fixed points of uniformly lipschitzian mappings abstract two fixed point theorems for uniformly lipschitzian mappings in metric spaces due respectively to e lifsic and to t c lim and h k xu are compared within the framework of the so called cat 0 spaces it is shown that both results apply in this setting and that lifsic s theorem gives a sharper result also a new property is introduced that yields a fixed point theorem for uniformly lipschitzian mappings in a class of hyperconvex spaces a class which includes those possessing property p of lim and xu

relaxation oscillations in a class of predator prey systems abstract we consider a class of three dimensional singularly perturbed predator prey systems having two predators competing exploitatively for the same prey in a constant environment by using dynamical systems techniques and the geometric singular perturbation theory we give precise conditions which guarantee the existence of stable relaxation oscillations for systems within the class such result shows the coexistence of the predators and the prey with quite diversified time response which typically happens when the prey population grows much faster than those of predators as an application a well known model will be discussed in detail by showing the existence of stable relaxation oscillations for a wide range of parameters values of the model

pointwise lipschitzian mappings in uniformly convex and uniformly smooth banach spaces abstract let x be a uniformly convex and uniformly smooth banach space let t c c be an asymptotic pointwise nonexpansive mapping where c is a bounded closed and convex subset of x in this paper we investigate conditions sufficient for the weak convergence of the generalized mann and ishikawa processes to a fixed point of t

remarks on competitive coexistence the asymptotic behavior of two predators competing exploitatively for the same prey in a constant environment is analyzed in this paper assuming that the prey have fast dynamics it is proved through a singular perturbation argument that the two predators can coexist if the prey and predators parameters lie within specified ranges it is also shown that coexistence occurs through a simple periodic behavior a poor season characterized by an almost endemic presence of the prey alternates with a rich season during which prey are abundant and predators regenerate this property follows from the geometric nature of the equilibrium manifold and is therefore generic the results are in agreement with some conjectures supported by computer simulation and with the most recent theoretical findings on competitive coexistence

fixed point iterations for asymptotically nonexpansive mappings in banach spaces in this paper we suggest and analyze a three step iterative scheme for asymptotically nonexpansive mappings in banach spaces the new iterative scheme includes ishikawa type and mann type interations as special cases the results obtained in this paper represent an extension as well as refinement of previous known results

a viscosity solutions approach to shape from shading the problem of recovering a lambertian surface from a single two dimensional image may be written as a first order nonlinear equation which presents the disadvantage of having several continuous and even smooth solutions a new approach based on hamilton jacobi bellman equations and viscosity solutions theories enables one to study non uniqueness phenomenon and thus to characterize the surface among the various solutions a consistent and monotone scheme approximating the surface is constructed thanks to the dynamic programming principle and numerical results are presented

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

approximating common fixed points of asymptotically nonexpansive maps in uniformly convex banach spaces we introduce three step iterative schemes with errors for two and three nonexpansive maps and establish weak and strong convergence theorems for these schemes mann type and ishikawa type convergence results are included in the analysis of these new iteration schemes the results presented in this paper substantially improve and extend the results due to s h khan h fukhar ud din weak and strong convergence of a scheme with errors for two nonexpansive mappings nonlinear anal 8 2005 1295 1301 n shahzad approximating fixed points of non self nonexpansive mappings in banach spaces nonlinear anal 61 2005 1031 1039 w takahashi t tamura convergence theorems for a pair of nonexpansive mappings j convex anal 5 1995 45 58 k k tan h k xu approximating fixed points of nonexpansive mappings by the ishikawa iteration process j math anal appl 178 1993 301 308 and h f senter w g dotson approximating fixed points of nonexpansive mappings proc amer math soc 44 1974 375 380

approximation schemes for viscosity solutions of hamilton jacobi equations abstract equations of hamilton jacobi type arise in many areas of applications including the calculus of variations control theory and differential games recently m g crandall and p l lions established the correct notion of generalized solutions for these equations this article discusses the convergence of general approximation schemes to this solution and gives under certain hypotheses explicit error estimates these results are then applied to obtain various representations as limits of solutions of general explicit and implicit finite difference schemes with error estimates

