repellers in systems with infinite delay abstract one of the most important questions concerning interacting species is whether all the species survive in the long term here models governed by a class of autonomous functional differential equations with infinite delay are considered long term survival being interpreted in terms of the criterion of permanent coexistence which appears to provide a biologically realistic test this criterion is based on the natural idea that it is enough if the boundary corresponding to extinction of at least one species is a repeller in a strong sense and the purpose of the present investigation is to present a mathematical theory which often resolves this problem even when the detailed asymptotics of the system are inaccessible to analysis section 3 contains a result which may be of some independent interest it is shown how to construct a space of initial functions so that when solutions are uniformly ultimately bounded then there is a compact forward invariant set absorbing all solutions

bifurcations for a predator prey system with two delays in this paper a predator prey system with two delays is investigated by choosing the sum of two delays as a bifurcation parameter we show that hopf bifurcations can occur as crosses some critical values by deriving the equation describing the flow on the center manifold we can determine the direction of the hopf bifurcations and the stability of the bifurcating periodic solutions in addition special attention is paid to the global continuation of local hopf bifurcations using a global hopf bifurcation result of j wu symmetric functional differential equations and neural networks with memory trans amer math soc 350 1998 4799 4838 we may show the global existence of periodic solutions

stability and bifurcation for a delayed predator prey model and the effect of diffusion abstract we consider a predator prey system with one or two delays and a unique positive equilibrium e its dynamics are studied in terms of the local stability of e and of the description of the hopf bifurcation that is proven to exist as one of the delays taken as a parameter crosses some critical values we also consider a reaction diffusion system with neumann conditions resulting from adding one spatial variable and diffusion terms in the previous model the spectral and bifurcation analysis in the neighborhood of e now as a stationary point of this latter system is addressed and the results obtained for the case without diffusion are applied

periodic solutions of a predator prey model with stage structure for predator a delayed periodic predator prey model with stage structure for predator is proposed it is assumed that immature individuals and mature individuals of the predator are divided by a fixed age and that immature predators do not have the ability to attack prey sufficient conditions are derived for the existence uniqueness and global asymptotic stability of positive periodic solutions of the model numerical simulations are presented to illustrate the feasibility of our main results

global stability in a periodic delayed predator prey system abstract in this paper we establish a periodic delayed predator prey system according to two types of single species growth population models with delay by using some analysis methods easily verifiable sufficient conditions for the existence and global asymptotic stability of positive periodic solution of the above system are derived some previous results are generalized and improved biological interpretations on the main results are also given

global attractivity of positive periodic solution to periodic lotka volterra competition systems with pure delay abstract we consider a periodic lotka volterra competition system without instantaneous negative feedbacks i e pure delay systems x i t x i t r i t j 1 n a i j t x j t i j t i 1 2 n we establish some 3 2 type criteria for global attractivity of a positive periodic solution of the system which generalize the well known wright s 3 2 criteria for the autonomous delay logistic equation and thereby address the open problem proposed by both kuang y kuang global stability in delayed nonautonomous lotka volterra type systems without saturated equilibria differential integral equations 9 1996 557 567 and teng z teng nonautonomous lotka volterra systems with delays j differential equations 179 2002 538 561

periodic solutions of a predator prey system with stage structures for predator and prey abstract by using the continuation theorem of coincidence degree theory the existence of a positive periodic solution for the predator prey system with stage structures for predator and prey is established

global stability of volterra models with time delay abstract easily verifiable conditions are obtained for the global stability of the positive steady state in volterra models with discrete and distributed time delays

harmless delays for uniform persistence abstract this paper studies a two dimensional predator prey system with a finite number of discrete delays our purpose is to demonstrate that the time delays are harmless for uniform persistence of the solutions of the system the results are obtained by constructing suitable persistence functionals

persistence and stability of a stage structured predator prey model with time delays a delayed predator prey model with stage structure for the predator is proposed and investigated sufficient conditions are derived for persistence the local and global asymptotic stability of a positive equilibrium of the model numerical simulations are presented to illustrate the feasibility of our main results

