convergence to nonlinear diffusion waves for solutions of a system of hyperbolic conservation laws with damping we consider a model of hyperbolic conservation laws with damping and show that the solutions tend to those of a nonlinear parabolic equation time asymptotically the hyperbolic model may be viewed as isentropic euler equations with friction term added to the momentum equation to model gas flow through a porous media in this case our result justifies darcy s law time asymptotically our model may also be viewed as an elastic model with damping

boundary layers for the navier stokes equations of compressible fluids the global unique solvability is proved for the navier stokes equations of compressible fluids for the one dimensional spiral flows between two circular cylinders the zero shear viscosity limit 0 is justified the value o 0 1 2 is established for the boundary layer thickness

approximate controllability of fractional stochastic differential equations driven by mixed fractional brownian motion via resolvent operators abstractin this manuscript we investigate the approximate controllability of a class of fractional stochastic differential equations driven by mixed fractional brownian motion in hilbert space with hurst parameter h 12 1 the main results are obtained by employing fractional calculus analytic resolvent operators and with the help of schaefer s fixed point theorem under the assumption that the corresponding linear system is approximately controllable finally in order to validate the obtained theoretical results an illustrative example is provided

asymptotic behavior of solution to nonlinear evolution equations with damping in this paper we consider the global existence and the asymptotic behavior of solutions to the cauchy problem for the following nonlinear evolution equations with ellipticity and dissipative effects e t 1 x xx t x 0 r t 1 x 2 x xx with initial data i x 0 0 x 0 x as x where and are positive constants such that 1 4 1 under the assumption that is sufficiently small we show that if the initial data is a small perturbation of the parabolic system defined by 2 4 which are obtained by the convection diffusion equations 2 1 and solutions to cauchy problem e and i tend asymptotically to the convection diffusion system with exponential rates precisely speaking we derive the asymptotic profile of e by gauss kernel g t x as follows 2 2e 1 4 t xg y t 1 1 sin 2 y 0 cos 2 y 0 dy e 1 t 2e 1 4 t rg t y cos 2 y 1 sin 2 y sin 2 y cos 2 y u0 x y v0 x y dy lp rx e 1 4 to 1 t 1 1p the same problem was studied by tang and zhao s q tang h j zhao nonlinear stability for dissipative nonlinear evolution equations with ellipticity j math anal appl 233 1999 336 358 nishihara k nishihara asymptotic profile of solutions to nonlinear dissipative evolution system with ellipticity z angew math phys 57 4 2006 604 614 for the case of 0 0

robust permanence for interacting structured populations abstract the dynamics of interacting structured populations can be modeled by d x i d t a i x x i where x i r n i x x 1 x k and a i x are matrices with non negative off diagonal entries these models are permanent if there exists a positive global attractor and are robustly permanent if they remain permanent following perturbations of a i x necessary and sufficient conditions for robust permanence are derived using dominant lyapunov exponents i of the a i x with respect to invariant measures the necessary condition requires max i i 0 for all ergodic measures with support in the boundary of the non negative cone the sufficient condition requires that the boundary admits a morse decomposition such that max i i 0 for all invariant measures supported by a component of the morse decomposition when the morse components are axiom a uniquely ergodic or support all but one population the necessary and sufficient conditions are equivalent applications to spatial ecology epidemiology and gene networks are given

repelling conditions for boundary sets using liapunov like functions ii persistence and periodic solutions abstract this paper deals with repulsivity conditions for the points of the boundary of a set g with respect to the solutions of the differential system x t x which are contained in the set g applications are given to the problem of persistence i e solutions starting at the interior of a set remain asymptotically far from its boundary and to the existence of periodic solutions using the nonejective fixed point theorem

