holder continuity of the rotation number for quasi periodic co cycles in sl 2 mathbb r we prove two results on the rotation number of the skew product system omega a theta y in mathbb t d times mathbb r 2 mapsto theta omega a theta y in mathbb t d times mathbb r 2 where is diophantine and a theta in sl 2 mathbb r is homotopic to the identity on the one hand we prove that this function has the behavior of a frac 1 2 holder function on the other we show that the length of the gaps has a sub exponential estimate which depends on its label given by the gap labeling theorem we give also an estimate of the complement of the spectrum these results are obtained by studying the reducibility of the quasi periodic co cycle a

almost reducibility and non perturbative reducibility of quasi periodic linear systems in this paper we prove that a quasi periodic linear differential equation in sl 2 with two frequencies 1 is almost reducible provided that the coefficients are analytic and close to a constant in the case that is diophantine we get the non perturbative reducibility we also obtain the reducibility and the rotations reducibility for an arbitrary irrational under some assumption on the rotation number and give some applications for schrodinger operators our proof is a generalized kam type iteration adapted to all irrational

stable equilibrium of systems of generalized volterra type abstract in this paper the global stability of systems of the generalized volterra type dx i dt x i j 1 n a ij x j b i i 1 n is investigated it is shown that a stable equilibrium point of 1 must be a solution of corresponding linear complementarity problem further when the structure of 1 is restricted the known stability condition is proved to be necessary and sufficient for the existence of a stable equilibrium point for every b rn some structures satisfying these restrictions are given

asymptotic behavior of a food limited lotka volterra mutualism model with markovian switching and levy jumps abstract in this paper we investigate a food limited lotka volterra mutualism model with markovian switching and levy jumps we present the analysis and the criteria of the asymptotic behavior for this perturbed model via lyapunov functions our results show that both colored noise and levy noise have important effects on the survival and extinction of the species

boundedness and exponential stability for nonautonomous rcnns with distributed delays some sufficient conditions for the ultimate boundedness and global exponential stability of a class of nonautonomous reaction diffusion cellular neural networks rcnns with distributed delays are obtained by means of the lyapunov functional method without assuming that the activation functions f i j l are bounded the results extend and improve the earlier publications

stability analysis for lotka volterra systems based on an algorithm of real root isolation based on the theory of monotone flows of solutions of systems of differential equations the routh hurwitz theorem and a real root isolation algorithm of multivariate polynomials are applied to a class of lotka volterra diffusion systems an algorithm to determine the location of equilibria and the stability of the nonlinear dynamics systems is implemented in maple

uniform persistence for a two species ratio dependent predator prey system with diffusion and variable time delays abstract a two species ratio dependent predator prey diffusion model with variable time delays is investigated by constructing some suitable lyapunov functionals and utilizing some analysis techniques we obtain the permanence of this system our results generalize and improve the results of 10 11

competition in an n vessel gradostat a mathematical model of the exploitative competition between two microbial species in a general multivessel gradostat is considered sufficient conditions for the two species to coexist in the grad

permanence of dispersal population model with time delays permanence of a dispersal single species population model is considered where environment is partitioned into several patches and the species requires some time to disperse between the patches the model is described by delay differential equations the existence of food rich patches and small dispersions among the patches are proved to be sufficient to ensure partial permanence of the model it is also shown that partial permanence ensures permanence if each food poor patch is connected to at least one food rich patch and if each pair in food rich patches is connected furthermore it is proved that partial persistence is ensured even under large dispersion among food rich patches if the dispersion time is relatively small

on the asymptotic behavior of a class of deterministic models of cooperating species in this paper the global behavior of solutions of a class of ordinary differential equations modeling n cooperating biological species is determined the class of systems includes the classical lot

