on a class of second order anti periodic boundary value problems of concern is the existence and uniqueness of anti periodic solutions to a class of abstract nonlinear second order differential equations the investigation relies on the theory of m accretive operators in banach or hilbert spaces examples of boundary value problems for ordinary and partial differential equations are also discussed

analysis of diffusive two competing prey and one predator systems with beddington deangelis functional response abstract in this paper a diffusive two competing prey and one predator system with beddington deangelis functional response is considered the sufficient and necessary conditions for the existence of coexistence states are provided using the fixed point index theory developed in addition the stability and uniqueness of coexistence states are investigated finally this paper discusses the sufficient conditions for extinction and permanence of the time dependent system

the existence bifurcation and stability of positive stationary solutions of a diffusive leslie gower predator prey model with holling type ii functional responses abstract in this paper we revisit a diffusive leslie gower predator prey model with holling type ii functional responses and dirichlet boundary condition it is shown that multiple positive steady state solutions exist under certain conditions on the parameters while for another parameter region the positive steady state solution is unique and locally asymptotically stable results are proved by using bifurcation theory fixed point index theory energy estimates and asymptotic behavior analysis

on the uniqueness and ordering of steady states of predator prey systems this paper discusses the relationship between the uniqueness and the ordering of strictly positive solutions of elliptic predator prey interacting systems if v and u v are two such solutions with u or v v then u v v when the positive solutions are numerically close to the extreme case the solution is unique

some uniqueness and exact multiplicity results for a predator prey model in this paper we consider positive solutions of a predator prey model with diffusion and under homogeneous dirichlet boundary conditions it turns out that a certain parameter m in this model plays a very important role a good understanding of the existence stability and number of positive solutions is gained when m is large in particular we obtain various results on the exact number of positive solutions our results for large m reveal interesting contrast with that for the well studied casem 0 i e the classical lotka volterra predator prey model

positive solutions of a prey predator model with predator saturation and competition abstract in this paper we study the existence multiplicity bifurcation and stability of positive solutions to a prey predator model with predator saturation and competition u u a u b v f u v x v v c v d u f u v x u v 0 x where f u v 1 1 u 1 v and parameters are all positive constants and u and v are the densities of the prey and predator respectively

on a predator prey system with cross diffusion representing the tendency of predators in the presence of prey species abstract in this paper a predator prey system with cross diffusion representing the tendency of predators to avoid the group defense by a large number of prey or diffuse in the direction of higher concentration of the prey species under homogeneous dirichlet boundary condition is considered using the method of upper and lower solutions developed by pao c v pao strongly coupled elliptic systems and applications to lotka volterra models with cross diffusion nonlinear anal 60 2005 1197 1217 sufficient conditions for the existence of positive solutions are provided when the induced cross diffusion coefficient is sufficiently small furthermore the investigation of non existence of positive solutions is also presented

p sv wave propagation in heterogeneous media velocity stress finite difference method i present a finite difference method for modeling p sv wave propagation in heterogeneous media this is an extension of the method i previously proposed for modeling sh wave propagation by using velocity and stress in a discrete grid the two components of the velocity cannot be defined at the same node for a complete staggered grid the stability condition and the p wave phase velocity dispersion curve do not depend on the poisson s ratio while the s wave phase velocity dispersion curve behavior is rather insensitive to the poisson s ratio therefore the same code used for elastic media can be used for liquid media where s wave velocity goes to zero and no special treatment is needed for a liquid solid interface typical physical phenomena arising with p sv modeling such as surface waves are in agreement with analytical results the weathered layer and corner edge models show in seismograms the same converted phases obtained by previous authors this method gives stable results for step discontinuities as shown for a liquid layer above an elastic half space the head wave preserves the correct amplitude finally the corner edge model illustrates a more complex geometry for the liquid solid interface as the poisson s ratio v increases from 0 25 to 0 5 the shear converted phases are removed from seismograms and from the time section of the wave field

coexistence theorem of steady states for nonlinear self cross diffusion systems with competitive dynamics in this paper we discuss the existence of positive solutions to certain nonlinear elliptic systems representing competitive interaction with self cross diffusions between two species the method employed is the fixed point index theory in a positive cone sufficient conditions for the existence of positive solutions are provided

on the existence and uniqueness of positive solutions for competing species models with diffusion in this paper we consider strictly positive solutions of competing species systems with diffusion under dirichlet boundary conditions we obtain a good understanding of when strictly positive solutions exist obtain new nonuniqueness results and a number of other results showing how complicated these equations can be in particular we consider how the shape of the underlying domain affects the behaviour of the equations the purpose of this paper is to obtain much better results on the existence and uniqueness of strictly positive stationary that is time independent solutions of

non constant positive steady states of a predator prey system with non monotonic functional response and diffusion this paper deals with non constant positive steady state solutions of a predator prey system with non monotonic functional response also called holling type iv interaction terms and diffusion under the homogeneous neumann boundary condition we first establish positive upper and lower bounds for such solutions and then study their non existence global existence and bifurcation

