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

coexistence states for systems of mutualist species coexistence states for a class of systems of mutualist species are obtained via bifurcation theory and monotone techniques

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

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 multiplicity and complete dynamics for a cooperative model abstract in this paper a two species cooperative model with diffusion and under homogeneous dirichlet boundary conditions is investigated it is shown the existence stability uniqueness and multiplicity of positive solutions in particular we study the global asymptotical stability of the unique positive solution when a 1 b d 1 d and is large our method of analysis is based on perturbation technique the lyapunov schmidt procedure and the bifurcation theory

stable coexistence states in the volterra lotka competition model with diffusion we study the existence uniqueness and stability of coexistence states in the lotka volterra model with diffusion for two competing species we assume that the parameters describing the interactio

codon distributions in dna the codons 64 in number are distributed over the coding parts of dna sequences the distribution function is the plot of frequency versus rank of the codons these distributions are characterized by parameters that are almost universal i e gene independent there is but a small part that depends on the gene we present the theory to calculate the universal gene independent part the part that is gene specific however has undetermined overlaps and fluctuations

multiparameter local bifurcation based on the linear part abstract in this paper we give a result in multiparameter local bifurcation theory this result is a generalization of the hopf bifurcation theorem and of a previous result by j k hale our result can be applied to fredholm operators with arbitrary index

a robust transfer matrix formulation for the ultrasonic response of multilayered absorbing media an improved version of the transfer matrix approach is presented for ultrasonic wave interaction in multilayered media generalized expressions are obtained for reflection and transmission coefficients in either fluid or solid half space and problems associated with numerical stability are solved efficiently the formulation is applicable to longitudinal and shear input waves alike at arbitrary incidence angles and for any sequence of solid or fluid layers also allowance is made for viscoelastic behavior by means of relaxation functions in the laplace transform domain finally the response to arbitrary incident pulse shapes and beam profiles is described through application of two dimensional numerical laplace inversion

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

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

a priori bounds and existence of positive solutions for semilinear elliptic systems abstract we provide a priori l bounds for classical positive solutions of semilinear elliptic systems in bounded convex domains when the nonlinearities are below the power functions v p and u q for any p q lying on the critical sobolev hyperbola our proof combines moving planes method and rellich pohozaev type identities for systems our analysis widens the known ranges of nonlinearities for which classical positive solutions of semilinear elliptic systems are a priori bounded using these a priori bounds and local and global bifurcation techniques we prove the existence of positive solutions for a corresponding parametrized semilinear elliptic system

global aspect of steady states for competitive diffusive systems with homogeneous dirichlet conditions abstract this paper is concerned with the competitive diffusive systems u t d l u xx a l b l u c l v u v t d 2 v xx a 2 b 2 u c 2 u v x t 0 1 0 with homogeneous dirichlet boundary conditions from a global bifurcation view point the dependency of steady states on the parameters a i b i c i and d i i 1 2 is investigated in particular bifurcation of coexist ence solutions amd their stabilities are our main interests

on the symbiotic lotka volterra model with diffusion and transport effects abstract in this work we analyze the existence stability and multiplicity of coexistence states for a symbiotic lotka volterra model with general diffusivities and transport effects global bifurcation theory blowing up arguments for a priori bounds singular perturbation results singularity theory and fixed point index in cones are among the techniques used to get our results and to explain the drastic change of behavior exhibited by the dynamics of the model between the cases of weak and strong mutualism between the species our methodology works out to treat much more general classes of symbiotic models

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

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 positive solutions of some pairs of differential equations ii on etudie l existence de solutions strictement positives de systemes predateur proie on demontre l unicite de la solution strictement positive dans le systeme de conway smoller

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

a sub supersolution method for nonlinear elliptic singular systems with natural growth and some applications abstract in this paper we give a sub supersolution method for nonlinear elliptic singular systems with quadratic gradient whose model system is the following u v u 2 u f 1 x u v in v u v 2 v f 2 x u v in u v 0 on where is a smooth bounded domain of r n n 3 0 0 1 and regular f 1 f 2 functions moreover we apply it to prove existence of solution for some systems including the classical lotka volterra models with gradient terms specifically we study the competition and the symbiotic lotka volterra systems