environmental noise impact on regularity and extinction of population systems with infinite delay abstract populations of biological species are often subject to different types of environmental noises these noises play crucial roles and have significant impact on the evolution and biodiversity to understand the effects of different types of noises on the asymptotic properties of the populations this paper reveals the influence of inherent net birth noise and the interaction noise among stochastically perturbed population systems by considering systems with infinite delays 1 this paper discovers that a the interaction noise may suppress the potential explosion and guarantee the existence of the global solution which yields regularity of the stochastic system and b the inherent net birth noise may lead to extinction of the populations 2 this paper provides sufficient conditions that ensure the stochastic persistence stochastic boundedness and asymptotic polynomial growth of the population system 3 this paper demonstrates that these asymptotic properties are completely determined by stochastic noises and are independent of other parameters

global existence of bifurcated periodic solutions in a commensalism model with delays abstract this paper is concerned with a commensalism model with a discrete delay and a distributed delay by linearizing the system at the positive equilibrium and analyzing the associated characteristic equation the asymptotic stability of the interior equilibrium is investigated it is found that the interior equilibrium is asymptotically stable when the discrete delay is less than a certain critical value and unstable when the discrete delay is greater than this critical value by regarding the delay as the bifurcation parameter the existence of hopf bifurcation is also considered furthermore the properties of hopf bifurcation are determined in particular the global existence of bifurcated periodic solutions is established by applying the topological global hopf bifurcation theorem which shows that the local hopf bifurcations imply the global ones after the second critical value of parameter finally numerical simulations supporting the theoretical analysis are also included

global existence of positive periodic solutions of periodic predator prey system with infinite delays abstract a set of easily verifiable sufficient conditions is derived for the global existence of periodic solutions with strictly positive components for a periodic predator prey system with infinite delays by using the method of coincidence degree

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

stochastic lotka volterra population dynamics with infinite delay we discover in this paper that when environmental noise is strongly dependent on the population size this noise may suppress the population explosion in a finite time and guarantee the global positive solution when the environmental noise is weakly dependent on the population size the conditions that guarantee the global positive solution are independent of this environmental noise we also discuss the pth moment boundedness stochastic ultimate boundedness and moment average boundedness in time under two classes of conditions these properties are natural requirements from the biological point of view

local hopf bifurcation and global periodic solutions in a delayed predator prey system abstract we consider a delayed predator prey system we first consider the existence of local hopf bifurcations and then derive explicit formulas which enable us to determine the stability and the direction of periodic solutions bifurcating from hopf bifurcations using the normal form theory and center manifold argument special attention is paid to the global existence of periodic solutions bifurcating from hopf bifurcations by using a global hopf bifurcation result due to wu trans amer math soc 350 1998 4799 we show that the local hopf bifurcation implies the global hopf bifurcation after the second critical value of delay finally several numerical simulations supporting the theoretical analysis are also given

a lotka volterra type food chain model with stage structure and time delays abstract a three species lotka volterra type food chain model with stage structure and time delays is investigated it is assumed in the model that the individuals in each species may belong to one of two classes the immatures and the matures the age to maturity is presented by a time delay and that the immature predators immature top predators do not have the ability to feed on prey predator by using some comparison arguments we first discuss the permanence of the model by means of an iterative technique a set of easily verifiable sufficient conditions are established for the global attractivity of the nonnegative equilibria of the model

stability switch and hopf bifurcation for a diffusive prey predator system with delay the increasing time delay usually destabilizes any dynamical system in this paper we give an example that in some special cases the opposite effect can be experienced if the time delay is sufficiently great we investigate the effect of both the parameter in the time delay kernel and diffusion coefficient on the stability of the positive steady state for a diffusive prey predator system with delay we obtain the condition of the occurrence of the stability switches of the positive steady state

global stability of a lotka volterra type predator prey model with stage structure and time delay a delayed lotka volterra type predator prey model with stage structure for predator is investigated it is assumed in the model that the individuals in the predator population may belong to one of two classes the immatures and the matures the age to maturity is presented by a time delay and that the immature predators do not have the ability to prey by analyzing characteristic equations and using an iterative technique a set of easily verifiable sufficient conditions are derived for the local and global stability of the nonnegative equilibria of the model numerical simulations are carried out to illustrate the validity of our results