steady states of a predator prey model with prey taxis abstract we study the steady states of a predator prey model with prey taxis incorporating holling type ii functional response under the homogeneous neumann boundary condition the stability of equilibrium points and the existence of non constant steady states are investigated we obtain that the prey tactic sensitivity coefficient delays the stability of the unique positive constant solution but for other equilibrium points stability the prey tactic sensitivity coefficient does not influence on it furthermore we derive some sufficient conditions relative to the prey tactic sensitivity coefficient which confines the existence of steady states and find that even if the interaction coefficient is sufficiently large there also exist non constant positive steady states under some conditions

coexistence states of a nonlinear lotka volterra type predator prey model with cross diffusion abstract in this paper a lotka volterra type predator prey elliptic system with nonlinear cross diffusion is considered representing the tendency of predators to get closer to prey under robin boundary condition the necessary and sufficient conditions for the existence of coexistence states are given in terms of principal eigenvalues involving semi trivial solutions using the degree theory this paper also discusses the ecological meaning and effect of decreasing cross diffusion induced on predators by prey in a specific model

le nombre de solutions de certains problemes semi lineaires elliptiques abstract in this paper we compute the exact number of solutions for certain semi linear elliptic problems in the first part we derive some complementary results to a theorem of ambrosetti and prodi the global behaviour of bifurcating branches is then studied for some classes of problems in the context of a concave or a convex nonlinearity in the second part we consider the branch of positive solutions lastly in the third part in dimension one for an autonomous equation we obtain a precise description of all the solutions to these problems the proofs rely on simple eigenvalue comparison arguments

an efficient symplectic reverse time migration method using a local nearly analytic discrete operator in acoustic transversely isotropic media with a vertical symmetry axis abstractreverse time migration rtm has become an extremely important imaging method due to its ability of handling complicated velocity models in recent years there has been an increasing need to perform rtm with anisotropic velocity models such as transversely isotropic media with a vertical symmetry axis vti finite difference fd is one of the most widely used numerical methods in rtm however it often suffers from serious numerical dispersion resulting in significant loss of imaging resolution over the years a nearly analytic discrete operator has been developed to approximate the high order spatial partial differential operators which is effective in suppressing numerical dispersion using this operator we developed a nearly analytic symplectic nas method to numerically solve acoustic vti wave equations which preserves the symplectic structure we have investigated its properties including the stability condition numerical dispersion relation and computational efficiency also we a

on positive solutions of some pairs of differential equations this paper is a sequel to the author s paper 6 which studied positive solutions of a pair of differential equations introduced by conway gardner and smoller 4 their equations were equations for population problems in biology their significance is discussed further in 141 the purpose of the present paper is to obtain further results for the conwat gardner smoller equations and to show how the methods in 6 can be modified to decide exactly when the classical predator prey system as in blat and brown 2 has a strictly positive solution we also show how the methods can be applied to a number of other problems in particular our results answer some questions in conway s secondly we show how the asymptotic methods developed in 6 can be used to study the existence and uniqueness of strictly positive solutions of competing species problems our results suggest that this is a much more complicated problem than the predator prey problem we do obtain a condition which is except for a few special cases necessary and sufficient for the existence of a strictly positive solution however the condition is complicated and rather implicit thirdly we prove the uniqueness of the strictly positive solution in the conway smoller system if d is small and n 1 that is the case of ordinary differential equations this partially answers a question in 4 our proof is a local result and can be used in other situations for example it can be used to show that in certain cases of asocial nonlinearities where our notation follows 4 sect 4 there are exactly two strictly positive solutions for small d we also show how our method applies to more general predator prey problems in section 1 we find necessary and sufficient conditions for the existence of strictly positive solutions of predator prey systems in section 2 we study competing species models by iteration and asymptotic methods finally in section 3 we prove our uniqueness results in an appendix we briefly discuss how the methods of section 3 apply to more general models

bifurcation of steady state solutions in predator prey and competition systems we discuss steady state solutions of systems of semilinear reaction diffusion equations which model situations in which two interacting species u and v inhabit the same bounded region it is easy to find solutions to the systems such that either u or v is identically zero such solutions correspond to the case where one of the species is extinct by using decoupling and global bifurcation theory techniques we prove the existence of solutions which are positive in both u and v corresponding to the case where the populations can co exist

some new results on the existence of periodic solutions to a kind of rayleigh equation with a deviating argument abstract by employing the continuation theorem of coincidence degree theory we study a kind of rayleigh equation with a deviating argument as follows x t f x t g x t t p t some new results on the existence of periodic solutions are obtained

coexistence of a general elliptic system in population dynamics this paper is concerned with a strongly coupled elliptic system representing a competitiveinteraction between two species we give a sufficient condition for the existence of positive solutions an example is also given to show that there is a coexistence of a steady state if the cross diffusions or the intraspecific competitions are weak