approximating fixed points of non self nonexpansive mappings in banach spaces abstract suppose k is a nonempty closed convex nonexpansive retract of a real uniformly convex banach space e with p as a nonexpansive retraction let t k e be a nonexpansive non self map with f t x k tx x suppose x n is generated iteratively by x 1 k x n 1 p 1 n x n n tp 1 n x n n tx n n 1 where n and n are real sequences in e 1 e for some e 0 1 1 if the dual e of e has the kadec klee property then weak convergence of x n to some x f t is proved 2 if t satisfies condition a then strong convergence of x n to some x f t is obtained

convergence of iterates with errors of asymptotically quasi nonexpansive mappings and applications in this paper we consider a generalized iterative process with errors to approximate the common fixed points of two asymptotically quasi nonexpansive mappings a convergence theorem has been obtained which generalizes a known result this theorem has then been used to prove another convergence theorem which in turn generalizes a number of results

a mathematical model of the chemostat with periodic washout rate in its simplest form the chemostat consists of several populations of microorganisms competing for a single limiting nutrient if the input concentration of nutrient and the washout rate are constant theory predicts and experiment confirms that at most one of the populations will survive in nature however one may expect the input concentration and washout rate to vary with time in this paper we consider a model for the chemostat with periodic washout rate conditions are found for competitive exclusion to hold and bifurcation techniques are employed to show that under suitable circumstances there will be coexistence of the competing populations in the form of positive periodic solutions

weak and strong convergence theorems for three step iterations with errors for asymptotically nonexpansive mappings abstract in the present paper several weak and strong convergence theorems are established for the three step iterative schemes with errors for asymptotically nonexpansive mappings our results extend and improve the recent ones announced by tan and xu xu and noor and many others

retracted a one step iterative process for two multivalued nonexpansive mappings in banach spaces weak and strong convergence a b s t r a c t in this paper we introduce a new one step iterative process to compute the common fixed points of two multivalued nonexpansive mappings furthermore we also prove some strong and weak convergence theorems in uniformly convex banach spaces

perpendicular distance models for line transect sampling summary perpendicular distance line transect models are examined to assess whether any single model can provide a general procedure for analysing line transect data of the two parameter models considered the hazard rate model appears promising whereas the exponential power series and exponential quadratic models do not of the nonparametric models the fourier series is the best developed and is favoured by many researchers as a general model however for a given data set the fourier series estimate may be highly dependent on the number of terms selected and so the model is not a clear improvement over the hazard rate model a similar variable term model using hermite polynomials is considered and is shown to be less dependent on the number of terms selected there has been some debate about whether the derivative of the density function of perpendicular distances evaluated at 0 should be 0 so that the function has a shoulder the problem is examined in detail and it is argued that reliable estimation is not possible from line transect data unless a shoulder exists many data sets appear to exhibit no shoulder possible reasons are examined

persistence and global stability for n species ratio dependent predator prey system with time delays abstract a n species ratio dependent predator prey food chain model with time delays is investigated it is shown that the system is permanent under some appropriate conditions and sufficient conditions are obtained for the global stability of the positive equilibrium of the system

nonparametric estimators for variable circular plot surveys a non parametric estimator of animal density d is proposed for variable circular plot surveys under the assumption that perfect radial detectability occurs at the station the estimation of d requires estimating the derivative at zero of the probability density function of the detected radial distances kernel techniques are used for that purpose

a mathematical model of the chemostat with a general class of functions describing nutrient uptake a model of the chemostat involving n microorganisms competing for a single essential growth limiting substrate is considered instead of assuming the familiar michaelis menten kinetics for nutrient uptake a general class of functions is used which includes all monotone increasing uptake functions but which also allows uptake functions that describe inhibition by the substrate at high concentrations the qualitative behaviour of this generalized model is determined analytically it is shown that the behaviour depends intimately upon certain parameters provided that all the parameters are distinct which is a biologically reaonable assumption at most one competitor survives the substrate and the surviving competitor if one exists approach limiting values thus there is competitive exclusion however unlike the standard model in certain cases the outcome is initial condition dependent

competitive exclusion and coexistence of a delayed reaction diffusion system modeling two predators competing for one prey in this work we study a time delayed reaction diffusion system with homogeneous neumann boundary conditions this system describes two predators competing for the same prey by the method of upper and lower solutions we obtain sufficient conditions for the competitive exclusion principle to hold and sufficient conditions of the global asymptotic stability of positive constant solution by taking time delay as the bifurcation parameter spatially homogeneous and inhomogeneous hopf bifurcation at the positive constant solution are proved to occur for a sequence of critical values of the delay parameter it is shown that there are three coexistence forms for the three species steady states spatial homogeneous and inhomogeneous periodic oscillations

