periodic solutions of a periodic lotka volterra system with delays a lotka volterra periodic delay model with m predators and n preys is studied in this paper sufficient conditions for the global existence of a positive periodic solutions of this delay model are obtained by means of topological degree finally a suitable example is given to illustrate that the conditions of the main theorem are feasible

isogeometric boundary element analysis using unstructured t splines we couple collocated isogeometric boundary element methods and unstructured analysis suitable t spline surfaces for linear elastostatic problems we extend the definition of analysis suitable t splines to encompass unstructured control grids unstructured meshes and develop basis functions which are smooth rational polynomials defined in terms of the bezier extraction framework and which pass standard patch tests we then develop a collocation procedure which correctly accounts for sharp edges and corners extraordinary points and t junctions this approach is applied to several three dimensional problems including a real world t spline model of a propeller we believe this work clearly illustrates the power of combining new analysis suitable computer aided design technologies with established analysis methodologies in this case the boundary element method

dimensions of spline spaces over t meshes a t mesh is basically a rectangular grid that allows t junctions in this paper we propose a method based on bezier nets to calculate the dimension of a spline function space over a t mesh when the order of the smoothness is less than half of the degree of the spline functions a dimension formula is derived which involves only the topological quantities of the t mesh the construction of basis functions is briefly discussed furthermore the dimension formulae for t meshes after mesh operations such as edge insertion and mesh merging are also obtained

smooth cubic spline spaces on unstructured quadrilateral meshes with particular emphasis on extraordinary points geometric design and isogeometric analysis considerations abstract we present a framework for geometric design and isogeometric analysis on unstructured quadrilateral meshes acknowledging the differing requirements posed by design e g the convenience of an intuitive control net and analysis e g good approximation behavior we propose the construction of a separate smooth spline space for each while ensuring isogeometric compatibility requiring the geometric models to be members of the analysis suitable spaces the methodology is simple and is presented for bi cubic splines extensions to higher degrees are possible and are briefly discussed the presentation has been structured to show compatibility with t splines a state of the art cad technology but the approach should extend to other locally refinable spline technologies based on local tensor product structures an instantiation of the framework is presented and several numerical tests focused on geometric design and isogeometric analysis demonstrate the versatility of the developed framework and show significantly higher convergence rates than attained previously in the considered setting

a stochastic algorithm for parametric sensitivity in smoluchowski s coagulation equation in this article a stochastic particle system approximation to the parametric sensitivity in the smoluchowski coagulation equation is introduced the parametric sensitivity is the derivative of the solution to the equation with respect to some parameter where the coagulation kernel depends on this parameter it is proved that the particle system converges weakly to the sensitivity as the number of particles mathrm n increases a monte carlo algorithm is developed and variance reduction techniques are applied numerical experiments are conducted for two kernels the additive kernel and one which has been used for studying soot formation in a free molecular regime it is shown empirically that the techniques for variance reduction are indeed very effective and that the order of convergence is mathrm o 1 mathrm n the algorithm is then compared to an algorithm based on a finite difference approximation to the sensitivity and it is found that the variance of the sensitivity estimators are considerably lower than that for the finite difference approach furthermore two methods of establishing efficiency are considered and the new algorithm is found to be significantly more efficient

isogeometric analysis of high order partial differential equations on surfaces we consider the numerical approximation of high order partial differential equations pdes defined on surfaces in the three dimensional space with particular emphasis on closed surfaces we consider computational domains that can be represented by b splines or nurbs as for example the sphere and we spatially discretize the pdes by means of nurbs based isogeometric analysis in the framework of the standard galerkin method we numerically solve benchmark laplace beltrami problems of the fourth and sixth order as well as the corresponding eigenvalue problems with the goal of analyzing the role of the continuity of the nurbs basis functions on closed surfaces in this respect we show that the use of globally high order continuous basis functions as allowed by the construction of periodic nurbs leads to the efficient solution of the high order pdes finally we consider the numerical solution of high order phase field problems on closed surfaces namely the cahn hilliard and crystal equations

global periodic solutions of a generalized n species gilpin ayala competition model abstract in this paper we investigate a generalized n species gilpin ayala competition system with several deviating arguments in periodic environment which is more general and more realistic than the classical lotka volterra competition systems by using the method of coincidence degree a set of easily verifiable sufficient conditions are derived for the existence of at least one strictly positive componentwise periodic solution some new results are obtained as applications we also apply our main results to some special cases of the system we consider here including the classical n species lotka volterra competition systems and n species gilpin ayala competition model which have been studied extensively in the literature some known results are improved and generalized the examples show that our criteria are new general and easily verifiable

