positive solutions of a predator prey model with cross diffusion abstract in this paper we consider the positive solutions for a predator prey model with cross diffusion and holling type ii functional response in particular the existence of positive solutions can be established by the bifurcation theory moreover the uniqueness and the exact number of positive solutions is studied when the parameter m is large furthermore for large cross diffusion rate with the spatial dimension is less than 5 we can derive the corresponding limit systems and also study the asymptotic behavior of positive solutions finally some numerical simulations are presented to supplement the analysis results in one dimension case this results give us some important information on the structure of positive solutions

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

dimension estimate of almost periodic attractors by simultaneous diophantine approximation abstract in this paper we estimate fractal dimensions of almost periodic trajectories for a semilinear parabolic partial differential equation u t d t u g t u f t where we assume periodicity d t 1 d t g t 2 g t for irrational numbers 1 2 which are linearly independent over the rationals and f t 1 equals f t by using simultaneous diophantine approximation we can show that the dimension of the almost periodic attractor is majorized by 1 1 2 2 where 1 is the minimum number of the exponents of holder s conditions on the periodic functions and 2 is the secondary minimum

existence and stability of periodic solutions for parabolic systems with time delays this paper is concerned with the existence and stability time periodic solutions for a class of coupled parabolic equations with time delay and time delays may appear in the nonlinear reaction functions the existence of time periodic solutions is for a class of locally lipschitz continuous reaction functions without any quasimonotone requirement our approach to the problem is by the method of upper and lower solution and using schauder fixed point theorem some methods for proving the stability of the periodic solution are also given the results for the general system can be applied to the standard parabolic equations without time delay and corresponding ordinary differential system finally a model arising from chemistry is used to illustrate the obtained results

voronoi delaunay analysis of voids in systems of nonspherical particles the voronoi network is known to be a useful tool for the structural description of voids in the packings of spheres produced by computer simulations in this article we extend the voronoi delaunay analysis to packings of nonspherical convex objects main properties of the voronoi network which are known for systems of spheres are valid for systems of any convex objects a general numerical algorithm for calculation of the voronoi network in three dimensions is proposed it is based on the calculation of the trajectory of the imaginary empty sphere of variable size moving inside a system the delaunay empty sphere method analysis of voids is presented for an ensemble of random straight lines and for a molecular dynamics model of liquid crystal the spatial distribution of voids and a simple percolation analysis are obtained the distributions of the bottleneck radii and the radii of spheres inscribed in the voids are calculated

tetrahedral mesh generation based on node insertion in crystal lattice arrangements and advancing front delaunay triangulation a method of unstructured technical mesh generation for general three dimensional domains is presented a conventional boundary representation is adopted as the basis for the description of solids with evolving geometry and topology the geometry of the surfaces is represented either analytically or by piecewise polynominal interpolation a preliminary surface mesh is generated by an advancing front method with the nodes inserted by hard sphere packing in physical space in accordance with a prescribed mesh density interior nodes are inserted in a face centered cubic fcc crystal lattice arrangements coupled to octree spatial subdivision with the local lattice parameter determined by a prespecified nodal density function prior to triangulation of the volume the preliminary surface mesh is preprocessed by a combination of local transformations and subdivisions in order to guarantee that the surface triangulation be a subcomplex of the volume delaunay triangulation a joint delaunay triangulation of the interior and boundary nodes which preserves the modified surface mesh is then constructed via an advancing front approach the resulting mesh is finally improved upon by the application of local transformations the overall time complexity of the mesher is o n log n the robustness and versatility of the approach as well as the good quality of the resulting meshes is demostrated with the aid of selected examples

a multigrid method with unstructured adaptive grids for steady euler equations the multigrid method based on multi stage jacobi relaxation earlier developed by the authors for structured grid calculations with euler equations is extended to unstructured grid applications the meshes are generated with delaunay triangulation algorithms and are adapted to the flow solution

critical points on the boundaries of siegel disks let be a polynomial map of the riemann sphere of degree at least two we prove that if has a siegel disk g on which the rotation number satisfies a diophantine condition then the boundary of g contains a critical point