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

bifurcation for an elliptic system coupled in the linear part we study linearly coupled elliptic systems without any assumption on the signs of the coefficients of the linear part we derive first the leray schauder degree of the associated linear system then we obtain sufficient conditions on the nonlinear terms for having bifurcation to coexistence states our results include the sublinear case keys words linearly coupled elliptic systems bifurcation to positive solutions coexistence states leray schauder degree email jfleck cict fr rpardo sunma4 mat ucm es

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

transient sound fields from impacted plates comparison between numerical simulations and experiments a comparison between measured and simulated transient acoustic fields generated by a thin rectangular impacted steel plate is reported the plate vibration is modelled in the time domain using a finite difference scheme of second order in time and fourth order in space 2 4 scheme and the radiated acoustic pressure is obtained by solving numerically the rayleigh integral equation by using a simple boundary element method trapezoidal rule the simulated results are evaluated in the form of the spatial pressure distribution at times short after the impact excitation the measurements are performed using an optical method pulsed two reference beam holographic interferometry results in the form of 2 d projections of the acoustic pressure field are obtained and compared with the simulations a high degree of similarity is found between the measured and simulated sound fields

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 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

nearfield acoustic holography nah ii holographic reconstruction algorithms and computer implementation the basic theory treating steady state acoustic radiation problems in the nearfield has been presented in several articles on nearfield acoustic holography in this article the approximations and assumptions necessary to reduce the infinite and continuous convolution integrals encountered in these problems to a finite and discrete form suitable for high speed numerical processing are illuminated theoretically and tested numerically to evaluate the convolution integrals two assumptions are made first the boundary field may be replaced with a patchwise constant field for reasonably small patches and second the field is negligible outside of a finite region with these two assumptions the problem reduces to one of representing the green s functions six methods of sampling or representing the green s functions are developed and these are compared theoretically and numerically

instantaneous bayesian regularization applied to real time near field acoustic holography real time near field acoustic holography rt nah is used to recover non stationary sound sources using a planar microphone array direct propagation is described by the convolution of the wavenumber spectrum of the source under study with a known impulse response the deconvolution operation is achieved by a singular value decomposition of the propagator and tikhonov regularization is performed to stabilize the solution the inverse problem has an innate ill posed characteristic and the regularization process is the key factor in obtaining acceptable results the purpose of this paper is to present the instantaneous regularization process applied to rt nah method bayesian estimation of the regularization parameter is introduced from prior knowledge of the problem the computation of the regularization parameter is updated for each block of constant time interval allowing one to take into account the fluctuating properties of the sound field the superiority of bayesian regularization compared to state of the art methods is observed numerically and experimentally for reconstruction of non stationary sources rt nah is also enhanced to allow the reconstruction of long signals updating the regularization parameter accordingly to the fluctuations of the snr is revealed to be a necessary effort to reconstruct highly non stationary sources

poincare recurrences and multifractal properties of genomic sequences we propose the return times spectra as a tool to analyze the genomic sequences the spectra discriminate between regular chaotic and mixed dynamical systems since generally their decay follows respectively an exponential law a power law or is a linear combination of them the analysis of words of n bases from a dna sequence exhibits the same exponential behavior for the coding and noncoding component the multifractal analysis shows a denite dierence which suggests a less uniform structure for the noncoding part

multiparameter bifurcation for some particular reaction diffusion systems in some cases a reaction diffusion system can be transformed into an abstract equation where the linear part is given by a polynomial of a linear operator say multiparameter bifurcation for this equation is considered as the coefficients of the operator polynomial in are varied

universality and shannon entropy of codon usage the distribution functions of codon usage probabilities computed over all the available genbank data for 40 eukaryotic biological species and five chloroplasts are best fitted by the sum of a constant an exponential and a linear function in the rank of usage for mitochondria the analysis is not conclusive these functions are characterized by parameters that strongly depend on the total guanine and cytosine gc content of the coding regions of biological species it is predicted that the codon usage is the same in all exonic genes with the same gc content the shannon entropy for codons also strongly dependent on the exonic gc content is computed

helmholtz equation least squares method for reconstructing the acoustic pressure field a method using spherical wave expansion theory to reconstruct acoustic pressure field from a vibrating object is developed the radiated acoustic pressures are obtained by means of an expansion of independent functions generated by the gram schmidt orthonormalization with respect to the particular solutions to the helmholtz equation on the vibrating surface under consideration the coefficients associated with these independent functions are determined by requiring the assumed form of solution to satisfy the pressure boundary condition at the measurement points the errors incurred in this process are minimized by the least squares method once these coefficients are specified the acoustic pressure at any point including the source surface is completely determined in this paper this method is used to reconstruct the surface acoustic pressures based on the measured acoustic pressure signals in the field it is shown that this method can be applied to both separable and nonseparable geometries and the