on the variable circular plot method of estimating animal density the development by ornithologists of the variable circular plot method of estimating bird densities from observer to bird distances has led to estimation problems similar to those of line transect sampling however to apply line transect methods without modification requires that the distance data be transformed to areas by squaring the implications of this transformation on the assumed shapes for the detection curve have not been investigated in the literature this paper illustrates that application of line transect models to area data may lead to poor model performance and erroneous conclusions developments based on distance data are discussed briefly and binomial models are derived for the special case in which birds are categorised simply according to whether they are within or beyond a specified distance

a comparison theorem for a piecewise lipschitz continuous hamiltonian and application to shape from shading problems the reconstruction from a shaded image of a lambertian and not self shadowing surface illuminated by a single distant pointwise light source may be written as a first order hamilton jacobi equation in this paper we continue the investigation begun in e rouy and a tourin into the uniqueness of the solution of this equation the approach is based on the viscosity solutions theory and the dynamic programming principle more precisely we concentrate here on the uniqueness of the viscosity solution of this equation in case the measured luminous intensity reflected by the surface is discontinuous along a smooth curve we prove a general comparison result for a piecewise lipschitz continuous hamiltonian and illustrate it by numerical experiments

two approximations of solutions of hamilton jacobi equations abstract equations of hamilton jacobi type arise in many areas of application including the calculus of variations control theory and differential games the associated initial value problems almost never have global time classical solutions and one must deal with suitable generalized solutions the correct class of generalized solutions has only recently been established by the authors this article establishes the convergence of a class of difference approximations to these solutions by obtaining explicit error estimates analogous results are proved by similar means for the method of vanishing viscosity author

a concept of convergence in geodesic spaces abstract a cat 0 space is a geodesic space for which each geodesic triangle is at least as thin as its comparison triangle in the euclidean plane a notion of convergence introduced independently several years ago by lim and kuczumow is shown in cat 0 spaces to be very similar to the usual weak convergence in banach spaces in particular many banach space results involving weak convergence have precise analogues in this setting at the same time many questions remain open

fixed point and convergence theorems for different classes of generalized nonexpansive mappings in cat 0 spaces in this paper we prove the existence of common fixed points in cat 0 spaces for three different classes of generalized nonexpansive mappings including a quasi nonexpansive single valued mapping a pointwise asymptotically nonexpansive mapping and a multivalued mapping satisfying the conditions e and c l for some email protected 0 1 moreover we introduce an iterative process for these mappings and prove convergence and strong convergence theorems for such an iterative process in cat 0 spaces

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

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

zip bifurcation in a competition model on considere le systeme s s 1 s k m 1 x 1 s a 1 s m 2 x 2 s a 2 s x 1 m 1 x 1 s a 1 s d 1 w 1 x 2 m 2 x 2 s a 2 s d 2 x 2 soit i a i d i m i d i on etudie le cas 1 2

the stable coexistence of competing species on a renewable resource abstract we consider a system of three autonomous ordinary differential equations modeling two competing species for a prey resource we obtain a simple criterion in terms of the specific growth of the prey for there to be an asymptotically stable equilibrium in a special case we show that a hopf bifurcation about this equilibrium could occur in another special case we show that the interior equilibrium could be globally asymptotically stable the results are illustrated by a numerical example finally it is shown that in the general case not all competition models posess the properties described in this paper

common fixed points noor iteration for a finite family of asymptotically quasi nonexpansive mappings in banach spaces in this paper we introduce a general iteration scheme for a finite family of asymptotically quasi nonexpansive mappings the new iterative scheme includes the modified mann and ishikawa iterations three step iterative scheme of xu and noor and khan and takahashi scheme as special cases our results are generalizations as well as refinement of several known results in the current literature

fixed point results for a generalized nonexpansive map in uniformly convex metric spaces abstract in this paper the existence of a unique fixed point of a map satisfying a very general contractive condition on a suitable subset of a uniformly convex metric space is proved this fixed point is approximated by averaging krasnosel skii iterations of a generalized nonexpansive map our results substantially improve and extend several known results existing in the literature

qualitative behavior of n dimensional ratio dependent predator prey systems abstract this paper deals with the qualitative properties of an n dimensional autonomous system of differential equations modeling the general ratio dependent predator prey interaction