a fully locking free isogeometric approach for plane linear elasticity problems a stream function formulation in this paper we study plane incompressible elastic problems by means of a stream function formulation such that a divergence free displacement field can be computed from a scalar potential the numerical scheme is constructed within the framework of nurbs based isogeometric analysis and we take advantage of the high continuity guaranteed by nurbs basis functions in order to obtain the displacement field from the potential differentiation as a consequence the obtained numerical scheme is automatically locking free in the presence of the incompressibility constraint a discontinuous galerkin approach is proposed to deal with multiple mapped possibly multiply connected domains extensive numerical results are provided to show the method capabilities 2007 elsevier b v all rights reserved

solving the triharmonic equation over multi patch planar domains using isogeometric analysis abstract we present a framework for solving the triharmonic equation over bilinearly parameterized planar multi patch domains by means of isogeometric analysis our approach is based on the construction of a globally c 2 smooth isogeometric spline space which is used as discretization space the generated c 2 smooth space consists of three different types of isogeometric functions called patch edge and vertex functions all functions are entirely local with a small support and numerical examples indicate that they are well conditioned the construction of the functions is simple and works uniformly for all multi patch configurations while the patch and edge functions are given by a closed form representation the vertex functions are obtained by computing the null space of a small system of linear equations several examples demonstrate the potential of our approach for solving the triharmonic equation

isogeometric collocation on planar multi patch domains abstract we present an isogeometric framework based on collocation to construct a c 2 smooth approximation of the solution of the poisson s equation over planar bilinearly parameterized multi patch domains the construction of the used globally c 2 smooth discretization space for the partial differential equation is simple and works uniformly for all possible multi patch configurations the basis of the c 2 smooth space can be described as the span of three different types of locally supported functions corresponding to the single patches edges and vertices of the multi patch domain for the selection of the collocation points which is important for the stability and convergence of the collocation problem two different choices are numerically investigated the first approach employs the tensor product greville abscissae as collocation points and shows for the multi patch case the same convergence behavior as for the one patch case 1 which is suboptimal in particular for odd spline degree the second approach generalizes the concept of superconvergent points from the one patch case cf 2 3 4 to the multi patch case again these points possess better convergence properties than greville abscissae in case of odd spline degree

dimension and basis construction for c2 smooth isogeometric spline spaces over bilinear like g2 two patch parameterizations abstract a particular class of planar two patch geometries called bilinear like g 2 two patch geometries is introduced this class includes the subclass of all bilinear two patch parameterizations and possesses similar connectivity functions along the patch interface it is demonstrated that the class of bilinear like g 2 two patch parameterizations is much wider than the class of bilinear parameterizations and can approximate with good quality given generic two patch parameterizations we investigate the space of c 2 smooth isogeometric functions over this specific class of two patch geometries the study is based on the equivalence of the c 2 smoothness of an isogeometric function and the g 2 smoothness of its graph surface cf groisser and peters 2015 and kapl et al 2015 the dimension of the space is computed and an explicit basis construction is presented the resulting basis functions possess simple closed form representations have small local supports and are well conditioned in addition we introduce a subspace whose basis functions can be generated uniformly for all possible configurations of bilinear like g 2 two patch parameterizations numerical results obtained by performing l 2 approximation and solving poisson s equation indicate that already the subspace possesses optimal approximation properties

an implicit multi patch b spline interpolation for kirchhoff love space rod abstract the paper presents a novel formulation for the isogeometric analysis of assemblies of kirchhoff love space rod elements introducing a multi patch implicit g 1 formulation so that an automatic non singular stiffness operator is obtained without the need of adding continuity conditions the goal is achieved using a polar decomposition of the deformation of the first and last segments of the control polygon that allows to introduce directly the end rotations as degrees of freedom both parametric and geometric continuity can be obtained in this way we use bezier and b spline interpolations and we show that they are able to attain very good accuracy for developing a 3d exact curve element with geometric torsion pre twisted rod in the paper the performance of the multi patch elements is examined comparing the rates of convergence of the l 2 error norm for the multi patch and single patch formulations it is shown that the rate of convergence remains the same although in certain cases the accuracy is lower for the multi patch solutions

