubotzky thom and lubotzky oppenheim we suggest a more flexible notion of stability that may repair this deficiency of stability with respect to u n d n hs and sym n d n hamming

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

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

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

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

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

on a nonautonomous predator prey model with prey dispersal we propose a nonautonomous dispersal predator prey model with functional response and delay where we assume the model of patches with a barrier only as far as the prey population is concerned whereas the predator population has no barriers between patches sufficient condition to guarantee the predator and prey species to be permanent is obtained examples show the feasibility of our result

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

existence and uniqueness of positive periodic solutions for a neutral logarithmic population model in this paper by using an abstract continuous theorem of k set contractive operator the criteria is established for the existence global attractivity of positive periodic solution of a neutral delay logarithmic population model with multiple delays the result improve the known ones in s p lu w g ge existence of positive periodic solutions for neutral logarithmic population model with multiple delays j comput appl math 166 2 2004 371 383

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

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