oscillatory coexistence in the chemostat a codimension two unfolding a nontrivial branch of stable oscillatory solutions of a two predator one prey competition model is found in the positive octant by a multiparameter bifurcation analysis the branch of solutions is global in that it is a continuous branch connecting the oscillations in each of the one predator one prey planes this result gives analytical verification of the numerical observations of other authors that a branch of nonplanar oscillations crosses the positive octant in certain parameter ranges

global dynamics of a predator weaker prey and stronger prey system abstract in this paper we propose and analyze a prey predator system consisting of two competitive prey populations and one predator population which depends on both the prey species we investigate the boundedness and persistence criteria of the system and existence conditions of all the possible equilibria further the dynamical behavior from the point of view of local and global stability at different equilibria are presented we also determine the explicit conditions so that the system has no periodic solutions finally we present some numerical examples to illustrate our analytical works

dynamics of food chain models with density dependent diffusion and ratio dependent reaction function abstract this paper is concerned with a 3 species and a 2 species food chain reaction diffusion systems in a bounded domain where the diffusion coefficients may be density dependent and the reaction functions are ratio dependent these equations are quasilinear where the diffusion coefficients may be degenerate on the boundary of the domain three basic types of dirichlet neumann and robin boundary conditions are considered and in each case some very simple conditions are obtained to ensure the dynamical behavior of the time dependent solution in relation to some positive solutions or quasi solutions of the steady state problem including the existence of these solutions this dynamical behavior leads to the coexistence and global attractor of the food chain systems in the case of neumann boundary condition sufficient conditions are given to ensure that the steady state problem has a unique positive constant solution which is a global attractor of the time dependent system

on δ convergence theorems in cat 0 spaces by using the concept of convergence introduced by lim t c lim remarks on some fixed point theorems proc amer math soc 60 1976 179 182 we are able to give the cat 0 space analogs of results on weak convergence of the picard mann and ishikawa iterates proved in uniformly convex banach spaces by opial z opial weak convergence of the sequence of successive approximations for nonexpansive mappings bull amer math soc 73 1967 591 597 ishikawa s ishikawa fixed points and iteration of a nonexpansive mapping in a banach space proc amer math soc 59 1976 65 71 and tan and xu k k tan h k xu approximating fixed points of nonexpansive mappings by the ishikawa iteration process j math anal appl 178 1993 301 308

low and high frequency oscillations in three dimensional food chain systems the dynamic behavior of a three trophic level food chain prey predator superpredator is analyzed in this paper prey is logistic while predator and superpredator have functional response of the holling type moreover the trophic levels are assumed to be characterized by increasing and quite diversified time responses using a singular perturbation approach explicit conditions for the persistence of the three populations are derived and the structure of the corresponding attractors is noted as well as the nature of transients the analysis shows that the system can have low frequency cycles due to the interactions between predator and superpredator nevertheless the interactions between prey and predator can give rise to high frequency oscillations which can arise during the transients toward the attractor or during the low frequency cycle this periodic burst of high frequency oscillations develops in particular when the two predators are fairly efficient these results note in a very concise w

stability analysis of predator prey models involving cross diffusion abstract in this paper we have considered a three dimensional system of partial differential equations to model the dynamical interactions of two predators competing for a single prey the model is developed by introducing cross diffusion in such a way as to take into account the migratory strategy adopted by the predators who take advantage of the defense switching behavior of the prey equilibria of the model are determined and a local stability analysis is discussed the main result presented here is that for certain range of values of the cross diffusion parameters the system has a continuum of equilibria and a zip type bifurcation occurs and this is not sustainable due to the emergence of turing type instability

strong convergence theorems for multivalued nonexpansive nonself mappings in banach spaces abstract let e be a uniformly convex banach space with a uniformly g teaux differentiable norm c a nonempty closed convex subset of e and t c k e a nonexpansive mapping for u c and t 0 1 let x t be a fixed point of a contraction g t c k e defined by g t x t t x 1 t u x c it is proved that if c is a nonexpansive retract of e x t is bounded and t z z for any fixed point z of t then the strong lim t 1 x t exists and belongs to the fixed point set of t furthermore we study the strong convergence of x t with the weak inwardness condition on t in a reflexive banach space with a uniformly g teaux differentiable norm

n dimensional ratio dependent predator prey systems with diffusion abstract this paper deals with a ratio dependent predator prey system with diffusion we will investigate under what conditions turing stability or instability occurs in higher dimensions