periodic solutions of quasilinear parabolic systems with nonlinear boundary conditions abstract this paper is concerned with the existence of maximal and minimal periodic solutions of a class of quasilinear parabolic systems with nonlinear boundary conditions our approach to the problem is based on the method of upper and lower solutions and its associated monotone iterations an application is also made to the reaction diffusion system of lotka volterra competition model

the voronoi tessellation generated from eigenvalues of complex random matrices the voronoi froth generated from eigenvalues of asymmetric complex random matrices is studied by numerical simulation it is more regular than the random voronoi froth irvf generated from a poisson process the existence of a unique tessellation called here random matrix voronoi froth rmvf follows from the universality of the distribution of eigenvalues which is also briefly commented on the geometrical and topological properties of the rmvf have been characterised an empirical and accurate distribution function is also proposed for the cell side length of a rvf deviations from the aboav weaire law are discussed their magnitude may be interpreted as a measure ofthe departure from an equilibrium structure in the frame of the statistical crystallography theory of rivier

structure of simple liquids as a percolation problem on the voronoi network analysis of the mutual arrangements of delaunay simplices is formulated as a site correlated percolation problem on the voronoi network typical cluster configurations of simplices of tetrahedral and octahedral form the main structural elements of simple liquids are found and percolation thresholds for them are obtained

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

the atomic strain tensor abstract a definition of the local atomic strain increments in three dimensions and an algorithm for computing them is presented an arbitrary arrangement of atoms is tessellated into delaunay tetrahedra identifying interstices and voronoi polyhedra identifying atomic domains the deformation gradient increment tensor for interstitial space is obtained from the displacement increments of the corner atoms of delaunay tetrahedra the atomic site strain increment tensor is then obtained by finding the intersection of the delaunay tetrahedra with the voronoi polyhedra accumulating the individual deformation gradient contributions of the intersected delaunay tetrahedra into the voronoi polyhedra an example application is discussed showing how the atomic strain clarifies the relative local atomic movement for a polymeric glass treated at the atomic level

rapid and accurate computation of the distance function using grids we present two fast and simple algorithms for approximating the distance function for given isolated points on uniform grids the algorithms are then generalized to compute the distance to piecewise linear objects by incorporating the geometry of huygens principle in the reverse order with the classical viscosity solution theory for the eikonal equation u 1 the algorithms become almost purely algebraic and yield very accurate approximations the generalized closest point formulation used in the second algorithm provides a framework for further extension to compute the distance accurately to smooth geometric objects on different grid geometries without the construction of the voronoi diagrams this method provides a fast and simple translator of data commonly given in computational geometry to the volumetric representation used in level set methods

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

asymptotic behavior of solutions of a periodic diffusion system this paper deals with a periodic reaction diffusion system of plankton allelopathy under homogeneous neumann boundary conditions based on the result of ahmad and lazer we show some estimates and nonexistence results for the positive solutions of the system furthermore we investigate the asymptotic behavior of the solutions of the system that is one species dies out and the other exists as time t tends to infinity

stability and attractivity of periodic solutions of parabolic systems with time delays abstract this paper is concerned with the existence stability and global attractivity of time periodic solutions for a class of coupled parabolic equations in a bounded domain the problem under consideration includes coupled system of parabolic and ordinary differential equations and time delays may appear in the nonlinear reaction functions our approach to the problem is by the method of upper and lower solutions and its associated monotone iterations the existence of time periodic solutions is for a class of locally lipschitz continuous reaction functions without any quasimonotone requirement using schauder fixed point theorem while the stability and attractivity analysis is for quasimonotone nondecreasing and mixed quasimonotone reaction functions using the monotone iterative scheme the results for the general system are applied to the standard parabolic equations without time delay and to the corresponding ordinary differential system applications are also given to three lotka volterra reaction diffusion model problems and in each problem a sufficient condition on the reaction rates is obtained to ensure the stability and global attractivity of positive periodic solutions

periodic solutions of parabolic systems with time delays existence of maximal and minimal periodic solutions of a coupled system of parabolic equations with time delays and with nonlinear boundary conditions is discussed the proof of the existence theorem is based on the method of upper and lower solutions and its associated monotone iterations this method is constructive and can be used to develop a computational algorithm for numerical solutions of the periodic parabolic system an application is given to a competitor competitor mutualist model which consists of a coupled system of three reaction diffusion equations with time delays