global decaying solution to dissipative nonlinear evolution equations with ellipticity abstract we establish the global existence and decaying results for the cauchy problem of nonlinear evolution equations e t 1 x x xx t 1 x 2 x xx forinitial data with different end states i x 0 x 0 0 x 0 x as x which displays the complexity in between ellipticity and dissipation although the nonlinear term x appears in equation e 1 which makes calculations more complicated due to smoothing effect of the parabolic operator we detail its regularity property and decay estimates when t 0 for the higher order spatial derivatives despite its relatively lower regularity of the initial data and we also discuss the decay estimates furthermore we do not restrict l1 bound on the initial data 0 x 0 x as in 2

nonlinear stability for dissipative nonlinear evolution equations with ellipticity we study the cauchy problem for a set of nonlinear evolution equations which has been proposed for the investigation of nonlinear interaction between ellipticity and dissipation the zero equilibrium is linearly stable for coefficients within certain range we further establish the global existence nonlinear stability and optimal decay rate of the solution for coefficients within the same range though with suitable restriction to initial data

uniform repellers for processes with applications to periodic differential systems where f w x 52 iw p is continuous and d is an open set in iw p let a4 e q be a closed set relative to q with non empty interior int m and compact boundary fr m equation 1 1 is said to be presistent for a4 if int m is a flow invariant set for eq l l and for each x solution of l l defined on to co with initial value x t int m there exists 7 1 0 such that lim inf m d x t fr m 9 d denotes the usual distance in w p if moreover 7 is independent of the solution x we say that uniform persistence occurs in other words fr m is a uniformly repelling set for eq 1 1 with respect to int m when 1 1 is autonomous and m is a compact set it is known that uniform persistence holds for the set m with respect to eq l l if for each u fr a4 there exists an outer normal v to m at u in the sense of bony 3 for which the usual inner product f u v is negative see for instance corollary 2 and theorem 1 in 6 however for nonautonomous equations no condition for f on the boundary of m guarantees uniform persistence as seen in 6 theorem 23 the aim of this paper is to provide a sufficient condition in order to get uniform persistence even in the nonautonomous case the main idea is a generalization to processes of a result about repellers for autonomous differential equations by j hofbauer 111 successively generalized for semi dynamical systems by v hutson 121 and a fonda s 141 0022 0396190 3 00

robust h filtering and control for a class of linear systems with fractional stochastic noise abstract in this paper a class of linear stochastic systems driven by fractional brownian motion are investigated the fractional infinitesimal operator and stability criterion based on the lyapunov approach for the systems with fractional stochastic noise are employed which are different from the results of classical stochastic systems firstly the robust h filtering problem is studied and the stochastic stability and h performance of the filtering error system are guaranteed by the feasibility of linear matrix inequalities secondly robust h control problem is investigated and the closed loop system driven by a fractional brownian motion is stochastically stable and has h performance if some linear matrix inequalities are feasible under the designed controller finally two numerical examples show the effectiveness and correctness of the proposed methods

permanence for non autonomous food chain systems with delay in this paper we first establish a new general criterion for the permanence of kolmogorov type systems of nonautonomous functional differential equations then as applications of this criterion we study the permanence of a class of n species general nonautonomous food chain systems with delay and new sufficient condition are established

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

evolution equations driven by a fractional brownian motion abstract in this paper we study nonlinear stochastic evolution equations in a hilbert space driven by a cylindrical fractional brownian motion with hurst parameter h 1 2 and nuclear covariance operator we establish the existence and uniqueness of a mild solution under some regularity and boundedness conditions on the coefficients and for some values of the parameter h this result is applied to stochastic parabolic equation perturbed by a fractional white noise in this case if the coefficients are lipschitz continuous and bounded the existence and uniqueness of a solution holds if h d 4 the proofs of our results combine techniques of fractional calculus with semigroup estimates

uniform persistence in processes with application to nonautonomous competitive models abstract an acyclicity theorem on uniform persistence is proved for continuous processes this result is applied to two species nonautonomous competitive lotka volterra models