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

persistence in a periodic competitor competitor mutualist diffusion system in this paper we investigate the existence and the asymptotic behavior of periodic solutions for a periodic reaction diffusion system of a competitor competitor mutualist model under dirichlet boundary conditions we shall prove that under certain conditions this system is persistent and under some other conditions it exhibits extinction or more exactly the species of mutualist extincts

permanence and global stability for a two species cooperative system with time delays in a two patch environment abstract a two species nonautonomous delayed system is considered the system models two population dispersal between two patches in a heterogeneous environment it is shown that the system is permanent under some appropriate conditions and sufficient conditions are established for global stability of the system

periodic solutions and stationary distribution of mutualism models in random environments abstract this paper is concerned with mutualism models in random environments for the periodic mutualism model disturbed by white noise using has minskii theory of periodic solution we show that this model admits a nontrivial positive periodic solution then sufficient conditions for the existence and global attractivity of the boundary periodic solutions are established for the mutualism model disturbed by both white noise and telephone noise sufficient conditions for positive recurrence and the existence of ergodic stationary distribution of the solution are established finally examples are introduced to illustrate the results developed

perturbation technique for non self adjoint systems with repeated eigenvalues the reanalysis of non self adjoint systems is computationally very expensive in the design of structural dynamics an effective even if approximate evaluation of the eigensolutions of a modified system is valuable to designers in a paper by meirovitch and ryland meirovitch l and ryland g a perturbation technique for gyroscopic systems with small internal and external damping journal of sound and vibration vol 100 no 3 1985 pp 393408 a perturbation technique was used to derive the perturhed solutions of a damped gyroscopic system with distinct eigenvalues that approach is extended to the case of systems with repeated eigenvalues a numerical example is presented to verify the present method and satisfactory results are observed

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

asymptotic behavior of solutions for a lotka volterra mutualism reaction diffusion system with time delays this paper is to investigate the asymptotic behavior of solutions for a time delayed lotka volterra n species mutualism reaction diffusion system with homogeneous neumann boundary condition it is shown under a simple condition on the reaction rates that the system has a unique bounded time dependent solution and a unique constant positive steady state solution and for any nontrivial nonnegative initial function the corresponding time dependent solution converges to the constant positive steady state solution as time tends to infinity this convergence result implies that the trivial steady state solution and all forms of semitrivial steady state solutions are unstable and moreover the system has no nonconstant positive steady state solution a condition ensuring the convergence of the time dependent solution to one of nonnegative semitrivial steady state solutions is also given

the rotation number for almost periodic potentials we define and analyze the rotation number for the almost periodic schrodinger operatorl d2 dx2 q x we use the rotation number to discuss i the spectrum ofl ii its relation to the korteweg de vries equation

global stability and predator dynamics in a model of prey dispersal in a patchy environment on considere un systeme d equations differentielles autonomes non lineaires on determine l equilibre de ce systeme

cooperative systems of differential equations with concave nonlinearities on considere le systeme dynamique discret engendre par une application monotone concave t r n r n on etudie ensuite des systemes d equations differentielles cooperatifs periodiques x f t x a non linearites concaves

competing subcommunities of mutualist and a generalized kamke theorem a model of a biological community of species is considered the community consists of two competing subcommunities each of which has the property that each pair of species of the subcommunity interact in a mutually beneficial or noninterfering manner sufficient conditions are given that the two subcommunities can coexist the coexistence state being a stable equilibrium the domains of attraction of stable equilibria are considered the sharpest results are for the special case of lotka volterra systems mathematically the fundamental tool is a generalized kamke theorem

examples of discontinuity of lyapunov exponent in smooth quasiperiodic cocycles we study the regularity of the lyapunov exponent for quasiperiodic cocycles t a where t is an irrational rotation x x 2 on s1 and a cl s1 sl 2 r 0 l for any fixed l 0 1 2 and any fixed of bounded type we construct dl cl s1 sl 2 r such that the lyapunov exponent is not continuous at dl in cl topology we also construct such examples in a smaller schrodinger class