regularization for improving the deconvolution in real time near field acoustic holography near field acoustic holography is a measuring process for locating and characterizing stationary sound sources from measurements made by a microphone array in the near field of the acoustic source plane a technique called real time near field acoustic holography rt nah has been introduced to extend this method in the case of nonstationary sources this technique is based on a formulation which describes the propagation of time dependent sound pressure signals on a forward plane using a convolution product with an impulse response in the time wavenumber domain thus the backward propagation of the pressure field is obtained by deconvolution taking the evanescent waves into account in rt nah improves the spatial resolution of the solution but makes the deconvolution problem ill posed and often yields inappropriate solutions the purpose of this paper is to focus on solving this deconvolution problem two deconvolution methods are compared one uses a singular value decomposition and a standard tikhonov regularization and the other one is based on optimum wiener filtering a simulation involving monopoles driven by nonstationary signals demonstrates by means of objective indicators the accuracy of the time dependent reconstructed sound field the results highlight the advantage of using regularization and particularly in the presence of measurement noise

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

forward projection of transient sound pressure fields radiated by impacted plates using numerical laplace transform forward propagation of the transient sound pressure radiated by an impacted plate is presented it is shown that direct and inverse time domain discrete fourier transforms involved in fourier transform based near field acoustical holography nah lead to aliasing errors in the reconstructed time signals adding trailing zeros to the initial time signals is an inefficient way to reduce time aliasing errors hence the numerical laplace transform is introduced and a fourier transform based transient nah tnah approach is formulated an error measure is introduced to compare both nah and tnah with respect to the propagation distance and the location of the observation point in the projection plane the percentage of error with tnah is reduced by more than a factor of 10 without adding trailing zeros to the initial signals simulation results are validated experimentally using a free plexiglas plate impacted at its center

diffusion mediated permanence problem for a heterogeneous lotka volterra competition model we analyse the dynamics of a prototype model for competing species with diffusion coefficients d 1 d 2 in a heterogeneous environment when diffusion is switched off at each point x we have a pair of ode s the kinetic if for some x kinetic has a unique stable coexistence state we show that there exist such that for every the rd model is persistent in the sense that it has a compact global attractor within the interior of the positive cone and has a stable coexistence state the same result is true if there exist x u x v such that the semitrivial coexistence states u 0 and 0 v of the kinetic are globally asymptotically stable at x x u and x x v respectively more generally our main result shows that for most kinetic patterns stable coexistence of xspopulations can be found for some range of the diffusion coefficients singular perturbation techniques monotone schemes fixed point index global analysis of persistence curves global continuation and singularity theory are some of the technical tools employed to get the previous results among others these techniques give us necessary and or sufficient conditions for the existence and uniqueness of coexistence states conditions which can be explicitly evaluated by estimating some principal eigenvalues of certain elliptic operators whose coefficients are solutions of semilinear boundary value problems we also discuss counterexamples to the necessity of the sufficient conditions through the analysis of the local bifurcations from the semitrivial coexistence states at the principal eigenvalues an easy consequence of our analysis is the existence of models having exactly two coexistence states one of them stable and the other one unstable we find that there are also cases for which the model has three or more coexistence states

coexistence and stability of a competition diffusion system in population dynamics abstract the coexistence and stability of the population densities of two competing species in a bounded habitat are investigated in the present paper where the effect of dispersion transportation is taken into consideration the mathematical problem involves a coupled system of lotka volterra type reaction diffusion equations together with some initial and boundary conditions including the dirichlet neumann and third type necessary and sufficient conditions for the coexistence and competitive exclusion are established and the effect of diffusion is explicitly given for the stability problem general criteria for the stability and instability of a steady state solution are established and then applied to various situations depending on the relative magnitude among the physical parameters also given are necessary and sufficient conditions for the existence of multiple steady state solutions and the stability or instability of each of these solutions special attention is given to the neumann boundary condition with respect to which some threshold results for the coexistence and stability or instability of the four uniform steady states are characterized it is shown in this situation that only one of the four constant steady states is asymptotically stable while the remaining three are unstable the stability or instability of these states depends solely on the relative magnitude among the various rate constants and is independent of the diffusion coefficients