existence and exponential stability for impulsive neutral stochastic functional differential equations driven by fbm with noncompact semigroup via monch fixed point abstract in this paper we investigate the existence and exponential stability of mild solutions for a class of impulsive neutral stochastic functional differential equations driven by fbm with noncompact semigroup in hilbert spaces sufficient conditions for the existence of mild solutions are obtained using the hausdorff measure of noncompactness and the monch fixed point theorem further we establish a new impulsive integral inequality to prove the exponential stability of mild solutions in the mean square moment finally an example is presented to illustrate our obtained results

impulsive neutral stochastic functional integro differential equations with infinite delay driven by fbm in this paper we study a class of impulsive neutral stochastic functional integro differential equations with infinite delay driven by a standard cylindrical wiener process and an independent cylindrical fractional brownian motion fbm with hurst parameter h 1 2 1 in the hilbert space we prove the existence and uniqueness of the mild solution for this kind of equations with the coefficients satisfying some non lipschitz conditions which include the classical lipschitz conditions as special case an example is provided to illustrate the theory some well known results are generalized and extended

on the appearance of multiple attractors in discrete food chains abstract klebanoff and hastings a klebanoff a hastings chaos in three species food chains journal of mathematical biology 32 1994 427 451 detected cases of multiple attractors in continuous food chains in this paper we discuss similar phenomena in the discrete food chains introduced by lindstrom t lindstrom on the dynamics of discrete food chains low and high frequency behavior and chaos journal of mathematical biology 45 2002 396 418 the results imply that the dynamical properties including species persistence may change due to disturbances that do not involve changes in the environmental parameters thus there are possibilities that species may be eradicated or start to oscillate at different frequencies without any changes in the environment since this is now shown to hold in both seasonal and non seasonal environments we expect that this is a rather general property of ecosystems

global convergence of nonlinear cascade flows with morse bott zero dynamics abstract we derive a sufficient condition that a flow captures the dynamics on an invariant submanifold this leads to a refinement of the lasalle invariance principle as a consequence we generalize a well known global asymptotic stability result of nonlinear cascade systems to show global convergence to a compact invariant set this includes the case where a globally asymptotically stable system is coupled to a morse bott flow

decay rates of solutions to the cauchy problem for dissipative nonlinear evolution equations abstract in this paper we study the global existence and the asymptotic behavior of the solutions to the cauchy problem for the following nonlinear evolution equations with ellipticity and dissipative effects e t 1 x x x t 1 x x x x with initial data i x 0 0 x 0 x as x where and are positive constants such that 1 1 through constructing a correct function x t defined by 2 13 and using the energy method we show sup x r x t x x x t 0 as t and the solutions decay with exponential rates the same problem was studied by tang and zhao s q tang h j zhao nonlinear stability for dissipative nonlinear evolution equations with ellipticity j math anal appl 233 1999 336 358 for the case of 0 0

bifurcations in persistence theory for models of population growth represented by systems of autonomous ordinary differential equations the question of whether persistence outcomes may be changed due to violation of one of the standard assumptions by means of a perturbation leading to bifurcations is investigated the results are illustrated by several examples

spreading speeds of a partially degenerate reaction diffusion system in a periodic habitat abstract this paper is devoted to the study of the spreading speeds of a partially degenerate reaction diffusion system with monostable nonlinearity in a periodic habitat we first obtain sufficient conditions for the existence of principal eigenvalues in the case where solution maps of the associated linear systems lack compactness and prove a threshold type result on the global dynamics for the periodic initial value problem then we establish the existence and computational formulae of spreading speeds for the general initial value problem it turns out that the spreading speed is linearly determinate

resolvent operators for integral equations in a banach space conditions are given which ensure the existence of a resolvent operator for an integrodifferential equation in a banach space the resolvent operator is similar to an evolution operator for nonautonomous differential equations in a banach space as in the finite dimensional case this operator is used to obtain a variation of parameters formula which can be used to obtain results concerning the asymptotic behaviour of solutions and weak solutions