diophantine conditions imply critical points on the boundaries of siegel disks of polynomials let f be a polynomial map of the riemann sphere of degree at least two we prove that if f has a siegel disk g on which the rotation number satisfies a diophantine condition then either the boundary b of g contains a critical point or b is a lakes of wada indecomposable continuum with one of the lakes containing a critical point consequently if the boundary b of g has only 2 complementary domains then b contains a critical point we also show without any assumption on the rotation number that each proper nondegenerate subcontinuum of the boundary b of g is tree like and any other bounded complementary domain of b is a preperiodic component of the grand orbit of g finally we establish some conditions under which b contains no periodic point

temporal evolution of the domain structure in a poisson voronoi nucleation and growth transformation results for one and three dimensions the distribution of spatial domain structures originated during one and three dimensional poisson voronoi transformations are computed analytically extending the recently obtained results for the two dimensional case the presented method gives a full description of the developed microstructure and is valid for tessellations of any dimensionality the temporal and spatial dependences of the domain structure are completely discriminated and separated showing the existence of geometric configurations independent of time a single computation of the probability distribution of these geometric configurations allows us to calculate the total free boundary and size probability distributions at any desired time the obtained results show full agreement with stochastic simulations and reproduce completely the previously existing partial results a discussion about the potential applications of the method to the calculation of other geometrical properties and the characteristics of the final static structure leading to a gamma distribution of sizes is also presented

on the size distribution of poisson voronoi cells abstract poisson voronoi diagrams are useful for modeling and describing various natural patterns and for generating random lattices although this particular space tessellation is intensively studied by mathematicians in two and three dimensional 3d spaces there is no exact result known for the size distribution of voronoi cells motivated by the simple form of the distribution function in the 1d case a simple and compact analytical formula is proposed for approximating the voronoi cell s size distribution function in the practically important 2d and 3d cases as well denoting the dimensionality of the space by d d 1 2 3 the f y const y 3 d 1 2 exp 3 d 1 y 2 compact form is suggested for the normalized cell size distribution function by using large scale computer simulations the viability of the proposed distribution function is studied and critically discussed

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

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

mesh duality and legendre duality we describe a sense in which mesh duality is equivalent to legendre duality that is a general pair of meshes which satisfy a definition of duality for meshes are shown to be the projection of a pair of piecewise linear functions that are dual to each other in the sense of a legendre dual transformation in applications the latter functions can be a tangent plane approximation to a smoother function and a chordal plane approximation to its legendre dual convex examples include one from meteorology and also the relation between the delaunay mesh and the voronoi tessellation the latter are shown to be the projections of tangent plane and chordal approximations to the same paraboloid

detecting structure in two dimensions combining voronoi tessellation and percolation conventional source detection algorithms in high energy astrophysics and other fields mostly use spherical or quadratic sliding windows of varying size on two dimensionally binned representations of spatial event distributions in order to detect statistically significant event enhancements sources within a given field while this is a reasonably reliable technique for nearly pointlike sources with good statistics poor and extended sources are likely to be incorrectly assessed or even missed at all as the calculations are governed by nonphysical parameters like the bin size and the window geometry rather than by the actual data the approach presented here does not introduce any artificial bias but makes full use of the unbinned two dimensional event distribution a voronoi tessellation on a finite plane surface yields individual densities or fluxes for every single event the distribution of which allows the determination of the contribution from a random poissonian background field noise the application of a nonparametric percolation to the tessellation cells exceeding this noise level leads directly to a source list which is free of any assumptions about the source geometry high density fluctuations from the random background field will still be included in this tentative source list but can be easily eliminated in most cases by setting a lower threshold to the required number of events per source since no finite size detection windows or the like have been used this analysis yields automatically straightforward fluxes for every source finally accepted the main disadvantage of this approach is the considerable cpu time required for the construction of the voronoi tessellation it is thus applicable only to either small fields or low event density regions

about the delaunay voronoi tesselation abstract the topological description of the neighborhood of the constituing atoms in a dense random material liquids glasses is of a major importance for their characterization we discuss an algorithm for the delaunay construction which is global and independent of the dimension of the space and derive from it the full dual voronoi tesselation by an original realization of duality