pattern recognition with moment invariants a comparative study and new results abstract moment invariants have been proposed as pattern sensitive features in classification and recognition applications in this paper the authors present a comprehensive study of the effectiveness of different moment invariants in pattern recognition applications by considering two sets of data handwritten numerals and aircrafts the authors also present a detailed study of zernike and pseudo zernike moment invariants including a new procedure for deriving the moment invariants in addition the authors introduce a new normalization scheme that reduces the large dynamic range of these invariants as well as implicit redundancies in these invariants based on a comprehensive study with both handwritten numerals and aircraft data the authors show that the new method of deriving zernike moment invariants along with the new normalization scheme yield the best overall performance even when the data are degraded by additive noise

the lyapunov functionals for delay lotka volterra type models by means of lyapunov functionals we have succeeded in establishing the global attractivity of the positive equilibrium of n species lotka volterra systems modeled by equations of the pure delay type with both finite and infinite delays involved as a corollary we show that if the delay system is dissipative and the coefficient matrix is vl stable then the global attractivity of the unique positive equilibrium is maintained provided the delays are small estimates on the allowable sizes of delays are indicated applications to 2 species prey predator models and n species food chains and competition models are included

representation and shape matching of 3 d objects a three dimensional scene analysis system for the shape matching of real world 3 d objects is presented various issues related to representation and modeling of 3 d objects are addressed a new method for the approximation of 3 d objects by a set of planar faces is discussed the major advantage of this method is that it is applicable to a complete object and not restricted to single range view which was the limitation of the previous work in 3 d scene analysis the method is a sequential region growing algorithm it is not applied to range images but rather to a set of 3 d points the 3 d model of an object is obtained by combining the object points from a sequence of range data images corresponding to various views of the object applying the necessary transformations and then approximating the surface by polygons a stochastic labeling technique is used to do the shape matching of 3 d objects the technique matches the faces of an unknown view against the faces of the model it explicitly maximizes a criterion function based on the ambiguity and inconsistency of classification it is hierarchical and uses results obtained at low levels to speed up and improve the accuracy of results at higher levels the objective here is to match the individual views of the object taken from any vantage point details of the algorithm are presented and the results are shown on several unknown views of a complicated automobile casting

stability analysis on a predator prey system with distributed delays abstract this paper concerns the local and global dynamical properties of the nonnegative and positive equilibria of a lotka volterra predator prey system with distributed delays it is shown that while the positive equilibrium does not exist the nonnegative equilibrium is globally asymptotically stable or globally attractive as long as the delays are small enough if the positive equilibrium exists it is shown that it is locally asymptotically stable when the delays are suitably small furthermore an explicit asymptotic stability region for the positive equilibrium is also obtained based on a liapunov functional

exponential stability of a competitive lotka volterra system with delays abstract in this paper the exponential stability of a two species competitive lotka volterra system with discrete delays has been studied by constructing appropriate lyapunov functional and using the linear matrix inequality lmi optimization approach a series of sufficient criteria is obtained which ensure the exponential stability of the positive equilibrium of the given lotka volterra system the results are new and improve some earlier work an illustrative example is given to demonstrate the effectiveness of the obtained results

combined analytical and numerical approaches in dynamic stability analyses of engineering systems abstract dynamic stability is a widely studied area that has attracted many researchers from various disciplines although dynamic stability is usually associated with mechanics theoretical physics or other natural and technical disciplines it is also relevant to social economic and philosophical areas of our lives therefore it is useful to occasionally highlight the general aspects of this amazing area to present some relevant examples and to evaluate its position among the various branches of rational mechanics from this perspective the aim of this study is to present a brief review concerning the dynamic stability problem its basic definitions and principles important phenomena research motivations and applications in engineering the relationships with relevant systems that are prone to stability loss encountered in other areas such as physics other natural sciences and engineering are also noted the theoretical background which is applicable to many disciplines is presented in this paper the most frequently used dynamic stability analysis methods are presented in relation to individual dynamic systems that are widely discussed in various engineering branches in particular the lyapunov function and exponent procedures routh hurwitz lienard and other theorems are outlined together with demonstrations the possibilities for analytical and numerical procedures are mentioned together with possible feedback from experimental research and testing the strengths and shortcomings of these approaches are evaluated together with examples of their effective complementing of each other the systems that are widely encountered in engineering are presented in the form of mathematical models the analyses of their dynamic stability and post critical behaviour are also presented the stability limits bifurcation points quasi periodic response processes and chaotic regimes are discussed the limit cycle existence and stability are examined together with their separating roles as attractors and repulsers two levels of stability loss recovery of the system is possible or final collapse is inevitable as can be observed in softening systems are noted time limited excitation and relevant transition effects e g seismic excitation are also discussed together with the evaluation of possible system reliability improvement the dynamic stability investigation of two degrees of freedom aero elastic systems in a linear formulation using several approaches is briefly highlighted further systems modelling problems that arise in transport engineering are also outlined a few hints for applications are given some open problems and possible future research strategies are outlined