spatial pattern in an ecosystem of phytoplankton nutrient from remote sensing abstract in this paper we consider an ecosystem of phytoplankton nutrient which comes from pelagic zone of the ocean by using remote sensing we are concerned with the pattern formation of the model we first give the asymptotic behavior of positive solutions of parabolic dynamical system then we discuss the stability of constant positive solution and the boundedness of stationary solutions finally the non existence and existence results of the pattern are investigated by considering some parameters the result shows that under certain range of these parameters the pattern of the model occurs

multiplicity and uniqueness of positive solutions for a predator prey model with b d functional response abstract in this paper we consider positive solutions of a predator prey model with beddington deangelis functional response first we establish the existence of positive solutions and present some sufficient and necessary conditions mainly using the standard fixed point index theory in cone second the multiplicity uniqueness and stability of positive solutions are obtained by means of bifurcation theory perturbation theory of eigenvalues and the fixed point index theory the parameters k and m play very important roles in deciding the number of positive solutions which are showed explicitly in this paper

coexistence states of a holling type ii predator prey system abstract this paper characterize the existence of coexistence states to a reaction diffusion predator prey model with holling type ii functional response subject to dirichlet boundary conditions we find the necessary and sufficient conditions for existence of coexistence states by fixed point index theory and bifurcation theory

non constant positive steady states of the sel kov model abstract this paper deals with the reaction diffusion system known as the sel kov model with the homogeneous neumann boundary condition this model has been applied to various problems in chemistry and biology we first give a priori estimates positive upper and lower bounds of positive steady states and then study the non existence bifurcation and global existence of non constant positive steady states as the parameters and are varied

coexistence of a diffusive predator prey model with holling type ii functional response and density dependent mortality in this paper we consider a two competitor one prey diffusive model in which both competitors exhibit holling type ii functional response and one of the competitors exhibits density dependent mortality rate first we study the local and global existence of strong solution by using the c0 analytic semigroup then we consider the local and global stability of the positive constant equilibrium by using the linearization method and laypunov functional method respectively furthermore we derive some results for the existence and non existence of non constant stationary solutions when the diffusion rate of a certain species is small or large the existence of non constant stationary solutions implies the possibility of pattern formation in this system

existence and uniqueness of anti periodic solutions for a kind of rayleigh equation with two deviating arguments abstract in this paper we use the leray schauder degree theory to establish new results on the existence and uniqueness of anti periodic solutions for a kind of rayleigh equation with two deviating arguments of the form x f t x t g 1 t x t 1 t g 2 t x t 2 t e t

stable p wave modeling for reverse time migration in tilted ti media we present an approach for p wave modeling in inhomogeneous transversely isotropic media with tilted symmetry axis tti media suitable for anisotropic reverse time migration the proposed approach is based on wave equations derived from first principles the equations of motion and hooke s law under the acoustic ti approximation consequently no assumptions are made about the spatial variation of medium parameters a rotation of the stress and strain tensors to a local coordinate system aligned with the ti symmetry axis makes it possible to benefit from the simple and sparse form of the ti elastic tensor in that system the resulting wave equations can be formulated either as a set of five first order or as a set of two second order partial differential equations for the constant density case the second order tti wave equations involve mixed and nonmixed second order spatial derivatives with respect to global nonrotated coordinates we propose a numerical implementation of these equations using high order centered finite differences to minimize modeling artifacts related to the use of centered first derivative operators we use discrete second derivative operators for the nonmixed second order spatial derivatives and repeated discrete first derivative operators for the mixed derivatives such a combination of finite difference operators leads to a stable wave propagator provided that the operators are designed properly in practice stability is achieved by slightly weighting down terms that contain mixed derivatives this has a minor practically negligible effect on the kinematics of wave propagation the stability of the presented scheme in inhomogeneous tti models with rapidly varying anisotropic symmetry axis direction is demonstrated with numerical examples

s shaped global bifurcation curve and hopf bifurcation of positive solutions to a predator prey model where d is a bounded domain in r n 1 with smooth boundary d and a b c d m are positive constants problem 1 0 is known as the predator prey model with holling tanner type interactions where u and v represent the densities of the prey and predator respectively hence we are only interested in positive solutions by which we mean that both u and v are positive in d it is easy to see that a 1 is necessary for the existence of positive solutions to 1 0 and we shall also assume that d 1 the case d 1 is rather different and will not be discussed here we are mainly interested in studying the number of positive solutions of 1 0 and the stability of these solutions in particular we shall show that when b d c and m fall into certain range the solution set u v a of 1 0 forms a s shaped smooth curve and that hopf bifurcation occurs along this curve this not only confirms rigorously similar numerical observations on 1 0 made in 4 but also shows that the corresponding parabolic system