space of c2 smooth geometrically continuous isogeometric functions on planar multi patch geometries dimension and numerical experiments abstract we study the space of c 2 smooth isogeometric functions on bilinearly parameterized multi patch domains r 2 where the graph of each isogeometric function is a multi patch spline surface of bidegree d d d 5 6 the space is fully characterized by the equivalence of the c 2 smoothness of an isogeometric function and the g 2 smoothness of its graph surface cf groisser and peters 2015 kapl et al 2015 this is the reason to call its functions c 2 smooth geometrically continuous isogeometric functions in particular the dimension of this c 2 smooth isogeometric space is investigated the study is based on the decomposition of the space into three subspaces and is an extension of the work kapl and vitrih 2017 to the multi patch case in addition we present an algorithm for the construction of a basis and use the resulting globally c 2 smooth functions for numerical experiments such as performing l 2 approximation and solving triharmonic equation on bilinear multi patch domains the numerical results indicate optimal approximation order

an isogeometric analysis approach to gradient damage models continuum damage formulations are commonly used for the simulation of diffuse fracture processes implicit gradient damage models are employed to avoid the spurious mesh dependencies associated with local continuum damage models the c 0 continuity of traditional finite elements has hindered the study of higher order gradient damage approximations in this contribution we use isogeometric finite elements which allow for the construction of higher order continuous basis functions on complex domains we study the suitability of isogeometric finite elements for the discretization of higher order gradient damage approximations

periodicity in a food limited population model with toxicants and state dependent delays abstract with the help of a continuation theorem based on gaines and mawhin s coincidence degree easily verifiable criteria are established for the global existence of positive periodic solutions of a food limited population model with toxicant and state dependent delays that is du t dt u t r t a t u t j 1 m b j t u t j t u t k t c t u t j 1 m d j t u t j t u t where r t k t a t bj t dj t j 1 2 m are continuous real valued periodic functions with period 0 and r t k t a t 0 bj t dj t 0 j 1 2 m are periodic continuous functions with period 0 j j are periodic with respect to their first arguments some new results are obtained

isogeometric analysis with geometrically continuous functions on two patch geometries we study the linear space of c s smooth isogeometric functions defined on a multi patch domain r 2 we show that the construction of these functions is closely related to the concept of geometric continuity of surfaces which has originated in geometric design more precisely the c s smoothness of isogeometric functions is found to be equivalent to geometric smoothness of the same order g s smoothness of their graph surfaces this motivates us to call them c s smooth geometrically continuous isogeometric functions we present a general framework to construct a basis and explore potential applications in isogeometric analysis the space of c 1 smooth geometrically continuous isogeometric functions on bilinearly parameterized two patch domains is analyzed in more detail numerical experiments with bicubic and biquartic functions for performing l 2 approximation and for solving poisson s equation and the biharmonic equation on two patch geometries are presented and indicate optimal rates of convergence

new results on positive periodic solutions of a periodic integro differential competition system considered is the periodic integro differential competition system with infinite delays recently studied by fan and wang z angew math mech 81 2001 197 using the method of coincidence degree we present another set of sufficient conditions for the existence of positive componentwise periodic solutions of the system our results improve and supplement those obtained by fan and wang z angew math mech 81 2001 197

existence and global attractivity of an almost periodic ecological model the almost periodic lotka volterra model with m predators and n preys is considered in this paper by constructing suitable lyapunov function some sufficient conditions are obtained for the existence and global attractivity of a unique positive almost periodic solution of this model examples show that our criteria are new general and easily verifiable

global attractivity of the periodic lotka volterra system a lotka volterra periodic model withm predators andn preys is studied in this paper a set of easily verifiable sufficient conditions that guarantee the existence uniqueness and global attractivity of the positive periodic solutions is obtained finally a suitable example is given to illustrate that the conditions of the main theorem are feasible

the qualitative analysis of n species nonlinear prey competition systems in this paper we consider an n species nonlinear prey competition system using the differential inequality theorem and the v function method we obtain some sufficient conditions for the permanence and global asymptotic stability of the system