numerical shape from shading for discontinuous photographic images the height u x y of a continuous lambertian surface of known albedo i e grayness is related to u x y information recoverable from a black and white flash photograph of the surface by the partial differential equation sqrt u 2 x u 2 y n 0 we review the notion of a unique viscosity solution for this equation when n is continuous and a recent unique extension of the viscosity solution when n is discontinuous we prove convergence to this extension for a wide class of the numerical algorithms that converge when n is continuous after discussing the properties of the extension and the order of error in the algorithms simulating the extension we point out warning signs which when observed in the numerical solution usually indicate that the surface is not continuous or that the viscosity solution or its extension does not correspond to the actual surface finally we discuss a method that in some of these cases allows us to correct the simulation and recover the actual surface again

on the dynamics of an n dimensional ratio dependent predator prey system with diffusion abstract the main concern of this paper is to study the dynamic of an n dimensional ratio dependent predator prey system with diffusion more concretely we study the dissipativeness the persistence of the system and we obtain condition under which the nontrivial equilibrium is globally asymptotically stable

nonexpansive iterations in hyperbolic spaces one of the most active research areas in nonlinear functional analysis is the asymptotics of nonexpansive mappings most of the results however have been obtained in normed linear spaces it is natural therefore to try to develop a theory of nonexpansive iterations in more general infinite dimensional manifolds this is the purpose of the present paper more specifically we propose the class of hyperbolic spaces as an appropriate background for the study of operator theory in general and of iterative processes for nonexpansive mappings in particular this class of metric spaces which is defined in section 2 includes all normed linear spaces and hadamard manifolds as well as the hilbert ball and the cartesian product of hilbert balls in section 3 we introduce co accretive operators and their resolvents and present some of their properties in the fourth section we discuss the concept of uniform convexity for hyperbolic spaces section 5 is devoted to two new geometric properties of infinite dimensional banach spaces theorem 5 6 provides a characterization of banach spaces having these properties in terms of nonlinear accretive operators in sections 6 7 and 8 we study explicit implict and continuous iterations repectively using the same approach in all three sections we illustrate this common approach with the following special case let c be a closed convex subset of a hyperbolic space x p let t c f c be a nonexpansive mapping and let x be a point in c in order to study the iteration t x n 0 1 2 we set z 1 l n x 0 l n t x k clco zj j i l and d inf p y ty y e c the first step is to show that p x k lim p x t x n d this leads to the convergence m of lz when x is uniformly convex and to the weak convergence of z when x is a banach space which is reflexive and strictly convex when t is an averaged mapping we are also able to establish the following triple equality for all k 2 1

erratum to mann and ishikawa iterative processes for multivalued mappings in banach spaces comput math appl 54 2007 872 877 we show strong convergence for mann and ishikawa iterates of multivalued nonexpansive mapping t under some appropriate conditions which revises a gap in panyanak b panyanak mann and ishikawa iterative processes for multivalued mappings in banach spaces comput math appl 54 2007 872 877 furthermore we also give an affirmative answer to panyanak s open question

periodic two predator one prey interactions and the time sharing of a resource niche a competition model involving two competing predator species and a single renewable resource prey species is studied under the assumption that the system parameters are periodic in time it is shown by means of global bifurcation techniques that a continuum of positive periodic solutions exists as a function of a selected averaged parameter and that the stability of these solutions at least locally near bifurcation depends on the direction of bifurcation in the special autonomous case of constant parameters the bifurcation is vertical and the spectrum of the continuum is a discrete point this autonomous case supports the principle of competitive exclusion in that coexistence of the predators on the single resource prey is possible in the sense that the system equilibrates only on a parameter set of measure zero in the more general case of periodic coefficients however it is shown that the spectrum can be an interval of positive length provided the predator parameter oscillations are out of phas

permanence for the michaelis menten type discrete three species ratio dependent food chain model with delay abstract a discrete three trophic level food chain model with ratio dependent michaelis menten type functional response is investigated it is shown that under some appropriate conditions the system is permanent the results indicate that to make the species coexist in the long run it is a surefire strategy to keep the death rate of the predator and top predator rather small and the intrinsic growth rate of the prey relatively large