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 asymptotic stability of reaction diffusion cohen grossberg neural networks with continuously distributed delays this paper is concerned with the global asymptotic stability of a class of reaction diffusion cohen grossberg neural networks with continuously distributed delays under some suitable assumptions and using a matrix decomposition method we apply the linear matrix inequality lmi method to propose some new sufficient stability conditions for the reaction diffusion cohen grossberg neural networks with continuously distributed delays the obtained results are easy to check and improve upon the existing stability results some remarks are given to show the advantages of the obtained results over the previous results an example is also given to demonstrate the effectiveness of the obtained results

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

optimal harvesting of a stochastic mutualism model with levy jumps in this letter a stochastic mutualism model with levy jumps and harvesting is considered under some simple assumptions sufficient and necessary criteria for the existence of optimal harvesting policy are established the optimal harvesting effort and the maximum of sustainable yield are also obtained the effects of random noises on the optimal harvesting of the model are discussed and some numerical simulations are introduced to illustrate the main results

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

sharp holder continuity of the lyapunov exponent of finitely differentiable quasi periodic cocycles we show that if the base frequency is diophantine then the lyapunov exponent of a c k quasi periodic sl 2 mathbb r cocycle is 1 2 holder continuous in the almost reducible regime as a consequence we show that if the frequency is diophantine and the potential is small then the integrated density of states of the corresponding quasi periodic schrodinger operator is 1 2 holder continuous

universal perturbation technique for reanalysis of non self adjoint systems a novel matrix perturbation technique for modal dynamic reanalysis of non self adjoint systems is presented this technique is established first by performing complex eigensubspace condensation and orthogonal decomposition procedure the lower order perturbations of eigensolutions i e complex eigenvalues complex left and right eigenvectors are obtained by solving two reduced eigenvalue problems the higher order perturbations of eigensolutions are then derived by implementing the successive approximation process the proposed technique is a kind of universal dynamic reanalysis method because it is universally applicable to systems with all of the three cases distinct repeated and closely spaced eigenvalues illustrative examples are given to verify the present method and satisfactory results are observed

analysis of a stochastic autonomous mutualism model abstract an autonomous lotka volterra mutualism system with random perturbations is investigated under some simple conditions it is shown that there is a decreasing sequence k which has the property that if 1 1 then all the populations go to extinction i e lim t x i t 0 1 i n if k 1 k 1 then lim t x j t 0 j k 1 n whilst the remaining k populations are stable in the mean i e lim t t 1 0 t x i s d s a positive constant i 1 k if n 1 then all the species are stable in the mean sufficient conditions for stochastic permanence and global asymptotic stability are also established

the effect of dispersal on permanence in a predator prey population growth model abstract in this paper we consider a periodic predator prey system where the prey can disperse between one patch with a low level of food and without predation and one patch with a higher level of food but with predation we assume a volterra within patch dynamic under the assumption that the average of dispersal rate from patch 1 to patch 2 is less than that of the intrinsic growth rate of prey in patch 1 we provide a sufficient and necessary condition to guarantee the prey and predator species to be permanent by using the main techniques in 1

absolutely continuous spectrum of multifrequency quasiperiodic schrodinger operator abstract in this paper we prove that for any d frequency analytic quasiperiodic schrodinger operator if the frequency is weak liouvillean and the potential is small enough then the corresponding operator has absolutely continuous spectrum moreover in the case d 2 we even establish the existence of ac spectrum under small potential and some super liouvillean frequency and this result is optimal due to a recent counterexample of avila and jitomirskaya 6

the effect of diffusion on the time varying logistic population growth abstract in this paper we consider the effect of diffusion on the species that live in changing patches environment different from the former studies 1 4 we pay attention to the more important situation in conservation biology that species live in a weak patches environment in the sense that species in some of the isolated patches will be extinct without the contribution from other patches we obtain an interesting result the identical species can persist for some diffusion rates and can also vanish for another set of restriction on diffusion rates

floquet solutions for the 1 dimensional quasi periodic schrodinger equation we show that the 1 dimensional schrodinger equation with a quasiperiodic potential which is analytic on its hull admits a floquet representation for almost every energye in the upper part of the spectrum we prove that the upper part of the spectrum is purely absolutely continuous and that for a generic potential it is a cantor set we also show that for a small potential these results extend to the whole spectrum