covolume techniques for anisotropic media the covolume method a new approach applicable on general meshes is extended to discretize and numerically solve the div curl system in anisotropic media the covolume method gives simple schemes and good approximations to the solution of the div curl system it works directly with the system and utilizes dual pairs of meshes that are orthogonally related central to the approach is the introduction of field components tangent and normal to the edges of one of the meshes and the employment of dual discretization on the dual mesh pairs the discretization procedures schemes and error analysis are presented the convergence of the method is proved

variational delaunay approach to the generation of tetrahedral finite element meshes we describe an algorithm which generates tetrahedral decomposition of a general solid body whose surface is given as a collection of triangular facets the principal idea is to modify the constraints in such a way as to make them appear in an unconstrained triangulation of the vertex set apriori the vertex set positions are randomized to guarantee existence of a unique triangulation which satisfies the delaunay empty sphere property algorithms for robust parallelized construction of such triangulations are available in order to make the boundary of the solid appear as a collection of tetrahedral faces we iterate two operations edge flip and edge split with the insertion of additional vertex until all of the boundary facets are present in the tetrahedral mesh the outcome of the vertex insertion is another triangulation of the input surfaces but one which is represented as a subset of the tetrahedral faces to determine if a constraining facet is present in the unconstrained delaunay triangulation of the current vertex set we use the results of rajan which re formulate delaunay triangulation as a linear programming problem

digital topology and geometry in medical imaging a survey digital topology and geometry refers to the use of topologic and geometric properties and features for images defined in digital grids such methods have been widely used in many medical imaging applications including image segmentation visualization manipulation interpolation registration surface tracking object representation correction quantitative morphometry etc digital topology and geometry play important roles in medical imaging research by enriching the scope of target outcomes and by adding strong theoretical foundations with enhanced stability fidelity and efficiency this paper presents a comprehensive yet compact survey on results principles and insights of methods related to digital topology and geometry with strong emphasis on understanding their roles in various medical imaging applications specifically this paper reviews methods related to distance analysis and path propagation connectivity surface tracking image segmentation boundary and centerline detection topology preservation and local topological properties skeletonization and object representation correction and quantitative morphometry a common thread among the topics reviewed in this paper is that their theory and algorithms use the principle of digital path connectivity path propagation and neighborhood analysis

local bisection refinement for n simplicial grids generated by reflection a simple local bisection refinement algorithm for the adaptive refinement of n simplicial grids is presented the algorithm requires that the vertices of each simplex be ordered in a special way re

triangle distribution and equation of state for classical rigid disks the triangle distribution function f 3 for three mutual near neighbors in the plane describes basic aspects of short range order and statistical thermodynamics in two dimensional many particle systems this paper examines prospects for constructing a self consistent calculation for the rigid disk system f 3 we present several identities obeyed by f 3 a rudimentary closure suggested by scaled particle theory is introduced in conjunction with three of the basic identities this closure leads to an unique f 3 over the entire density range the pressure equation of state exhibits qualitatively correct behaviors in both the low density and the close packed limits but no intervening phase transition appears we discuss extensions to improved disk closures and to the three dimensional rigid sphere system

are there critical points on the boundaries of singular domains generalizing a result of e ghys we prove a general theorem that implies that if a rational functionf of the riemann sphere of degree 2 leaves invariant a singular domainc a disk or a ring on which the rotation number off satisfies a diophantine condition provided that on bar c f is injective then each boundary component ofc contains critical point off the injectivity condition is always satisfied for singular disks associated to linearizable periodic elliptic points off z z n a withne n 2 andae we also show that the singular disks associated to periodic elliptic points off z e az that satisfy a diophantine condition are unbounded in in the end of the paper we give a survey of the theory of iteration of entire functions of

analysis on the existence of the steady states for an ecological mathematical model with predator prey dependent functional response abstract we establish a reaction diffusion ecological mathematical model with predator prey dependent functional response and the neumann boundary conditions first we study the bifurcation solution emitting from the unique positive constant solution by considering the local bifurcation finally we mainly analyze the coexistence of the prey and predator with the help of the fixed point index theory where we use a different approach in calculating one of the fixed point indices