finding nondegenerate hopf bifurcation points for four dimensional two parametric systems we establish a numerically feasible algorithm to find a simplicial approximation a to a certain part h41 of the boundary of the set h4 r4 of stable or hurwitz polynomials of degree 4 moreover we have that a hn using this we build an algorithm to find a piecewise linear approximation to the intersection curve of a given surface contained in r4 with h41 we have also devised an efficient computer program to perform all these operations the main motivation is to find the curve of nondegenerate bifurcation points in parameter space for a given 2 parametric hopf bifurcation problem of dimension 4

a pde based approach to nondominated sorting nondominated sorting is a fundamental combinatorial problem in multiobjective optimization and is equivalent to the longest chain problem in combinatorics and random growth models for crystals in materials science in a previous work siam j math anal 46 2014 pp 603 638 we showed that nondominated sorting has a continuum limit that corresponds to solving a hamilton jacobi equation in this work we present and analyze a fast numerical scheme for this hamilton jacobi equation and show how it can be used to design a fast algorithm for approximate nondominated sorting

weak convergence of almost orbits of asymptotically nonexpansive commutative semigroups we give three equivalent conditions for weak convergence of almost orbits of an asymptotically nonexpansive commutative semigroup acting on a nonempty bounded closed convex subset of a uniformly convex banach space whose dual has the kadec property

hopf bifurcation in a two competitor one prey system with time delay in this paper we consider a delayed two competitor one prey system in which both two competitors exhibit holling ii functional response by choosing the time delay as a bifurcation parameter it is found that the hopf bifurcation occurs when the delay passes through a certain critical value numerical simulations are performed to illustrate the analytical results

permanence for a delayed periodic predator prey model with prey dispersal in multi patches and predator density independent in this paper we study two species time delayed predator prey lotka volterra type dispersal systems with periodic coefficients in which the prey species can disperse among n patches while the density independent predator species is confined to one of patches and cannot disperse sufficient conditions on the boundedness permanence and existence of positive periodic solution for this systems are established the theoretical results are confirmed by a special example and numerical simulations

best simultaneous approximations asymptotically nonexpansive mappings and variational inequalities in banach spaces abstract the existence of common fixed points is established for three mappings where t is either generalized f g nonexpansive or asymptotically f g nonexpansive on a nonempty subset of a banach space as applications the invariant best simultaneous approximation results are proved and the existence of solution of variational inequalities is obtained our results unify and substantially improve several recent results existing in the current literature

a new approximation method for common fixed points of a finite family of asymptotically quasi nonexpansive mappings in banach spaces in this paper we consider a new iterative scheme to approximate a common fixed point for a finite family of asymptotically quasi nonexpansive mappings we prove several strong and weak convergence results of the proposed iteration in banach spaces these results generalize and refine many known results in the current literature

permanence and extinction analysis for a delayed periodic predator prey system with holling type ii response function and diffusion abstract in this paper it is studied that two species predator prey lotka volterra type dispersal system with delay and holling type ii response function in which the prey species can disperse among n patches while the density independent predator species is confined to one of the patches and cannot disperse sufficient conditions of integrable form for the boundedness permanence extinction and the existence of positive periodic solution are established respectively

mann and ishikawa iterative processes for multivalued mappings in banach spaces let k be a nonempty compact convex subset of a uniformly convex banach space and t k p k a multivalued nonexpansive mapping we prove that the sequences of mann and ishikawa iterates converge to a fixed point of t this generalizes former results proved by sastry and babu k p r sastry g v r babu convergence of ishikawa iterates for a multi valued mapping with a fixed point czechoslovak math j 55 2005 817 826 we also introduce both of the iterative processes in a new sense and prove a convergence theorem of mann iterates for a mapping defined on a noncompact domain

radial distance models for the line transect method line transect estimation of wildlife populations can be based on either right angle distances or radial distances estimation based on radial distances requires more restrictive assumptions about the mechanism by which observations are generated we examine this mechanism and show that the mean sighting angle may frequently be larger than predicted by hayne s fixed distance model or by eberhardt s variable distance model the modified and generalized hayne s models are also investigated an alternative approach based on hazard rate analysis is suggested but we conclude that a nonparametric right angle distance model will generally result in more reliable estimation than any radial distance model

an application of the separation principle for detecting slow fast limit cycles in a three dimensional system a geometric method called the separation principle is used in this paper for detecting limit cycles in a slow fast dynamical system describing a food chain with trophic levels with diversified time responses the analysis is very simple and based on singular perturbation arguments the limit cycle resulting from the method is composed of a concatenation of catastrophic transitions occuring at different speeds