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

existence of stable equilibrium point for dynamical systems of volterra type this paper presents sufficient conditions for the existence of a nonnegative and stable equilibrium point of a dynamical system of volterra type 1 ddt xi t xi t fi x1 t xn t qi i 1 n for every q q1 qn t rn results of a nonlinear complementarity problem are applied to obtain the conditions system 1 has a nonnegative and stable equilibrium point if i f x f1 x fn x t is a continuous and differentiable m function and it satisfies a certain surjectivity property or ii f x is continuous and strongly monotone on r 0n

on the existence and uniqueness of connecting orbits the question of existence and uniqueness of orbits connecting two critical points of a vector field arises in ordinary and partial differential equations 11 2 5 using monotonicity and stable manifold theory we prove an n dimensional result which is the same as that of conlon 2 except we replace his c2 vector field with a c vector field and we weaken his positivity assumption on the off diagonal terms of the jacobian of the vector field conlon s result is a generalization of a 2 dimensional result of conley and smoller l

mathematical models of population interactions with dispersal ii differential survival in a change of habitat abstract the paper considers a model of dispersing populations in the form of a system of nonlinear ordinary differential equations dispersal pressure is density dependent and a parameter measures the barrier strength the model also incorporates a transition probability to allow for a risk in changing habitats for the two dimensional case the region in parameter space for existence of a stable equilibrium solution is exactly determined bounded in part by a branch of a hyperbola for the n dimensional case similar but less complete results are obtained

sharp phase transitions for the almost mathieu operator it is known that the spectral type of the almost mathieu operator amo depends in a fundamental way on both the strength of the coupling constant and the arithmetic properties of the frequency we study the competition between those factors and locate the point where the phase transition from singular continuous spectrum to pure point spectrum takes place which solves jitomirskaya s conjecture together with a previous work by avila this gives the sharp description of phase transitions for the amo for the a e phase

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

permanence for a class of periodic time dependent competitive system with delays and dispersal in a patchy environment in this paper we study m species time delayed competitive lotka volterra type dispersal system with periodic coefficients in n patches by utilizing analytic method sufficient and realistic conditions on permanence and the existence of periodic solution are established the theoretical results are confirmed by a special example and numerical simulations

three limit cycles for a three dimensional lotka volterra competitive system with a heteroclinic cycle abstract three limit cycles are constructed for a three dimensional lotka volterra competitive system with a heteroclinic cycle this gives a partial answer to a problem proposed by hofbauer and so in 1

permanence and extinction in logistic and lotka volterra systems with diffusion abstract 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 differing from former studies our discussion includes the important situation in conservation biology in which species live in a weak patchy environment in the sense that species will become extinct in some of the isolated patches for the single population model we show that identical species can persist for some diffusion rates and can also vanish for another set of restrictions on the diffusion rates although the single endangered species will vanish in some isolated patches without contributions from other patches furthermore we consider the existence uniqueness and global stability of the positive periodic solution for prey predator systems we can make both the prey and the predator species permanent by choosing the diffusion rates appropriately even if the prey species has a negative intrinsic growth rate in some patches moreover we introduce an exotic competitive species y into the habitat occupied by the native species x competitive permanence and competitive exclusion both are considered the implications of these results are significant for the conservation of endangered species

oscillation of a class of partial functional population model abstract this paper is concerned with the oscillation of a class of partial functional population model and some sufficient conditions for all positive solutions of the model to oscillate about the positive equilibrium are obtained the approach is based on the upper and lower solution method of the partial functional differential equations and the oscillation theory of the functional differential equation moreover some numerical simulations are also given to illustrate our 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