global stability for large systems of volterra lotka type integrodifferential population delay equations on considere l equation integrodifferentielle non lineaire x i t x i t e i j 1 n p ij x j t j 1 n o r s ij k ij x j t d i 1 n ou 1 i j n e i p ij s ij sont des constantes on etudie la stabilite globale de la solution q 1 q n par rapport aux solutions positives

curvature based fuzzy surface classification in this paper a fuzzy surface classification paradigm which is an extension to the conventional techniques based on the sign of the mean h and gaussian k curvatures respectively is presented with the conventional methods two of the major problems that limit object descriptions are 1 their inability to describe surfaces in a natural way and 2 computation of curvatures being highly sensitive to noise as well as limited by resolution problem 1 is addressed by treating the transitional regions between distinct surface types as smoothly varying fuzzy surface types problem 2 gets partially resolved while fuzzifying the signs of the surface curvatures for surface description the new segmentation technique is demonstrated in a model based object recognition system and its performance is compared with a system based on conventional surface classification

permanence of a predator prey system with stage structure and time delay abstract a stage structured predator prey system stage structure for both predator and prey with discrete time delay has been presented in this paper by analyzing the model and using the standard comparison theorem the sufficient conditions are derived for permanence of the system and non permanence of predators

periodic solutions of a discrete time lotka volterra type food chain model with delays a periodic discrete time three trophic level lotka volterra type food chain model is investigated by using gaines and mawhin s continuation theorem of coincidence degree theory sufficient conditions are derived for the existence of positive periodic solutions of the model

permanence of variable coefficients predator prey system with stage structure abstract we studied a finite delay predator prey model with stage structure for predator by analyzing right hand of function and the standard comparison theorem some new sufficient conditions are derived for the permanence of population and some biological explanations are made

on a periodic predator prey system with time delays abstract this paper deals with discuss the global existence of positive periodic solutions for a predator prey system with time delays based on the theory of coincidence degree

three dimensional shape analysis using moments and fourier descriptors a procedure for using moment based feature vectors to identify a three dimensional object from a two dimensional image recorded at an arbitrary viewing angle and range is presented a moment form called standard moments rather than the usual moment invariants is considered a standard six airplane experiment was used to compare different techniques fourier descriptors and moment invariants were both compared to the present scheme for normalized moments various experiments were conducted using mixtures of silhouette and boundary moments and different normalization techniques standard moments gave slightly better results than fourier descriptors for this experiment both of these techniques were much better than moment invariants

stability and hopf bifurcation for a delayed prey predator system with diffusion effects abstract this paper is concerned with a delayed lotka volterra prey predator system with diffusion effects and neumann boundary conditions the main purpose is to investigate the stability of spatially homogeneous positive equilibrium and give the explicit formulae determining the direction and stability of hopf bifurcation by linearizing the system at positive equilibrium and analyzing the associated characteristic equation the stability of positive equilibrium and the existence of hopf bifurcation are demonstrated by means of the normal form theory and the center manifold reduction for partial functional differential equations pfdes the direction and stability of periodic solutions occurring through hopf bifurcation are determined finally in order to verify our theoretical results some numerical simulations are also included

identification of three dimensional objects using range information a method for identifying unoccluded three dimensional objects from arbitrary viewing angles is presented the technique uses synthetically generated range data in a model based feature vector classification scheme fourier descriptors and moments are used for feature vector generation from respectively contour imagery and silhouette or range imagery a method is developed for generating an exhaustive set of library views and worst case test views that is based on a polyhedral approximation to a sphere analysis of the success of this approach is made with experiments on a six airplane data set a model of range data noise is developed and results are presented for both ideal and noisy lower resolution image classification tests the use of multiple views for object identification is discussed and results for one two and three view tests are presented