modeling the scalar wave equation with nystrom methods high accuracy numerical schemes for modeling of the scalar wave equation based on nystrom methods are developed in this paper space is discretized by using the pseudospectral algorithm for the time discretization nystrom methods are used a fourth order symplectic nystrom method with pseudospectral spatial discretization is presented this scheme is compared with a commonly used second order scheme and a fourth order nonsymplectic nystrom method for a typical time step size the second order scheme exhibits spatial dispersion errors for long time simulations while both fourth order schemes do not suffer from these errors numerical comparisons show that the fourth order symplectic algorithm is more accurate than the fourth order nonsymplectic one the capability of the symplectic nystrom method in approximately preserving the discrete energy for long time simulations is also demonstrated

on antiperiodic solutions for cohen grossberg shunting inhibitory neural networks with time varying delays and impulses in this letter a class of cohen grossberg shunting inhibitory neural networks with time varying delays and impulses is investigated sufficient conditions for the existence and exponential stability of antiperiodic solutions of such a class of neural networks are established our results are new and complementary to previously known results an example is given to illustrate the feasibility and effectiveness of our main results

positive steady states for a prey predator model with some nonlinear diffusion terms abstract this paper discusses a prey predator system with strongly coupled nonlinear diffusion terms we give a sufficient condition for the existence of positive steady state solutions our proof is based on the bifurcation theory some a priori estimates for steady state solutions will play an important role in the proof

on positive solutions of a nonlinear equilibrium boundary value problem abstract we give necessary and sufficient conditions for the existence of positive solutions to a nonlinear elliptic system arising from mathematical ecology with the dirichlet boundary data assigned by the equilibria of the corresponding ode system the main result is theorem 1 the tools are dancer fixed point index and degree theory

positive solutions for ratio dependent predator prey interaction systems abstract in this paper we study the dynamics of predator prey interaction systems between two species with ratio dependent functional responses first we provide sufficient and necessary conditions for positive steady state solutions and then we investigate the relationships between positive equilibria and positive solutions of the system over a large domain furthermore we deal with the uniqueness and the stability of positive steady states solutions with some assumptions in addition we discuss the extinction and the persistence results of time dependent positive solutions to the system

stationary patterns of strongly coupled prey predator models abstract we study some elliptic systems arising from 3 component predator prey models where cross diffusions are included in such a way that predator chases the prey and the prey runs away from the predator we establish the existence and non existence of non constant positive solutions our results show that the cross diffusions can create the stationary patterns

an acoustic wave equation for anisotropic media a wave equation derived using the acoustic medium assumption for p waves in transversely isotropic ti media with a vertical symmetry axis vti media yields a good kinematic approximation to the familiar elastic wave equation for vti media the wavefield solutions obtained using this vti acoustic wave equation are free of shear waves which significantly reduces the computation time compared to the elastic wavefield solutions for exploding reflector type applications from this vti acoustic wave equation the eikonal and transport equations that describe the ray theoretical aspects of wave propagation in a ti medium are derived these equations based on the acoustic assumption shear wave velocity 0 are much simpler than their elastic counterparts yet they yield an accurate description of traveltimes and geometrical amplitudes numerical examples prove the usefulness of this acoustic equation in simulating the kinematic aspects of wave propagation in complex ti models

a general monotone scheme for elliptic systems with applications to ecological models we consider weakly coupled elliptic systems of the type with each f i being either an increasing or a decreasing function of each u j assuming the existence of coupled super and subsolutions we prove the existence of solutions and provide a constructive iteration scheme to approximate the solutions we then apply our results to study the steady states of two species interaction in the volterra lotka model with diffusion

on the indices of fixed points of mappings in cones and applications abstract assume that k is a cone in a banach space and a k k is completely continuous we obtain a formula for the index in k of a fixed point of a under the assumption that a linearization exists and satisfies an invertibility condition we then use this formula to generalize some results of amann on the number of fixed points of a to the case where k has empty interior

coexistence problem for a prey predator model with density dependent diffusion abstract we study a prey predator model with nonlinear diffusions in a case when the spatial dimension is less than 5 a universal bound for coexistence steady states is found by using the bound and the bifurcation theory we obtain the bounded continuum of coexistence steady states

coexistence states for a diffusive one prey and two predators model with b d functional response abstract in this paper we study a diffusive one prey and two predators system with beddington deangelis functional response the sufficient and necessary conditions for the existence of coexistence states are obtained by means of the fixed point index theory in addition the stability and uniqueness of coexistence states are investigated finally we give the sufficient conditions for extinction and permanence of the time dependent system

non constant positive steady state of one resource and two consumers model with diffusion abstract in this paper a predator prey reaction diffusion system with one resource and two consumers is considered assume that one consumer species exhibits holling ii functional response while the other consumer species exhibits beddington deangelis functional response and they compete for the common resource first it is proved that the unique positive constant steady state is stable for the ode system and the reaction diffusion system second a prior estimates of positive steady state is given finally the non existence of non constant positive steady state the existence and bifurcation of non constant positive steady state are studied