holder continuity of the integrated density of states for quasi periodic schrodinger equations and averages of shifts of subharmonic functions in this paper we consider various regularity results for discrete quasiperiodic schr6dinger equations n l pn 1 v 9 nw on eon with analytic potential v we prove that on intervals of positivity for the lyapunov exponent the integrated density of states is holder continuous in the energy provided w has a typical continued fraction expansion the proof is based on certain sharp large deviation theorems for the norms of the monodromy matrices and the avalanche principle the latter refers to a mechanism that allows us to write the norm of a monodromy matrix as the product of the norms of many short blocks in the multi frequency case the integrated density of states is shown to have a modulus of continuity of the form exp log tl for some 0 a 1 but currently we do not obtain holder continuity in the case of more than one frequency we also present a mechanism for proving the positivity of the lyapunov exponent for large disorders for a general class of equations the only requirement for this approach is some weak form of a large deviation theorem for the lyapunov exponents in particular we obtain an independent proof of the herman sorets spencer theorem in the multi frequency case the approach in this paper is related to the recent nonperturbative proof of anderson localization in the quasi periodic case by j bourgain and m goldstein

global theory of one frequency schrodinger operators we study schrodinger operators with a one frequency analytic potential focusing on the transition between the two distinct local regimes characteristic respectively of large and small potentials from the dynamical point of view the transition signals the emergence of non uniform hyperbolicity so the dependence of the lyapunov exponent with respect to parameters plays a central role in the analysis though often ill behaved by conventional measures we show that the lyapunov exponent is in fact remarkably regular in a stratified sense which we define the irregularity comes from the matching of nice analytic or smooth functions along sets with complicated geometry this result allows us to establish that the critical set for the transition lies within countably many codimension one subvarieties of the infinite dimensional parameter space a more refined renormalization based analysis shows that the critical set is rather thin within those subvarieties and allows us to conclude that a typical potential has no critical energies such acritical potentials also form an open set and have several interesting properties only finitely many phase transitions may happen but never at any specific point in the spectrum and the lyapunov exponent is minorated in the region of the spectrum where it is positive on the other hand we do show that the number of phase transitions can be arbitrarily large

a perturbation technique for gyroscopic systems with small internal and external damping abstract the response of linear damped gyroscopic systems can be obtained by means of techniques of linear systems theory which involves the computation of the transition matrix the response is in terms of complex quantities which is likely to cause computational difficulties as the order of the system increases in the absence of damping it is possible to derive the response of a linear gyroscopic system with relative ease by working with real quantities alone when damping is small one can use a perturbation approach to produce the response by regarding the undamped gyroscopic system as the unperturbed system in a previous paper a perturbation analysis was used to derive the response of a gyroscopic system with small internal damping this paper extends the approach to the case of external damping which is characterized not only by symmetric coefficients multiplying velocities but also by skew symmetric coefficients multiplying displacements where the latter terms are known as circulatory a numerical example is presented

derivatives of complex eigenvectors with distinct and repeated eigenvalues in this paper we investigate the computation of the first order derivatives of complex eigenvectors for general non defective eigensystems a new normalization condition is proposed with which we can compute unique first order derivatives of arbitrary differentiable eigenvectors of systems with distinct and repeated eigenvalues we also present an efficient algorithm to compute the particular solutions to the governing equations of the first order derivatives of eigenvectors finally numerical examples are included to demonstrate the validity of the proposed method copyright 2007 john wiley sons ltd