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

permanence and periodicity of a delayed ratio dependent predator prey model with stage structure a periodic ratio dependent predator prey model with time delays and stage structure for both prey and predator is investigated it is assumed that immature individuals and mature individuals of each species are divided by a fixed age and that immature predators do not have the ability to attack prey sufficient conditions are derived for the permanence and existence of positive periodic solutions of the model numerical simulations are presented to illustrate the feasibility of our main results

stability and hopf bifurcation in a delayed ratio dependent holling tanner type model in this study a delayed ratio dependent holling tanner type predator prey model is investigated first the local stability of a positive equilibrium is studied and then the existence of hopf bifurcations is established by using the normal form theory and center manifold theorem the explicit algorithm determining the stability direction of the bifurcating periodic solutions are derived finally we perform the numerical simulations for justifying the theoretical results

enumerating stationary multiple points given a map f x y an r fold point off is a point xi of x such that there exist points x2 x of x which all have the same image underf we say that an r fold point is strict if x x are all distinct points of x and stationary if some of the xi have coalesced to lie infinitely near the infinitely near points determine tangent directions along the iibref f x in the sense that they constitute ramification points of f this paper enlarges on the work of 9 to develop under appropriate hypotheses enumerative formulas for loci of arbitrary stationary r fold points in terms of invariants of the map multiple point theory has a long and rich history we may trace work back to clebsch 1864 who gave a formula for the number of nodes of a plane curve in terms of the degree and genus of the curve perhaps the most famous example of a stationary multiple point result is the riemann hurwitz formula let f x y be a finite separable surjective map between smooth projective curves the riemann hurwitz theorem gives a formula for deg r where r is the ramification divisor of j it may be easily seen that deg r is simply a weighted number of stationary doublepoints off modern multiple point theory is concerned with developing formulas for general classes of maps the subject has been of considerable interest in differential geometry and topology as well as in algebraic geometry surveys of the work in these fields can be found in lo 9 introduction or 8 chap v pp 365 3911 in algebraic geometry multiple point theory has presently culiminated in two basic approaches the hilbert scheme see lo for a survey and the method of iteration we shall only be concerned with the latter technique in the body of this work both approaches share a 149 oool 8708 87 7 50

asymptotic stability of grazing systems with unbounded delay abstract a system of nonlinear integro differential equations with unbounded delay for grazing a grassland by a cattle population is considered sufficient conditions for asymptotic stability of a positive equilibrium are investigated under fairly general types of growth conditions on the nonlinear functions the main tools in our analysis are the liapunov razumikhin technique construction of liapunov functionals and krasovskii s method several examples are presented and a few remarks are made to illustrate the generality of the hypotheses

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

persistence and global stability in a delayed gause type predator prey system without dominating instantaneous negative feedbacks abstract a delayed gause type predator prey system without dominating instantaneous negative feedbacks is investigated it is proved that the system is uniformly persistent under some appropriate conditions by means of constructing a suitable lyapunov functional sufficient conditions are derived for the local and global asymptotic stability of the positive equilibrium of the system

stability and bifurcation analysis for a delayed lotka volterra predator prey system the present paper deals with a delayed lotka volterra predator prey system by linearizing the equations and by analyzing the locations on the complex plane of the roots of the characteristic equation we find the necessary conditions that the parameters should verify in order to have the oscillations in the system in addition the normal form of the hopf bifurcation arising in the system is determined to investigate the direction and the stability of periodic solutions bifurcating from these hopf bifurcations to verify the obtained conditions a special numerical example is also included

global attractivity of non autonomous lotka volterra competition system without instantaneous negative feedback abstract we consider a non autonomous lotka volterra competition system with distributed delays but without instantaneous negative feedbacks i e pure delay systems we establish some 3 2 type and m matrix type criteria for global attractivity of the positive equilibrium of the system which generalise and improve the existing ones