qualitative analysis for a diffusive predator prey model in this paper we study the qualitative properties of a diffusive predator prey model subject to the homogeneous neumann boundary condition by a comparison argument and iteration technique under some hypotheses we prove that the positive constant steady state is globally asymptotically stable we also establish the existence and non existence of non constant positive steady states stationary patterns by use of the degree theory and the a priori estimates

periodic solutions for a kind of lienard equation with a deviating argument abstract by means of continuation theorem of coincidence degree theory we study a kind of lienard equation with a deviating argument as follows x t f x t x t g x t t x t e t some new results on the existence of periodic solutions are obtained

positive steady state solutions of a leslie gower predator prey model with holling type ii functional response and density dependent diffusion abstract in this paper we consider a leslie gower predator prey model with holling type ii functional response and density dependent diffusion under zero dirichlet boundary condition using degree theory bifurcation theory energy estimates and asymptotical behavior analysis the existence and multiplicity of positive steady state solutions were shown under certain conditions on the parameters

global attractivity in a periodic chemostat with general uptake functions a system of ode s is considered as a model of two populations competing for a nutrient where nutrient inputs and chemostat washouts are periodic as well general nutrient uptake functions which may also be time dependent and periodic are considered criteria are derived for there to exist a globally attracting positive periodic solution and a theorem on global monotonicity of attracting solutions between different systems is proved

multiple coexistence states for a prey predator system with cross diffusion abstract we study the multiple existence of positive solutions for the following strongly coupled elliptic system 1 v u u a u cv 0 in 1 u v v b du v 0 in u v 0 on where a b c d are positive constants and is a bounded domain in r n this is the steady state problem associated with a prey predator model with cross diffusion effects and u resp v denotes the population density of preys resp predators in particular the presence of represents the tendency of predators to move away from a large group of preys assuming that is small and that is large we show that the system admits a branch of positive solutions which is s or shaped with respect to a bifurcation parameter so that the system has two or three positive solutions for suitable range of parameters our method of analysis uses the idea developed by du lou j differential equations 144 1998 390 and is based on the bifurcation theory and the lyapunov schmidt procedure

positive solutions for large elliptic systems of interacting species groups by cone index methods abstract this article considers the existence of positive solutions for various systems of four nonlinear coupled elliptic partial differential equations subjected to zero dirichlet boundary conditions in applications the components can be interpreted as concentrations of four interacting populations or chemicals the species are divided into two groups which interact in prey predator or cooperating volterra lotka type of relations within each group the species can interact in other possibilities topological cone index method is used for proving the existence of positive coexistence solutions sufficient conditions are found in terms of the signs of the principal eigenvalues of various simple related operators

on the existence of dead cores for degenerate lotka volterra models in this work we study the existence and qualitative properties of non negative solutions of the lotka volterra models with nonlinear diffusion under homogeneous dirichlet boundary conditions we consider the three typical interactions prey predator competition and symbiosis unlike the linear diffusion models non trivial non negative solutions can exist which are not strictly positive sufficient conditions in terms of the coefficients involved in the setting of the models are given assuring that one species or both does not survive on a set of its habitat called dead core of positive measure

coexistence of three species in a strongly coupled elliptic system abstract a strongly coupled elliptic system which describes three interacting species with homogeneous dirichlet boundary conditions is considered it is shown that there is no coexistence state if diffusion rates are strong or if the intrinsic growth rates are slow making use of the schauder fixed point theory we derive some sufficient conditions to have a semi coexistence or a coexistence state for the strongly coupled elliptic problem moreover our results reveal that this problem possesses at least one coexistence state if cross diffusions and intra specific competitions are weak

a survey on symplectic and multi symplectic algorithms we simply review symplectic and multi symplectic algorithms in the paper these algorithms have many superiorities to general non symplectic algorithms such as they have long time behavior they can preserve the symplectic geometry structure of the hamiltonian system exactly and they can simulate original physical phenomena well some commonly used methods to construct symplectic and multi symplectic schemes are simply surveyed numerical examples are also enumerated to illustrate their performances

on nonlinear reaction diffusion systems abstract this paper presents a qualitative analysis for a coupled system of two reaction diffusion equations under various boundary conditions which arises from a number of physical problems the nonlinear reaction functions are classified into three basic types according to their relative quasi monotone property for each type of reaction functions an existence comparison theorem in terms of upper and lower solutions is established for the time dependent system as well as some boundary value problems three concrete physical systems arising from epidemics biochemistry and engineering are taken as representatives of the basic types of reacting problems through suitable construction of upper and lower solutions various qualitative properties of the solution for each system are obtained these include the existence and bounds of time dependent solutions asymptotic behavior of the solution stability and instability of nontrivial steady state solutions estimates of stability regions and finally the blowing up property of the solution special attention is given to the homogeneous neumann boundary condition

coexistence of a one prey two predators model with ratio dependent functional responses abstract we examine the positive coexistence of one prey and two competing predators in an interacting system with ratio dependent functional responses under a hostile environment furthermore we examine the extinction conditions for all three interacting species and for one or two of the three species in addition we present the biological interpretation and simulations based on the result the methods employed are a comparison argument for the elliptic problem and the fixed point theory applied to a positive cone on a banach space