uniform persistence and chain recurrence soit 7b e d un espace metrique localement compact et e un sous ensemble clos de 7b e soit un systeme dynamique sur e on reconsidere la notion de persistance uniforme dans le cadre de la theorie de conley des ensembles invariants

locating omega limit sets using height functions this work deals with the problem of locating the limit set of a bounded solution of a given autonomous vector field f on a riemannian manifold assuming to know that the limit set is contained in an embedded submanifold s and using an auxiliary function that we call height function w for f and s we show how to obtain a better estimate of the location of under mild assumptions several consequences and an application to a type of polynomial vector fields are presented

persistence criteria for a chemostat with variable nutrient input abstract the standard single species chemostat model is modified to include a variable nutrient input which is assumed only to be nonnegative bounded and continuous we obtain necessary and sufficient conditions for persistence and show that all solutions of any given chemostat system have the same long time behavior independent of the initial conditions counterexamples shed light on the results obtained

dynamic model of worms with vertical transmission in computer network an e epidemic seirs model for the transmission of worms in computer network through vertical transmission is formulated it has been observed that if the basic reproduction number is less than or equal to one the infected part of the nodes disappear and the worm dies out but if the basic reproduction number is greater than one the infected nodes exists and the worms persist at an endemic equilibrium state numerical methods are employed to solve and simulate the system of equations developed we have analyzed the behavior of the susceptible exposed infected and recovered nodes in the computer network with real parametric values

existence uniqueness and stability of the solutions to neutral stochastic functional differential equations with infinite delay in this paper we obtain the existence and uniqueness of solutions to neutral stochastic functional differential equations with infinite delay at phase space bc 0 r d which denotes the family of bounded continuous r d value functions f defined on 0 with norm email protected sup q 0 f q under non lipschitz condition with lipschitz condition being considered as a special case and a weakened linear growth condition the solution is constructed by the successive approximation furthermore we give the continuous dependence of solutions on the initial value by means of the corollary of bihari inequality

global smooth solutions to the spatially periodic cauchy problem for dissipative nonlinear evolution equations abstract the existence and uniqueness are proved for global classical solutions of the spatially periodic cauchy problem to the following system of parabolic equations formula which was proposed as a substitute for the rayleigh benard equation and can lead to lorenz equations

zero viscosity limit of the linearized navier stokes equations for a compressible viscous fluid in the half plane the zero viscosity limit for an initial boundary value problem of the linearized navier stokes equations of a compressible viscous fluid in the half plane is studied by means of the asymptotic analysis with multiple scales we first construct an approximate solution of the linearized problem of the navier stokes equations as the combination of inner and boundary expansions next by carefully using the technique on energy methods we show the pointwise estimates of the error term of the approximate solution which readily yield the uniform stability result for the linearized navier stokes solution in the zero viscosity limit 1999 john wiley sons inc

large time profile of solutions for a dissipative nonlinear evolution system with conservational form we examine the cauchy problem for a nonlinear dissipative evolution system with conservation form with initial condition where and are positive constants such that and 1 we establish the global existence and decay rate of the solution subject to the parameter restriction the optimal decay rate is obtained if 0 0 l1 r r2 furthermore the global existence of the solution to the same problem has been studied in jian and chen 1998 acta math sin 14 17 34 without giving the decay rate and optimal decay order of the solution in which 0 0 h1 r r2 l1 r r2

dulac criteria for autonomous systems having an invariant affine manifold abstract for a class of higher dimensional autonomous systems that have an invariant affine manifold conditions are derived to preclude the existence of periodic solutions on the invariant manifold it is established that these conditions are robust under certain types of local perturbations of the vector field as a consequence each bounded semitrajectory on the invariant manifold is shown to converge to a single equilibrium using a c 1 closing lemma for this class applications to autonomous systems that are homogeneous of degree 1 are also considered