periodicity and stability for a lotka volterra type competition system with feedback controls and deviating arguments abstract this paper deals with the general periodic lotka volterra type competition systems with feedback controls and deviating arguments by employing fixed point index theory on cone an explicit necessary and sufficient condition for the global existence of the positive periodic solution of the systems is proved by constructing a suitable lyapunov functional a set of easily verifiable sufficient conditions for the global asymptotic stability of the positive periodic solution of the systems is given

on projective varieties of codimension 2 one of the important developments of the early 1970 s in algebraic geometry was the discovery by barth 1 subsequently enlarged on by many others that submanifolds x of projective space whose codimension is small compared with their dimension look homologically like complete intersections this focused attention on the fact that no such x were known other than complete intersections and led hartshorne 4 to conjecture that x must in fact be a complete intersection if 2 codim x dim x hartshorne and independently barth and van de ven 3 proved that if the degree hence also the codimension of x are much smaller than its dimension then x is a complete intersection the purpose of this paper is to contribute to the program of proving that projective varieties of small codimension are complete intersections by proving the following

stability and delays in a predator prey system abstract sufficient conditions for both local and global stability of the positive equilibrium in a predator prey system with time delays are obtained by constructing suitable lyapunov functionals a remark on the mistake by k n murty and m a s srinivas j math anal appl 158 1991 333 341 is also included

hopf bifurcation and global periodic solutions in a delayed predator prey system this paper is concerned with a delayed predator prey system with same feedback delays of predator and prey species to their growth respectively we prove that a sequence of hopf bifurcations occur at the positive equilibrium as the delay increases monotonously from zero by using the theory of normal norm and center manifold reduction an explicit algorithm for determining the direction of hopf bifurcations and the stability of bifurcating periodic solutions is derived in addition the global existence results of periodic solutions bifurcating from hopf bifurcations are established by using a global hopf bifurcation result due to wu j wu symmetric functional differential equations and neural networks with memory trans amer math soc 350 1998 4799 4838 finally a numerical example supporting our theoretical prediction is also given our findings are contrasted with recent studies on a delayed predator prey system with the feedback time delay of prey species to its growth by song and wei y song j wei local hopf bifurcation and global periodic solutions in a delayed predator prey system j math anal appl 301 2005 1 21 as the feedback time delay increases monotonously from zero the positive equilibrium of the latter switches k times from stability to instability to stability in contrast the positive equilibrium of our system appears to lose the above property

stability and hopf bifurcation of a mathematical model describing bacteria fish interaction in marine environment abstract in this work we present and study a model of a host parasite system in marine environment which describes the population dynamics of fish tilapia which can be infected by botulinum the mathematical model is structured by levels of infection using the characteristic curves method we transform the model into a system of distributed delay differential equations we study the existence of hopf bifurcation following the method presented by hassard et al 1981 5 we prove analytically the stability of limit cycle periodic solutions we present numerical and computer simulations of the model

a predator prey system with stage structure for predator abstract this paper studies the asymptotoc behavior of a predator prey model with stage structure it is found that an orbitally asymptotically stable periodic orbit exists in that model when time delay due to gestation of predator and time delay from crowding effect of prey are incorporated we establish the condition for the permanence of populations and sufficient conditions under which positive equilibrium of the model is globally stable

subcritical hopf bifurcations in a car following model with reaction time delay a nonlinear car following model of highway traffic is considered which includes the reaction time delay of drivers linear stability analysis shows that the uniform flow equilibrium of the system loses its stability via hopf bifurcations and thus oscillations can appear the stability and amplitudes of the oscillations are determined with the help of normal form calculations of the hopf bifurcation that also handles the essential translational symmetry of the system we show that the subcritical case of the hopf bifurcation occurs robustly which indicates the possibility of bistability we also show how these oscillations lead to spatial wave formation as can be observed in real world traffic flows