the relationships between equilibria and positive solutions of certain nonlinear elliptic systems abstract letm u v 0 n u v 0 define two distinct phase curves 1 2in the u v phase plane this paper presents results on the relationships among the positive equilibria the phase curves and the existence of positive solutions to the pde system u um u v 0 v vn u v 0 in r n under dirichlet boundary conditions where is a bounded domain andm nare monotone functions

asymptotic behavior and multiplicity for a diffusive leslie gower predator prey system with crowley martin functional response abstract a diffusive predator prey system with modified leslie gower and crowley martin functional response is considered the extinction and permanence of the time dependent system are determined by virtue of the comparison principle then the sufficient and necessary conditions for the existence of coexistence states are obtained furthermore the stability uniqueness and exact multiplicity of coexistence states are investigated by means of the combination of the perturbation theory bifurcation theory and degree theory our results indicate that c 1 have an effect on the stability and exact multiplicity of coexistence states finally some numerical simulations are presented to verify and complement the theoretical results

stability of steady state solutions to a prey predator system with cross diffusion abstract this paper is concerned with a cross diffusion system arising in a prey predator population model the main purpose is to discuss the stability analysis for coexistence steady state solutions obtained by kuto and yamada j differential equations to appear we will give some criteria on the stability of these coexistence steady states furthermore we show that the hopf bifurcation phenomenon occurs on the steady state solution branch under some conditions

coupled equations for reverse time migration in transversely isotropic media reverse time migration rtm images reflectors by using time extrapolation modeling codes to synthesize source and receiver wavefields in the subsurface asymptotic analysis of wave propagation in transversely isotropic ti media yields a dispersion relation describing coupled p and sv wave modes this dispersion relation can be converted into a fourth order scalar partial differential equation pde increased computational efficiency can be achieved using equivalent coupled second order pdes analysis of the corresponding dispersion relations as matrix eigenvalue systems allows one to characterize all possible coupled linear second order systems equivalent to a given linear fourth order pde and to determine which ones yield optimally efficient finite difference implementations setting the shear velocity along the axis of symmetry to zero yields a simpler approximate ti wave equation that is more efficient to implement this simpler approximation however can become unstable for some plausible combinations of anisotropic parameters the same eigensystem analysis can be applied using finite vertical shear velocity to obtain solutions that avoid these instability problems

diffusion self diffusion and cross diffusion u1 x 0 u 1 0 x u2 x 0 u 2 0 x i n 0 where 2 n 1 2 x 2 is the laplace operator 0 is a bounded smooth domain of r n with n1 0 and 0 are the boundary and the closure of 0 respectively 0t 0 0 t and 0t 0 0 t for some t 0 is the outward unit normal vector on 0 di ai bi ci i 1 2 are all positive constants while ij i j 1 2 denote non negative constants the initial values u1 0 and u2 0 are non negative smooth func tions which are not identically zero the mathematical model 1 1 was proposed by shigesada et al 27 in their study of spatial segregation of interacting species where u1 and u2 represent the densities of two competing species d1 and d2 are their diffu sion rates a1 and a2 denote the intrinsic growth rates b1 and c2 account for intra specific competitions b2 and c1 are the coefficients of inter specific competitions 11 and 22 are usually referred as self diffusion pressures and 12 and 21 are cross diffusion pressures an interesting feature of 1 1 is that the movements of these two competing species are affected by the population pressures due to the mutual interference between the individuals and it was hoped that the nonlinear dispersive force due to the

simulation of acoustic wavefields in heterogeneous media a robust method for automatic suppression of numerical dispersion numerical dispersion limits the application of numerical simulation methods for solving the acoustic wave equation in largescalecomputation thenearlyanalyticdiscretemethodnadm and its improved version for suppressing numerical dispersion weredevelopedrecently thisnewmethodisarefinementoftwo previousmethodsandfurtherincreasestheabilityofsuppressing numerical dispersion for modeling acoustic wave propagation in 2d heterogeneous media which uses acoustic wave displacement particle velocity and their gradients to restructure the acoustic wavefield via the truncated taylor expansion and the high order interpolation approximate method for the method proposed weinvestigateitsimplementationandcompareitwith the higher order lax wendroff correction lwc scheme the original nearly analytic discrete method nadm and its improved version with regard to numerical dispersion computational costs and computer storage requirements the numerical dispersionrelationsprovidedbytherefinedalgorithmfor1dand 2d cases are analyzed as well as the numerical results obtained bythismethodagainsttheexactsolutionforthe2dacousticcase numerical results show that the refined method gives no visible numericaldispersionforverylargespatialgridincrements itcan simulatehigh frequencywavepropagationforagivengridinterval and automatically suppress the numerical dispersion when the acoustic wave equation is discretized when too few samples per wavelength are used or when models have large velocity contrasts unlike the high order lwc methods our present methodcansavesubstantialcomputationalcostsandmemoryrequirements because very large grid increments can be used the refined method can be used for the simulation of large scale wavefields