predator influence on the growth of a population with three genotypes iii persistence and extinction abstract a predator prey system in which the prey population consists of three genotypes is analyzed the paper generalizes previous results on extinction of two genotypes leaving a homozygous population in addition conditions when the heterozygote has the lower predation are given under which all three genotypes persist the case where a bifurcation of periodic solutions from one of the coordinate planes into the positive cone is also considered finally it is shown that when predation on both homozygotes are the same there exists a three dimensional invariant manifold which either attracts or repels depending on the heterozygote predation

threshold dynamics of a diffusive siri model with nonlinear incidence rate abstract this work is concerned with the dynamics of a diffusive siri epidemic model with nonlinear incidence rate we first establish the well posedness of the model then we show the basic reproduction number r 0 is a threshold parameter for the stability of the model in fact the disease free equilibrium is globally asymptotically stable when r 0 1 while the phenomena of uniform persistence occurs when r 0 1 if r 0 1 the disease free equilibrium is globally asymptotically stable under some assumptions we also clarify the relationship between r 0 and the local basic reproduction number moreover we establish the local and global stability of the endemic equilibrium provided that all parameters of this model are constants

the existence and exponential behavior of solutions to stochastic delay evolution equations with a fractional brownian motion abstract in this paper we investigate the existence uniqueness and exponential asymptotic behavior of mild solutions to stochastic delay evolution equations perturbed by a fractional brownian motion b q h t d x t a x t f t x t d t g t d b q h t with hurst parameter h 1 2 1 we also consider the existence of weak solutions

asymptotics of dissipative nonlinear evolution equations with ellipticity different end states in this paper we consider the global existence and asymptotic behaviors of solutions to the cauchy problem for the following nonlinear evolution equations with ellipticity and dissipative effects e t 1 x xx t 1 x 2 x xx with initial data i x 0 0 x 0 x as x where and are positive constants such that 1 4 1 under the assumption that is sufficiently small we show that if the initial data is a small perturbation of the diffusion waves defined by 2 5 which are obtained by the diffusion equations 2 1 solutions to cauchy problem e and i tend asymptotically to those diffusion waves with exponential rates the analysis is based on the energy method the same problem was studied by tang and zhao j math anal appl 233 1999 336 358 for the case of 0 0

optimal decay rates to diffusion wave for nonlinear evolution equations with ellipticity abstract we derive the optimal convergence rates to diffusion wave for the cauchy problem of a set of nonlinear evolution equations with ellipticity and dissipative effects t 1 x x x t 1 x x x x subject to the initial data with end states x 0 0 x 0 x as x where and are positive constants such that 1 4 1 introducing the auxiliary function to avoid the difference of the end states we show that the solutions to the reformulated problem decay as t with the optimal decay order the decay properties of the solution in the l 2 sense which are not optimal were already established in paper c j zhu z y zhang h yin convergence to diffusion waves for nonlinear evolution equations with ellipticity and damping and with different end states acta math sinica english ed in press the main element of this paper is to obtain the optimal decay order in the sense of l p space for 1 p which is based on the application of fourier analysis and interpolation inequality under some suitable restrictions on coefficients and moreover we discuss the asymptotic behavior of the solution to general system 1 1 at the end however the optimal decay rates of the solution to general system 1 1 remains unknown

existence of mild solutions to stochastic neutral partial functional differential equations with non lipschitz coefficients under a non lipschitz condition with the lipschitz condition being considered as a special case and a weakened linear growth condition the existence and uniqueness of mild solutions to stochastic neutral partial functional differential equations snpfdes is investigated some results in govindan 2003 2005 2 6 are generalized to cover a class of more general snpfdes

on the asymmetric may leonard model of three competing species in this paper we analyze the global asymptotic behavior of the asymmetric may leonard model of three competing species frac dx i dt x i 1 x i beta ix i 1 alpha ix i 1 x i 0 0 i 1 2 3 with x 0 x 3 x 4 x 1 under the assumption 0 b1b2b3 and p is a saddle point with one dimensional stable manifold gamma if a1a2a3 b1b2b3 then p is global asymptotically stable in int r3 ii if a1a2a3 b1b2b3 then for each initial condition x 0 not in gamma the solution v