isogeometric analysis of large deformation thin shells using rht splines for multiple patch coupling we present an isogeometric thin shell formulation for multi patches based on rational splines over hierarchical t meshes rht splines nitsche s method is employed to efficiently couple the patches the rht splines have the advantages of allowing a computationally feasible local refinement are free from linear dependence possess high order continuity and satisfy the partition of unity and non negativity in addition the c1c1 continuity of the rht splines avoids the rotational degrees of freedom the good performance of the present method is demonstrated by a number of numerical examples

a different consideraton about the globally asymptotically stable solution of the periodic n competing species problem abstract we consider the volterra lotka equations for n competing species n 2 in which the right hand sides are periodic in time we show that conditions given by k gopalsamy j austral math soc ser b 27 1985 66 72 which imply the existence of a periodic solution with positive components also imply the uniqueness and asymptotic stability of the solution

isogeometric analysis for sixth order boundary value problems of gradient elastic kirchhoff plates abstract sixth order boundary value problems of a one parameter gradient elastic kirchhoff plate model are formulated in a weak form within an h 3 sobolev space setting with the corresponding equilibrium equations and general boundary conditions the corresponding conforming galerkin method is proposed with error estimates for discretizations satisfying c 2 continuity requirements continuity coercivity and consistency of the corresponding bilinear form are utilized for proving the theoretical results numerical computations with conforming isogeometric discretizations of c p 1 continuous nurbs basis functions of order p 3 confirm the theoretical results and illustrate the features of the problem for both statics and free vibrations in particular the effects of the additional boundary conditions and parameter dependent boundary layers corresponding to the gradient elasticity theory are addressed by the numerical examples

isogeometric analysis with geometrically continuous functions on planar multi patch geometries abstract we generate a basis of the space of bicubic and biquartic c 1 smooth geometrically continuous isogeometric functions on bilinear multi patch domains r 2 the basis functions are obtained by suitably combining c 1 smooth geometrically continuous isogeometric functions on bilinearly parameterized two patch domains cf 18 they are described by simple explicit formulas for their spline coefficients these c 1 smooth isogeometric functions possess potential for applications in isogeometric analysis which is demonstrated by several examples such as the biharmonic equation in particular the numerical results indicate optimal approximation power

space of c 2 smooth geometrically continuous isogeometric functions on two patch geometries abstract the space of c 2 smooth geometrically continuous isogeometric functions on bilinearly parameterized two patch domains is considered the investigation of the dimension of the spaces of biquintic and bisixtic c 2 smooth geometrically continuous isogeometric functions on such domains is presented in addition c 2 smooth isogeometric functions are constructed to be used for performing l 2 approximation and for solving triharmonic equation on different two patch geometries the numerical results indicate optimal approximation order

nonautonomous lotka volterra systems with delays abstract the paper studies the general nonautonomous lotka volterra multispecies systems with finite delays the ultimate boundedness permanence global attractivity and existence and uniqueness of strictly positive solutions positive periodic solutions and almost periodic solutions are obtained these results are basically an extension of the known results for nonautonomous lotka volterra multispecies systems without delay to systems with delay

on a nonlinear nonautonomous predator prey model with diffusion and distributed delay in this paper a nonlinear nonautonomous predator prey model with diffusion and continuous distributed delay is studied where all the parameters are time dependent the system which is composed of two patches has two species the prey can diffuse between two patches but the predator is confined to one patch we first discuss the uniform persistence and global asymptotic stability of the model after that by constructing a suitable lyapunov functional some sufficient conditions for the existence of a unique almost periodic solution of the system are obtained an example shows the feasibility of our main results

multi degree smooth polar splines a framework for geometric modeling and isogeometric analysis we develop a multi degree polar spline framework with applications to both geometric modeling and isogeometric analysis first multi degree splines are introduced as piecewise non uniform rational b splines nurbs of non uniform or variable polynomial degree and a simple algorithm for their construction is presented then an extension to two dimensional polar configurations is provided by means of a tensor product construction with a collapsed edge suitable combinations of these basis functions encoded in a so called isogeometric analysis suitable extraction operator yield ckck smooth polar splines for any k 0k 0 we show that it is always possible to construct a set of smooth polar spline basis functions that form a convex partition of unity and possess locality explicit constructions for k 0 1 2 k 0 1 2 are presented optimal approximation behavior is observed numerically and examples of applications to free form design smooth hole filling and high order partial differential equations demonstrate the applicability of the developed framework