on positive solutions of the lotka volterra cooperating models with diffusion abstract in this paper using the existence and comparison conclusion for the time periodic quasimonotone nondecreasing systems given by pao c v and iterative method we investigate the time periodic lotka volterra cooperating model and present some existence uniqueness and nonexistence results we also use similar methods to treat the corresponding stationary system to give parallel results

periodic solutions of parabolic systems with nonlinear boundary conditions this paper is concerned with the existence and stability of periodic solutions for a coupled system of nonlinear parabolic equations under nonlinear boundary conditions the approach to the problem is by the method of upper and lower solutions and its associated monotone iterations this method leads to the existence of maximal and minimal periodic solutions which can be computed from a linear iteration process in the same fashion as for parabolic initial boundary value problems a sufficient condition for the stability of a periodic solution is also given these results are applied to three model problems arising from chemical kinetics ecology and population biology

properties of a three dimensional poisson voronoi tesselation a monte carlo study a complete statistical description of the properties of a cellular microstructure generated by a three dimensional poisson voronoi tesselation has been obtained by a rigorous computer simulation involving several hundred thousand cells a two parameter gamma distribution is found to be a good fit to the cell s face volume and surface area distributions for a sample size of several thousand cells or less a lognormal distribution can also be used to approximate these distributions the individual face area and edge length distributions are also obtained

spin models on random lattices under certain conditions phase transitions in systems with quenched disorder are expected to exhibit a dierent behaviour than in the corresponding pure system here we discuss a series of monte carlo studies of a special type of such disordered systems namely spin models dened on quenched random lattices exhibiting geometrical disorder in the connectivity of the lattice sites in two dimensions we present results for the q state potts model on random tri valent 3 planar graphs which appear quite naturally in the dynamically triangulated random surface dtrs approach to quantum gravity as well as on poissonian random lattices of voronoi delaunay type both cases q64 and 4 are discussed which in the pure model without disorder give rise to second and rst order phase transitions respectively in three dimensions results for the ising model on poissonian random lattices are briey described we conclude with a comparison of the two types of connectivity disorder with the more standard case of bond disorder and a discussion of the distinguishing dierences c 2000 elsevier science b v all rights reserved

periodic solutions of a class of degenerate parabolic system with delays this paper is concerned with a class of periodic degenerate parabolic system with time delays in a bounded domain under mixed boundary condition under locally lipschitz condition on reaction functions we apply schauder fixed point theorem to obtain the existence of periodic solutions of the periodic problem with quasi monotonicity in addition we also show that the periodic problem has a maximal and a minimal periodic solutions applications of the obtained results are also given to some nonlinear diffusion models arising from ecology

voronoi cell finite difference method for the diffusion operator on arbitrary unstructured grids voronoi cells and the notion of natural neighbours are used to develop a finite difference method for the diffusion operator on arbitrary unstructured grids natural neighbours are based on the voronoi diagram which partitions space into closest point regions the sibson and the laplace non sibsonian interpolants which are based on natural neighbours have shown promise within a galerkin framework for the solution of partial differential equations in this paper we focus on the laplace interpolant with a two fold objective first to unify the previous developments related to the laplace interpolant and to indicate its ties to some well known numerical methods and secondly to propose a voronoi cell finite difference scheme for the diffusion operator on arbitrary unstructured grids a conservation law in integral form is discretized on voronoi cells to derive a finite difference scheme for the diffusion operator on irregular grids the proposed scheme can also be viewed as a point collocation technique a detailed study on consistency is conducted and the satisfaction of the discrete maximum principle stability is established owing to symmetry of the laplace weight a symmetric positive definite stiffness matrix is realized which permits the use of efficient linear solvers on a regular rectangular or hexagonal grid the difference scheme reduces to the classical finite difference method numerical examples for the poisson equation with dirichlet boundary conditions are presented to demonstrate the accuracy and convergence of the finite difference scheme copyright 2003 john wiley sons ltd

on the statistics of area size in two dimensional thick voronoi diagrams cells of voronoi diagrams in two dimensions are usually considered as having edges of zero width however this is not the case in several experimental situations in which the thickness of the edges of the cells is relatively large in this paper the concept of a thick voronoi tessellation that is with edges of non zero width is introduced and the statistics of cell areas as thickness changes are analyzed