remarks on strongly flow invariant sets abstract conditions ensuring the strong flow invariance property for a compact set m with respect to the differential system x t x are considered an answer to a question raised in gard applicable anal 10 1980 285 293 is given in the case of autonomous systems

existence results for impulsive neutral functional integrodifferential equations with infinite delay abstract this paper is concerned with the existence of mild solutions for impulsive neutral functional integrodifferential equations with infinite delay in banach spaces the results are obtained by using the krasnoselski schaefer type fixed point theorem an example is provided to illustrate the theory

asymptotic behavior of solutions for p system with relaxation in this paper we consider the asymptotic behavior of solutions for the cauchy problem for p system with relaxationvt ux 0 ut p v x 1e f v u e with initial data v u x 0 v 0 x u 0 x v u v 0 asx i we are interested to show the solutions of e i tend also to the equilibrium rarefaction waves and the traveling waves even if the limits v u of the initial data at x do not satisfy the equilibrium equation i e u f v when the limits of the initial data at infinity satisfy equilibrium states liu 9 studied the stability of rarefaction waves and traveling waves for the general 2 2 hyperbolic conservation laws with relaxation

a note on exponential stability for second order neutral stochastic partial differential equations with infinite delays in the presence of impulses in this work the problem on the exponential stability for second order neutral stochastic partial differential equations with infinite delays is considered in the presence of impulses under some conditions by employing the new integral inequality technique some algebraic criteria of stability are established for the concerned problem and some existing results are generalized and improved finally an illustrative example is given to demonstrate the effectiveness of the obtained results

on the finite dimensional dynamical systems with limited competition the asymptotic behavior of dynamical systems with limited competition is investigated we study index theory for fixed points permanence global stability convergence everywhere and coexistence it is shown that the system has a globally asymptotically stable fixed point if every fixed point is hyperbolic and locally asymptotically stable relative to the face it belongs to a nice result is the necessary and sufficient conditions for the system to have a globally asymptotically stable positive fixed point it can be used to establish the sufficient conditions for the system to persist uniformly and the convergence result for all orbits applications are made to time periodic ordinary differential equations and reaction diffusion equations

stability bifurcation and global existence of a hopf bifurcating periodic solution for a class of three neuron delayed network models in this paper a system of three delay differential equations representing a hopfield type general model for three neurons with two way bidirectional time delayed connections between the neurons and time delayed self connection from each neuron to itself is studied delay independent and delay dependent sufficient conditions for linear stability instability and the occurrence of a hopf bifurcation about the trivial equilibrium are addressed the partition of the resulting parametric space into regions of stability instability and hopf bifurcation in the absence of self connection is realized to extend the local hopf branches for large delay values a particular bidirectional delayed tri neuron model without self connection is investigated sufficient conditions for global existence of multiple non constant periodic solutions are obtained for such a model using the global hopf bifurcation theorem for functional differential equations due to j wu and the bendixson criterion for higher dimensional ordinary differential equations due to li and muldowney and following the approach developed by wei and li

analytic resolvent operators for integral equations in banach space on etudie l equation integrodifferentielle x t a 0 x t 0 t b t s x s ds f t t 0 x 0 x 0 ed a x et l equation integrale x t 0 t a t s x s ds f t dans un espace de banach x les operateurs a a 0 b t et a t sont des operateurs clos sur x a domaine dense