exit time problems in optimal control and vanishing viscosity method the authors study the connections between deterministic exit time control problems and possibly discontinuous viscosity solutions of a first order hamilton jacobi hj equation up to the boundary this equation admits a maximum and a minimum solution that are the value functions associated to stopping time problems on the boundary when these solutions are equal they can be obtained through the vanishing viscosity method finally when the hj equation has a continuous solution it is proved to be the value function for the first exit time of the domain it is also the vanishing viscosity limit arising in particular in some large deviations problems

weak and strong convergence of a scheme with errors for two nonexpansive mappings abstract in this paper we are concerned with the study of an iterative scheme with errors involving two nonexpansive mappings we approximate the common fixed points of these two mappings by weak and strong convergence of the scheme in a uniformly convex banach space under a condition weaker than compactness

permanence and extinction of a three species ratio dependent food chain model with delay and prey diffusion abstract in this paper we study a diffusive three species ratio dependent food chain model using differential inequality to obtain sufficient conditions that ensure the permanence of the system and the extinction of predator species our results reinforce the main result of sun wen shihua chen and huihai mei positive periodic solution of a more realistic three species lotka volterra model with delay and density regulation chaos solitons and fractals in press

local shading analysis local analysis of image shading in the absence of prior knowledge about the viewed scene may be used to provide information about the scene the following has been proved every image point has the same image intensity and first and second derivatives as the image of some point on a lambertian surface with principal curvatures of equal magnitude further if the principal curvatures are assumed to be equal there is a unique combination of image formation parameters up to a mirror reversal that will produce a particular set of image intensity and first and second derivatives a solution for the unique combination of surface orientation etc is presented this solution has been extended to natural imagery by using general position and regional constraints to obtain estimates of the following surface orientation at each image point the qualitative type of the surface i e whether the surface is planar cylindrical convex concave or saddle the illuminant direction within a region algorithms to recover illuminant direction and estimate surface orientation have been evaluated on both natural and synthesized images and have been found to produce useful information about the scene

periodicity and limit cycle perturbation analysis of a predator prey model with interspecific species interference predator additional food and dispersal we formulate a robust mathematical model for two predators having an overlapping dietary niche breadth we use the beddington deangelis functional and numerical responses which are relevant in addressing the principle of competitive exclusion as species interact the stabilizing effect of additional food in relation to the relative diffusivity d and wave number k has been investigated stability dissipativity permanance persistence and periodicity of the model have been studied using the routine and limit cycle perturbation methods besides revealing irregular periodic travelling wave behaviour due to predator interference numerical results also show oscillatory temporal dynamics resulting from additional food supplements combined with high predation rates

linear shape from shading in many situations the reflectance function of a surface is approximately linear and there is an effielent closed form solution to the shape from shading problem when boundary conditions e g edges singular points are not available good estimates of shape may still be extracted by using the assumption of general viewing position an improved method for estimating the illuminant direction is also presented

viscosity solutions and convergence of monotone schemes for synthetic aperture radar shape from shading equations with discontinuous intensities the shape from shading sfs equation relating u y r the unknown angular height of a surface to i y r the known synthetic aperture radar sar intensity data from the surface is i frac u r 2 sqrt 1 u r 2 u y 2 where y and r are axial and radial cylindrical coordinates unlike the more common eikonal sfs equation which relates surface height in cartesian coordinates to optical photographic intensity data the above radar equation can be transformed into hamilton jacobi cauchy form ur g i uy 0 we explore the case where i is a discontinuous function which occurs commonly in radar data by considering sequences of continuous intensity functions that converge to i we obtain corresponding sequences of viscosity solutions we prove that these sequences must converge we also establish conditions that guarantee that these sequences converge to a common limit which we define as the solution to the radar equation finally we establish and demonstrate that when this common limit exists monot

a dynamical system with hopf bifurcations and catastrophes a well known second order positive dynamical system describing the dynamics of a renewable resource together with its consumers prey predator model is first considered such a dynamical system is recognized to be a subtle hopf bifurcation without catastrophes then the model is slightly modified by including a control parameter which represents the indirect exploitation of the resource this new system is shown to have a much richer and interesting dynamics in particular catastrophes of the fold type hysteresis may arise moreover when the control value corresponding to the hopf bifurcation is greater than the lower threshold of the hysteresis one of the two transitions characterizing the catastrophe is a transition between a stableequilibrium and a limit cycle the results are illustrated in the control phase portrait