a tunable distance measure for coloured solid models abstract people are willing to rank simple objects of different shape and colour on the basis of similarity if machines are to reason about structure this comparison process must be formalized that is a distance measure between formal object representations must be defined if the machine is reasoning with information to be presented to a human the distance measure needs to accord with human notions of object similarity since our perception of similarity is subjective and strongly influenced by situation the measure should be tunable to particular users and contexts this paper describes a distance measure between solid models which incorporates heuristics of the mental mappings humans use to compare objects the first step is to formally represent objects in a way that reflects human visual segmentations we use a modified boundary representation scheme in colour physical space the next step is to define a family of maps between these representations motivated by considerations of how humans match shapes the distance between two objects is essentially the cost of the lowest cost map between them the cost of a map incorporates a geometric measure of the smooth deformation required of edges and faces a feature measure based on visually significant singular points and a topological measure based on correspondence of visually significant vertices edges and faces tunable features of the match are the relative cost of ignoring parts of objects the treatment of colour and whether or not the distance measure is required to be rotation invariant an important application for such distance measures is to the development of user friendly query of cad and image databases query by example depends on implementation of a concept of likeness between object models in the database which to be useful must reflect the user s concepts another important application for distance measures is in automatic recognition of objects into classes whose members are not identical so that the concept that this object is like object x is required in the common situation that classes are based on human perceptions of visual similarity the distance measure between the class prototype and the object to be classified should reflect those human perceptions

bifurcation analysis of a chemostat model with a distributed delay a chemostat model of a single species feeding on a limiting nutrient supplied at a constant rate is proposed the model incorporates a general nutrient uptake function and a distributed delay the delay indicates that the growth of the species depends on the past concentration of nutrient using the average time delay as a bifurcation parameter it is proven that the model undergoes a sequence of hopf bifurcations stability criteria for the bifurcating periodic solutions are derived it is also found that the periodic solutions become unstable if the dilution rate is increased computer simulations illustrate the results

solution of the stability problem for a class of generalized volterra prey predator systems where ei pij and qj are real constants ui are real valued continuous functions of t for t 0 and zii dui dt both equations are required for i 1 2 m condition lb is here considered to be a restriction on the vector e ei rather than on the matrix p pii as is more usual the hypothesis 0 0 qi 0 is appropriate in applications but as far as the mathematical development is concerned it could be replaced by qiui 0 0 a discussion of historical background can be found in the papers 4 5 to which the present paper is a sequel suffice it to say here that the chief landmarks are volterra s book 6 la salle s theorem 1 21 and krikorian s analysis of the case n 3 3 references 4 5 provide useful

permanence and stability of a predator prey system with stage structure for predator a stage structured predator prey system with delays for prey and predator respectively is proposed and analyzed mathematical analysis of the model equations with regard to boundedness of solutions permanence and stability are analyzed some sufficient conditions which guarantee the permanence of the system and the global asymptotic stability of the boundary and positive equilibrium respectively are obtained

stable oscillations in a predator prey model with time lag the lotka volterra model with carrying capacity at the prey and time delay in the equation concerning the predator is considered the time delay is taken into consideration by an integral with the weight function a exp at it is shown that under certain conditions imposed upon the parameters of the system a supercritical hopf bifurcation takes place at a certain value a0 of a and the bifurcating closed paths are orbitally asymptotically stable for values of a below a0

degenerate lyapunov functionals of a well known prey predator model with discrete delays it is commonly believed that as far as stabilities are concerned small delays are negligible in some modelling processes however to have an affirmative answerfor this common belief is still an open problem for many nonlinear equations in this paper the classical lotka volterra prey predator equation with discrete delays is considered and by using degenerate lyapunov functionals method an affirmative answer to this open problem on both local and global stabilities of the prey predator delay equations is given it is shown that degenerate lyapunov functional method is a powerful tool for studying the stability of such nonlinear delay systems a detailed and explicit procedure of constructing such functionals is provided furthermore some explicit estimates on the allowable sizes of the delays are obtained

existence uniqueness and global asymptotic stability of positive solutions of a predator prey system with holling ii functional response with random perturbation abstract this paper discusses a randomized two species predator prey system with holling ii functional response we show that the positive solution of the associated stochastic delay differential equation does not explode to infinity in a finite time in addition the existence uniqueness and global asymptotic stability of the positive solutions are studied