impact of network connectivity on the synchronization and global dynamics of coupled systems of differential equations abstract the global dynamics of coupled systems of differential equations defined on an interaction network are investigated local dynamics at each vertex when interactions are absent are assumed to be simple solutions to each vertex system are assumed to converge to an equilibrium either on the boundary or in the interior of the feasible region the interest is to investigate the collective behaviours of the coupled system when interactions among vertex systems are present it was shown in li and shuai 2010 that if the interaction network is strongly connected then solutions to the coupled system synchronize at a single equilibrium we focus on the case when the underlying network is not strongly connected and the coupled system may have mixed equilibria whose coordinates are in the interior at some vertices while on the boundary at others we show that solutions on a strongly connected component of the network will synchronize considering a condensed digraph by collapsing each strongly connected component we are able to introduce a partial order on the set p of all equilibria and show that all solutions of the coupled system converge to a unique equilibrium p that is the maximizer in p we further establish that behaviours of the coupled system at minimal elements of the condensed digraph determine whether the global limit p is a mixed equilibrium the theory are applied to mathematical models from epidemiology and spatial ecology

convergence rates of vanishing diffusion limit on nonlinear hyperbolic system with damping and diffusion the aim of this paper is to study the global unique solvability on c solution to the cauchy problem of a special 2 2 nonlinear hyperbolic system with damping and diffusion furthermore we also investigate the convergence rates as the diffusion parameter goes to zero it is shown that the convergence rates in c norm is of the order o the novelty of analysis taken in the present article is to obtain the uniform in a priori estimates on hs norm for any s n which are implemented by introducing induction we focus on two cases in this paper both and since the uniform in a priori estimates obtained are distinctly different for different cases

persistence of a class of periodic kolmogorov systems in this paper we study the persistence of a periodic kolmogorov system which models the growth of n interacting biological species the system is assumed to have a simple dynamic in the sense that each coordinate subsystem possesses a global attractor our research is mainly addressed to the case in which there exists at least a predator among the n species however we also obtain a result about persistence for a class of competitive systems

on partial differential equations related to lorenz system partial differential equations are constructed such that a truncation scheme as adopted by lorenz j atmos sci 20 130 1963 will lead to lorenz equations the partial differential equations are much simpler than those of the rayleigh bernard problem and are essentially of the mixed type various aspects of the partial differential equations are explored it is suggested that the switching back and forth between the elliptic and hyperbolic regimes represents the chaotic behavior of the system in the context of partial differential equations

asymptotic properties of solutions to quasi linear differential systems abstract using some previous author s results or their slight modifications two theorems concerning the existence of a bounded and a periodic solution are presented for the system whose one part of components is uniformly ultimately bounded while the other tends mostly to infinity this type of results seems to be new

dependencies between competition and predation and their consequences for initial value sensitivity we commence with a discussion of dependencies between various processes in discrete consumer resource models two basic models are formulated these models are closely related and differ only in terms of which dependencies are assumed the models can be regarded as hybrids of the lotka volterra model the beverton holt model and the nicholson bailey model a complete stability analysis of the equilibria is given with the conclusion that the stability properties of these models are closely related to gause type predator prey systems the numerical part of our analysis brings out remarkable qualitative differences concerning the initial value sensitivity of the oscillations of the two basic models initial value sensitivity was measured by lyapunov exponents and the observed differences cannot be brought to light by a study of limiting cases or by equilibrium analysis the actual reasons behind these results remain a delicate mathematical question properties associated directly with the time series like

persistence in dynamical systems soit un espace metrique localement compact de metrique d et soit e un sous ensemble clos de a frontiere e et interieur e on suppose que l on a un flot continu 7b f defini sur e tel que e est invariant par 7b f on considere la notion de persistance et on donne un critere de persistance

uniform persistence and hopf bifurcations in r n we consider parameterized families of flows in locally compact metrizable spaces and give a characterization of those parameterized families of flows for which uniform persistence continues on the other hand we study the generalized poincare andronov hopf bifurcations of parameterized families of flows at boundary points of r n or more generally of an n dimensional manifold and show that this kind of bifurcations produce a whole family of attractors evolving from the bifurcation point and having interesting topological properties in particular in some cases the bifurcation transforms a system with extreme non permanence properties into a uniformly persistent one we study in the paper when this phenomenon happens and provide an example constructed by combining a holling type interaction with a pitchfork bifurcation