building blocks for quadratic julia sets we obtain results on the structure of the julia set of a quadratic polynomial p with an irrationally indifferent fixed point zo in the iterative dynamics of p in the cremer point case under the assumption that the julia set is a decomposable continuum we obtain a building block structure theorem for the corresponding julia set j j p there exists a nowhere dense subcontinuum b c j such that p b b b is the union of the impressions of a minimally invariant cantor set a of external rays b contains the critical point and b contains both the cremer point zo and its preimage in the siegel disk case under the assumption that no impression of an external ray contains the boundary of the siegel disk we obtain a similar result in this case b contains the boundary of the siegel disk properly if the critical point is not in the boundary and b contains no periodic points in both cases the julia set j is the closure of a skeleton s which is the increasing union of countably many copies of the building block b joined along preimages of copies of a critical continuum c containing the critical point in addition we prove that if p is any polynomial of degree d 2 with a siegel disk which contains no critical point on its boundary then the julia set j p is not locally connected we also observe that all quadratic polynomials which have an irrationally indifferent fixed point and a locally connected julia set have homeomorphic julia sets

coexistence and optimal control problems for a degenerate predator prey model abstract in this paper we present a predator prey mathematical model for two biological populations which dislike crowding the model consists of a system of two degenerate parabolic equations with nonlocal terms and drifts we provide conditions on the system ensuring the periodic coexistence namely the existence of two non trivial non negative periodic solutions representing the densities of the two populations we assume that the predator species is harvested if its density exceeds a given threshold a minimization problem for a cost functional associated with this process and with some other significant parameters of the model is also considered

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

population systems with nonlinear discrete diffusion terms where fi gi r r r are continuous functions which are t periodic in t and locally lipschitz continuous in xi yi and d d1 dn e e1 en are t periodic nonlinear diffusion functions in the sense of 9 that is d t x e t x are positive homogeneous in x cooperative and irreducible 9 as usual xi yi represent the population density of the species at the patch i we will assume that

nontrivial solutions of predator prey systems with small diffusion on considere le systeme elliptique non lineaire u x au bu 2 cuv pour xed d v x ev fv 2 guv d region bornee de r n on etudie comment la famille des solutions non negatives de ce systeme change quand les parametres du systeme changent

complex analytic dynamics on the riemann sphere dichotomie dynamique de fatou et julia points periodiques consequences du theoreme de montel l ensemble de julia est la fermeture de l ensemble des points periodiques repulseurs resultats classiques sur l ensemble de fatou classification de sullivan de l ensemble de fatou une condition pour le developpement sur l ensemble de julia la dynamique des polynomes l ensemble de mandelbrot et le travail de douady et hubbard le theoreme d application de riemann mesurable et la dynamique analytique

asymptotic behavior of solutions of a periodic reaction diffusion system of a three species of competition model this paper concerns a three species periodic competition system which subjects to homogeneous neumann boundary conditions using a result obtained by ahmad and lazer we give some estimates and nonexistence results for the positive solutions of the system furthermore we investigate the asymptotic behavior of the solutions of the system definitely we refer to that one species dies out and the other two coexist as time t tends to infinity

domain size distribution in a poisson voronoi nucleation and growth transformation we present an analytical result for the evolution of the domain size distribution during the growth of simultaneously nucleated domains the final stage of this transformation is the well known poisson voronoi tessellation the method can be easily extended to the calculation of the probability distribution of any other geometric characteristic as far as we know it is the first time that an exact result is given for this classic system

a new algorithm for three dimensional voronoi tessellation abstract a new efficient algorithm for computing the voronoi tessellation in three dimensions is presented the voronoi tessellation is obtained by constructing delaunay tetrahedra the complete set of these tetrahedra corresponds to that of a single voronoi polyhedron

on the construction of the voronoi mesh on a sphere abstract a new construction of the voronoi mesh on the sphere is presented the main feature is that the algorithm adds points one at a time until the final voronoi mesh is built up by adding one point to an existing voronoi mesh of k points only local changes are needed to construct a voronoi mesh of k 1 points this construction is particularly well suited to time dependent problems since using information from the voronoi mesh at the previous time step allows us to reduce the construction to o n operations when the two configurations are close while the algorithm does not break down when they are far apart numerical experiments are presented to substantiate the o n operation count for a typical case