qualitative analysis of a producer scrounger model abstract in this paper we consider a producer scrounger model proposed in 6 we prove that when the trivial steady state solution or the semi trivial steady state solution to the system is stable then the system admits no positive steady state solution while if both the trial steady state solution and the semi trivial steady state solution are unstable then the system admits at least one positive steady state solution furthermore in the one dimension case we prove that the positive steady state solution if exists is unique

stability and bifurcation of a ratio dependent prey predator system with cross diffusion abstract this paper is purported to investigate a ratio dependent prey predator system with cross diffusion in a bounded domain under no flux boundary condition the asymptotical stabilities of nonnegative constant solutions are investigated to this system moreover without estimating the lower bounds of positive solutions the existence multiplicity of positive steady states are considered by using fixed points index theory bifurcation theory energy estimates and the differential method of implicit function and inverse function

positive solutions of certain nonlinear elliptic systems with self diffusions nondegenerate vs degenerate diffusions abstract we discuss the existence of positive solutions to certain strongly coupled nonlinear elliptic systems with self diffusions under homogeneous dirichlet boundary conditions using the global positive coexistence results for predator prey competition and symbiotic interactions between two species sufficient conditions for the positive solutions of the degenerate self diffusive systems are studied we also investigate the local behavior namely the local existence uniqueness and stability of positive solutions for predator prey and competition interactions our method is based on the decoupling technique and bifurcation theory

an effective imaging condition for reverse time migration using wavefield decomposition reverse time migration rtm exhibits great superiority over other imaging algorithms in handling steeply dipping structures and complicated velocity models however low frequency high amplitude noises commonly seen in a typical rtm image have been one of the major concerns because they can seriously contaminate the signals in the image if they are not handled properly we propose a new imaging condition to effectively and efficiently eliminate these specific noises from the image the method works by first decomposing the source and receiver wavefields to their one way propagation components followed by applying a correlation based imaging condition to the appropriate combinations of the decomposed wavefields we first give the physical explanation of the principle of such noises in the conventional rtm image then we provide the detailed mathematical theory for the new imaging condition finally we propose an efficient scheme for its numerical implementation it replaces the computationally intensiv

asymptotic behavior and stability of positive solutions to a spatially heterogeneous predator prey system abstract in this paper we continue to study a spatially heterogeneous predator prey system where the interaction is governed by a holling type ii functional response which has been studied in du and shi 2007 14 we further study the asymptotic profile of positive solutions and give a complete understanding of coexistence region moreover a good understanding of the number stability and asymptotic behavior of positive solutions is gained for large m finally we further compare the difference of steady state solutions between m 0 and m 0 it turns out that the spatial heterogeneity of the environment and the holling type ii functional response play a very important role in this model

global existence of solutions for a strongly coupled quasilinear parabolic system we are interested in existence uniqueness and a priori estimates of non negative solutions to the following problem begin gathered u t delta left left 1 alpha v right u right uf u v hfill v t delta v vg u v quad in 0 infty times omega hfill u v 0 quad in 0 infty times partial omega hfill u 0 u 0 v 0 v 0 quad in omega hfill end gathered 1 0

the application of high order differencing to the scalar wave equation the second order central difference is often used to approximate the derivatives of the wave equation it is demonstrated that gains in computational efficiency can be made by using high order approximations for these derivatives a one dimensional model is used to illustrate the relative accuracy of o t2 x2 o t2 x4 o t4 x4 ando t4 x10 central difference schemes for comparison o t2 ando t4 pseudospectral schemes are used as an additional measure of performance the results indicate that o t4 x10 differencing can achieve similar accuracy as the o t4 spectral scheme for practical illustration a two dimensional form of the o t4 x10 algorithm is used to compute the exploding reflector response of a salt dome model and compared with a fine grid o t2 x4 result transmissive sponge like boundary conditions are also examined and shown to be effective

turing patterns of a strongly coupled predator prey system with diffusion effects abstract the main purpose of this work is to investigate the effects of cross diffusion in a strongly coupled predator prey system by a linear stability analysis we find the conditions which allow a homogeneous steady state stable for the kinetics to become unstable through a turing mechanism in particular it is shown that turing instability of the reaction diffusion system can disappear due to the presence of the cross diffusion which implies that the cross diffusion induced stability can be regarded as the cross stability of the corresponding reaction diffusion system furthermore we consider the existence and non existence results concerning non constant positive steady states patterns of the system we demonstrate that cross diffusion can create non constant positive steady state solutions these results exhibit interesting and very different roles of the cross diffusion in the formation and the disappearance of the turing instability