strong and δ convergence of some iterative schemes in cat 0 spaces in this paper we get some results on strong and convergence in cat 0 spaces for an iterative scheme which is both faster than and independent of the ishikawa scheme we also obtain some results for two mappings using the ishikawa type iteration scheme the motivation of the present work comes from that of dhompongsa and panyanak 2008 3

qualitative stability of linear systems abstract this paper provides a finitely computable graph theoretic answer to the following question concerning linear dynamical systems when given only the signs of entries or 0 in a real square matrix a can one be certain that all positive trajectories of the system ax are bounded matrices having such sign patterns are called sign quasistable with bounded replaced by convergent to the origin the matrices are called sign stable and were fully described in earlier papers however when a s digraph has several strong components so that the system is actually a hierarchy of subsystems and when some of those subsystems fail to be sign stable the recognition of sign quasistability is a very delicate matter by means of certain graph color tests it is possible to identify the system variables that are capable for some choice of matrix entry magnitudes and initial conditions of emitting nonzero constant

dynamics in a ratio dependent predator prey model with predator harvesting abstract the objective of this paper is to study systematically the dynamical properties of a ratio dependent predator prey model with nonzero constant rate predator harvesting it is shown that the model has at most two equilibria in the first quadrant and can exhibit numerous kinds of bifurcation phenomena including the bifurcation of cusp type of codimension 2 i e bogdanov takens bifurcation the subcritical and supercritical hopf bifurcations these results reveal far richer dynamics compared to the model with no harvesting and different dynamics compared to the model with nonzero constant rate prey harvesting in d xiao l jennings bifurcations of a ratio dependent predator prey system with constant rate harvesting siam appl math 65 2005 737 753 biologically it is shown that nonzero constant rate predator harvesting can prevent mutual extinction as a possible outcome of the predator prey interaction and remove the singularity of the origin which was regarded as pathological behavior for a ratio dependent predator prey model in p yodzis predator prey theory and management of multispecies fisheries ecological applications 4 2004 51 58

lim s theorems for multivalued mappings in cat 0 spaces let x be a complete cat 0 space we prove that if e is a nonempty bounded closed convex subset of x and t e k x a nonexpansive mapping satisfying the weakly inward condition i e there exists p e such that p 1 tx ie x x e 0 1 then t has a fixed point in banach spaces this is a result of lim on asymptotic centers and fixed points of nonexpansive mappings canad j math 32 1980 421 430 the related result for unbounded r trees is given

some properties of viscosity solutions of hamilton jacobi equations abstract recently m g crandall and p l lions introduced the notion of viscosity solutions of scalar nonlinear first order partial differential equations viscosity solutions need not be differentiable anywhere and thus are not sensitive to the classical problem of the crossing of characteristics the value of this concept is established by the fact that very general existence uniqueness and continuous dependence results hold for viscosity solutions of many problems arising in fields of application the notion of a viscosity solution admits several equivalent formulations here we look more closely at two of these equivalent criteria and exhibit their virtues by both proving several new facts and reproving various known results in a simpler manner moreover by forsaking technical generality we hereby provide a more congenial introduction to this subject than the original paper author

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

δ convergence theorems for multi valued nonexpansive mappings in hyperbolic spaces the purpose of this paper is to introduce the mixed agarwal o regan sahu type iterative scheme agarwal et al 2007 for finding a common fixed point of the multi valued nonexpansive mappings in the setting of hyperbolic spaces under suitable conditions some convergence theorems of the iterative sequence generated by the proposed scheme to approximate a common fixed point of multi valued nonexpansive mappings are proved the results presented in the paper extend and improve some recent results announced in the current literature

the interaction of steady state and hopf bifurcations in a two predator one prey competition model the existence of a stable periodic solution in the positive octant of a two predator one prey competition model is shown to result from the interaction of a steady state bifurcation with a hopf bifurcation this result confirms the conjectures based on numerical simulations of several authors that coexistence in the form of periodic oscillations in all three population sizes takes place for some parameter values of the model

shape from shading viscosity solutions and edges this article deals with the so called shape from shading problem which arises when recovering a shape from a single image the general case of a distribution of light sources illuminating a lambertian surface is considered this involves original definitions of three types of edges mainly the apparent contours the grazing light edges and the shadow edges the elevation of the shape is expressed in terms of viscosity solution of a first order hamilton jacobi equation with various boundary conditions on these edges various existence and uniqueness results are presented