positive periodic solutions of neutral lotka volterra system with feedback control with the help of a continuation theorem based on gaines and mawhin s coincidence degree easily verifiable criteria are established for the global existence of positive periodic solutions of neutral lotka volterra system with periodic delays and feedback control our results extend and improve existing results and have further applications in population dynamics

sufficient conditions for the existence positive periodic solutions of a class of neutral delay models with feedback control with the help of a continuation theorem based on gaines and mawhin s coincidence degree easily verifiable criteria are established for the global existence of positive periodic solutions of a neutral model with periodic delays and feedback controldndt n t a t email protected t n t email protected i 1nb i t n email protected i t email protected i 1nc i t n email protected i t email protected t u t email protected i 1nd i t u email protected i t dudt e t u t f t n t email protected i 1ng i t n email protected i t our results extend and improve existing results and have further applications in population dynamics

global asymptotic stability of a periodic ecological model the periodic lotka volterra model with m predators and n preys is considered in this paper under the suppose that the intrinsic growth rate of the prey species may be negative while the total intrinsic growth rate in a period are positive sufficient conditions are obtained for existence and global asymptotic stability of the periodic solution of this model

positive periodic solutions of neutral lotka volterra system with periodic delays in this paper several sufficient conditions are investigated for the existence of positive periodic solutions of a general neutral lotka volterra system with unbounded delays by using the theory of coincidence degree our results extend and improve existing results and have further applications in population dynamics

periodic solutions for delay lotka volterra competition systems abstract by using the continuation theorem of coincidence degree theory sufficient and realistic conditions are obtained for the existence of positive periodic solutions for the periodic distributed delay lotka volterra competition system du i t dt u i t r i t a ii t u i t j 1 j i n a ij t 0 t ij k ij s u j t s ds i 1 2 n and the periodic state dependent delay lotka volterra competition system du i t dt u i t r i t a ii t u i t j 1 j i n a ij t u j t j t u 1 t u n t i 1 2 n where ri aii 0 aij 0 j i i j 1 2 n are continuous periodic functions tij 0 j i i j 1 2 n kij c tij 0 0 0 tijkij s ds 1 j i i j 1 2 n i c rn 1 r and i i 1 2 n are periodic with respect to their first arguments respectively

c1 finite elements on non tensor product 2d and 3d manifolds geometrically continuous gk constructions naturally yield families of finite elements for isogeometric analysis iga that are ck also for non tensor product layout this paper describes and analyzes one such concrete c1 geometrically generalized iga element short giga element that generalizes bi quadratic splines to quad meshes with irregularities the new giga element is based on a recently developed g1 surface construction that recommends itself by its a b spline like control net low least polynomial degree good shape properties and reproduction of quadratics at irregular extraordinary points remarkably for poisson s equation on the disk using interior vertices of valence 3 and symmetric layout we observe o h3 convergence in the l norm for this family of elements numerical experiments confirm the elements to be effective for solving the trivariate poisson equation on the solid cylinder deformations thereof a turbine blade modeling and computing geodesics on smooth free form surfaces via the heat equation for solving the biharmonic equation on the disk and for koiter type thin shell analysis

periodicity in a logistic type system with several delays with the help of a continuation theorem based on gaines and mawhin s coincidence degree easily verifiable criteria are established for the global existence of positive periodic solutions of the following several delays logistic type system du t dt u t a t j 1mb j t u t t j t q j where a t b j t are positive periodic continuous functions with periodic w 0 t j t are nonnegative continuous periodic functions with periodic w 0 after that by constructing a suitable lyapunov functional some sufficient conditions which guarantee the stability of the positive periodic solutions are obtained

existence uniqueness and stability of positive periodic solution for a nonlinear prey competition model with delays a nonlinear periodic predator prey model with m preys and n m predators and delays is proposed in this paper which can be seen as the modification of the traditional lotka volterra prey competition model sufficient conditions which guarantee the existence of a unique globally attractive positive periodic solution of the system are obtained

on the periodic solutions of periodic multi species competitive systems with delays the paper considers general n species periodic kolmogorov competitive systems of functional differential equations with finite or infinite delays applying schauder s fixed point theorem a criterion on the existence of the positive periodic solutions is established as applications the existence and global asymptotic stability of the single species logistic periodic model and n species lotka volterra type periodic model with delays are discussed