strongly coupled elliptic systems and applications to lotka volterra models with cross diffusion abstract the aim of this paper is to investigate the existence and method of construction of solutions for a general class of strongly coupled elliptic systems by the method of upper and lower solutions and its associated monotone iterations the existence problem is for nonquasimonotone functions arising in the system while the monotone iterations require some mixed monotone property of these functions applications are given to three lotka volterra model problems with cross diffusion and self diffusion which are some extensions of the classical competition prey predator and cooperating ecological systems the monotone iterative schemes lead to some true positive solutions of the competition system and to quasisolutions of the prey predator and cooperating systems also given are some sufficient conditions for the existence of a unique positive solution to each of the three model problems

existence of positive solutions for a prey predator model with refuge and diffusion abstract we are concerned with a prey predator reaction diffusion model with monotonic functional response and specific refuge size we discuss both existence and nonexistence of positive solutions of the model by using fixed point index theory and bifurcation theory as the main argument tools we also discuss bifurcation solutions of which stability is established by using spectrum analysis methods moreover we analyze the effects of refuge size on the dynamics of the model

analysis of a prey predator model with disease in prey abstract in this paper a system of reaction diffusion equations arising in eco epidemiological systems is investigated the equations model a situation in which a predator species and a prey species inhabit the same bounded region and the predator only eats the prey with transmissible diseases a number of existence and non existence results about the non constant steady states of a reaction diffusion system are given it is proved that if the diffusion coefficient of the predator is treated as bifurcation parameter non constant positive steady state solutions may bifurcate from the constant steady state solution under some conditions

anisotropic wave propagation through finite difference grids an algorithm is presented to solve the elastic wave equation by replacing the partial differentials with finite differences it enables wave propagation to be simulated in three dimensions through generally anisotropic and heterogeneous models the space derivatives are calculated using discrete convolution sums while the time derivatives are replaced by a truncated taylor expansion a centered finite difference scheme in cartesian coordinates is used for the space derivatives leading to staggered grids the use of finite difference approximations to the partial derivatives results in a frequency dependent error in the group and phase velocities of waves for anisotropic media the use of staggered grids implies that some of the elements of the stress and strain tensors must be interpolated to calculate the hook sum this interpolation induces an additional error in the wave properties the overall error depends on the precision of the derivative and interpolation operators the anisotropic symmetry system its orientation and the degree of anisotropy the dispersion relation for the homogeneous case was derived for the proposed scheme since we use a general description of convolution sums to describe the finite difference operators the numerical wave properties can be calculated for any space operator and an arbitrary homogeneous elastic model in particular phase and group velocities of the three wave types can be determined in any direction we demonstrate that waves can be modeled accurately even through models with strong anisotropy when the operators are properly designed

positive solutions of a diffusive predator prey model with modified leslie gower and holling type ii schemes abstract in this paper we investigate the existence multiplicity and stability of positive solutions to a prey predator model with modified leslie gower and holling type ii schemes p u u a 1 b u c 1 v u k 1 in v v a 2 c 2 v u k 2 in u 0 v 0 in u v 0 on where r n n 1 is a bounded domain with a smooth boundary the parameters a i b c i k i i 1 2 are positive numbers u and v are the respective populations of prey and predator here we say u v with u v 0 is a positive solution of problem p if u v is a solution of p and u v 0 in

the effect of mutual interference between predators on a predator prey model with diffusion abstract we consider a diffusive predator prey model with beddington deangelis functional response under homogeneous dirichlet boundary conditions the effect of large k which represents the extent of mutual interference between predators is extensively studied by making use of the fixed point index theory we obtain a complete understanding of the existence uniqueness and stability of positive steady states when k is sufficiently large moreover we present some numerical simulations that supplement the analytic results in one dimension

coexistence theorems of steady states for predator prey interacting systems on donne des conditions necessaires et suffisantes pour l existence des solutions positives des etats stationnaires pour des systemes predateur proie sous des conditions aux limites de dirichlet sur r n

reverse time migration in acoustic vti media using a high order stereo operator abstractwith the capability of handling complicated velocity models reverse time migration rtm has become a powerful imaging method improving imaging accuracy and computational efficiency are two significant but challenging tasks in the applications of rtm despite being the most popular numerical technique applied in rtm finite difference fd methods often suffer from undesirable numerical dispersion leading to a noticeable loss of imaging resolution a new and effective fd operator called the high order stereo operator has been developed to approximate the partial differential operators in the wave equation from which a numerical scheme called the three step stereo method tsm has been developed and has shown effectiveness in suppressing numerical dispersion numerical results show that compared with the conventional numerical methods such as the lax wendroff correction lwc scheme and the staggered grid sg fd method this new method significantly reduces numerical dispersion and computati

an initial boundary value problem for a certain density dependent diffusion system on considere le systeme parabolique quasilineaire u t x c 1 d 1 v v e 1 a 1 v b 1 u u v t x c 2 d 2 u v e 2 a 2 u b 2 o v dans o t u x s 0 v x s sur o t u x o w 1 x v x o w 2 x sur ou r n est un domaine borne a frontiere lisse