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 stability in generalized lotka volterra diffusion systems abstract this paper analyzes the existence conditions of a nonnegative global stable equilibrium point in generalized lotka volterra systems with diffusion for a patchtype environment applying the extended stability theory of lasalle and complementarity theorem several structures of patches with a globally stable equilibrium are derived it is shown that diffusion cannot be destabilizing for systems with such structures

a comprehensive review of stability analysis of continuous time recurrent neural networks stability problems of continuous time recurrent neural networks have been extensively studied and many papers have been published in the literature the purpose of this paper is to provide a comprehensive review of the research on stability of continuous time recurrent neural networks including hopfield neural networks cohen grossberg neural networks and related models since time delay is inevitable in practice stability results of recurrent neural networks with different classes of time delays are reviewed in detail for the case of delay dependent stability the results on how to deal with the constant variable delay in recurrent neural networks are summarized the relationship among stability results in different forms such as algebraic inequality forms m matrix forms linear matrix inequality forms and lyapunov diagonal stability forms is discussed and compared some necessary and sufficient stability conditions for recurrent neural networks without time delays are also discussed concluding remarks and future directions of stability analysis of recurrent neural networks are given

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

derivatives of eigenvalues and eigenvectors of a general complex matrix a survey of methods for sensitivity analysis of the algebraic eigenvalue problem for non hermitian matrices is presented in addition a modification of one method based on a better normalizing condition is proposed methods are classified as direct or adjoint and are evaluated for efficiency operation counts are presented in terms of matrix size number of design variables and number of eigenvalues and eigenvectors of interest the effect of the sparsity of the matrix and its derivatives is also considered and typical solution times are given general guidelines are established for the selection of the most efficient method

two limit cycles in three dimensional lotka volterra systems abstract among the six classes of zeeman s classification for three dimensional lotka volterra competitive systems with limit cycles besides the heteroclinic cycle case case 27 we construct in three cases without heteroclinic cycle cases 26 28 29 two limit cycles our construction gives a partial answer to hofbauer and so s problem to these systems

uniform positivity and continuity of lyapunov exponents for a class of c 2 quasiperiodic schrodinger cocycles abstract we show that for a class of c 2 quasiperiodic potentials and for any fixed diophantine frequency the lyapunov exponent of the corresponding schrodinger cocycles as a function of energies are uniformly positive and weakly holder continuous as a corollary we obtain that the corresponding integrated density of states is weakly holder continuous as well our approach is of purely dynamical systems which depends on a detailed analysis of asymptotic stable and unstable directions we also apply it to more general sl 2 r cocycles which in turn can be applied to get uniform positivity and continuity of lyapunov exponents around unique nondegenerate extremal points of any smooth potential and to a certain class of c 2 szeg cocycles

continuity of the lyapunov exponent for quasiperiodic operators with analytic potential we study regularity properties of the lyapunov exponent l of one frequency quasiperiodic operators with analytic potential under no assumptions on the diophantine class of the frequency we prove joint continuity of l in frequency and energy at every irrational frequency

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

holder continuity of absolutely continuous spectral measure for multi frequency schrodinger operators abstract we establish sharp results on the modulus of continuity of the distribution of the spectral measure for multi frequency schrodinger operators with diphantine frequencies and small analytic potentials

on the persistence of a nonautonomous n species lotka volterra cooperative system in this paper a special nonautonomous n species lotka volterra cooperative system is studied sufficient conditions for the uniform strong persistence uniform weak average persistence and uniform strong average persistence of population are obtained

embedding of analytic quasi periodic cocycles into analytic quasi periodic linear systems and its applications in this paper we prove that any analytic quasi periodic cocycle close to constant is the poincare map of an analytic quasi periodic linear system close to constant which bridges both methods and results in quasi periodic linear systems and cocycles we also show that the almost reducibility of an analytic quasi periodic linear system is equivalent to the almost reducibility of its corresponding poincare cocycle by the local embedding theorem and the equivalence we transfer the recent local almost reducibility results of quasi periodic linear systems hou and you in invent math 190 209 260 2012 to quasi periodic cocycles and the global reducibility results of quasi periodic cocycles avila in almost reducibility and absolute continuity 2010 avila et al in geom funct anal 21 1001 1019 2011 to quasi periodic linear systems finally we give a positive answer to a question of avila et al geom funct anal 21 1001 1019 2011 and use it to study point spectrum of long range quasi periodic operator with liouvillean frequency the embedding also holds for some nonlinear systems