abstract functional differential equations and reaction diffusion systems functional differential equations and reaction diffusion systems r h martin jr and h l smith abstract several fundamental results on the existence and behavior of solutions to semilinear functional differential equations are developed in a banach space setting the ideas are applied to reaction diffusion systems that have time delays in the nonlinear reaction terms the techniques presented here include differential inequalities invariant sets and lyapunov functions and therefore they provide for a wide range of applicability the results on inequalities and especially strict inequalities are new even in the context of semilinear equations whose nonlinear terms do not contain delays several fundamental results on the existence and behavior of solutions to semilinear functional differential equations are developed in a banach space setting the ideas are applied to reaction diffusion systems that have time delays in the nonlinear reaction terms the techniques presented here include differential inequalities invariant sets and lyapunov functions and therefore they provide for a wide range of applicability the results on inequalities and especially strict inequalities are new even in the context of semilinear equations whose nonlinear terms do not contain delays suppose q is a bounded domain in rn with aq smooth and a is the laplacian operator on q also let m be a positive integer z a positive number and f fi m a continuous bounded function from 0 xc x q x c z 0 m into rm where c t 0 is the space of continuous functions from z 0 into r the purpose of this paper is to apply abstract results for semilinear functional differential equations in banach spaces to reactiondiffusion systems with time delays having the form a tu x t diau x t i t x ut x t a xeq i 1 m rdd ai x ui x t au i x t 81 x t t a x eaq u x a 0 x x 0 5 t 0 di 0 and ca q 0 o is c and i q x 0 oo r is c2 here an is the outward normal derivative on aq and if di 0 it is assumed that no boundary conditions are specified for this i also tu x t denotes the partial with respect to t whereas ut x denotes the member of c z 0 defined by 0 u x t 0 u x t 0 m our techniques provide basic existence criteria but the main point is that they can also be effectively applied to obtain estimates for solutions especially received by the editors october 7 1987 and in revised form october 7 1988 1980 mathematics subject classification 1985 revision primary 35r10 34k30

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

permanence of periodic holling type predator prey system with stage structure for prey abstract in this paper we study the permanence of the following periodic holling type predator prey system with stage structure for prey x 1 t a t x 2 t b t x 1 t d t x 1 2 t e t x 1 t p t x 1 t y t x 2 t c t x 1 t f t x 2 2 t y t y t g t h t x 1 t p t x 1 t q t y t sufficient and necessary condition which guarantee the predator and the prey species to be permanent is obtained some new results are obtained

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

trust region based solver for nonlinear transport in heterogeneous porous media we describe a new nonlinear solver for immiscible two phase transport in porous media where viscous buoyancy and capillary forces are significant the flux fractional flow function f is a nonlinear function of saturation and typically has inflection points and can be non monotonic the non convexity and non monotonicity of f are major sources of difficulty for nonlinear solvers of coupled multiphase flow and transport in natural porous media we describe a modified newton algorithm that employs trust regions of the flux function to guide the newton iterations the flux function is divided into saturation trust regions delineated by the inflection unit flux and end points the updates are performed such that two successive iterations cannot cross any trust region boundary if a crossing is detected the saturation value is chopped back to the appropriate trust region boundary the proposed trust region newton solver which is demonstrated across the parameter space of viscous buoyancy and capillary effects is a significant extension of the inflection point strategy of jenny et al jcp 2009 5 for viscous dominated flows we analyze the discrete nonlinear transport equation obtained using finite volume discretization with phase based upstream weighting then we prove convergence of the trust region newton method irrespective of the timestep size for single cell problems numerical results across the full range of the parameter space of viscous gravity and capillary forces indicate that our trust region scheme is unconditionally convergent for 1d transport that is for a given choice of timestep size the unique discrete solution is found independently of the initial guess for problems dominated by buoyancy and capillarity the trust region newton solver overcomes the often severe limits on timestep size associated with existing methods to validate the effectiveness of the new nonlinear solver for large reservoir models with strong heterogeneity we compare it with state of the art nonlinear solvers for two phase flow and transport using the spe 10 model compared with existing nonlinear solvers our trust region solver results in superior convergence performance and achieves reduction in the total newton iterations by more than an order of magnitude together with a corresponding reduction in the overall computational cost

adaptive implicit finite element methods for multicomponent compressible flow in heterogeneous and fractured porous media this work presents adaptive implicit first order and second order discontinuous galerkin dg methods for the transport of multicomponent compressible fluids in heterogeneous and fractured porous media discretized by triangular quadrilateral and hexahedral grids the adaptive implicit method aim combines the advantages of purely explicit or implicit methods in time in grid cells with high fluxes or low pore volumes the transport update is done implicitly to alleviate the courant friedrichs lewy cfl time step constraints of the conditionally stable explicit approach grid cells with a large cfl condition are updated explicitly combined this allows higher efficiency than explicit methods but it reduces the penalty of implicit methods which exhibit high numerical dispersion and are more computationally and storage expensive per time step the advantages of aim are modest for uniform grids and rock properties however in heterogeneous or fractured reservoirs explicit methods may become impractical while a fully implicit approach introduces unnecessary numerical dispersion and is overkill for low permeability layers and matrix blocks in such applications aim is shown to be significantly more efficient and accurate the division between explicit and implicit grid cells is made adaptively in space and time this allows for a high level of explicitness and can also adapt to high fluxes caused by e g viscous and gravitational flow instabilities numerical examples demonstrate the powerful features of aim to model e g solute transport carbon sequestration in saline aquifers and miscible gas injection in fractured oil and gas reservoirs

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

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

minimal wave speed in a diffusive epidemic model with temporal delay abstract taking incubation period into account we modify capasso et al s epidemic model and consider a reaction diffusion system with time delay by the method of upper and lower solutions to a related second order ordinary differential equation with infinite time delay we establish the existence of the minimal wave speed for the modified epidemic model and show that incubation period reduces the minimal wave speed of epidemic model indeed

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

competitive systems with stage structure of distributed delay type this paper considers a delay differential equation model for the interaction among n species the adult members of which are in competition for each of the n species the model incorporates an infinite distributed time delay which represents the time from birth to maturity of that species thus the time delays appear in the adult recruitment terms the dynamics of the model are determined and sharp global stability criteria are established for the interior equilibrium as well as the axial equilibrium

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

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

global stability and wavefronts in a cooperation model with state dependent time delay abstract this article deals with a diffusive cooperative model with state dependent delay which is assumed to be an increasing function of the population density with lower and upper bounds for the cooperative dde system the positivity and boundedness of solutions are firstly given using the comparison principle of the state dependent delay equations obtained the stability criterion of model is analyzed both from local and global points of view when the diffusion is properly introduced the existence of traveling waves is obtained by constructing a pair of upper lower solutions and schauder s fixed point theorem calculating the minimum wave speed shows that the wave is slowed down by the state dependent delay finally the traveling wavefront solutions for large wave speed are also discussed and the fronts appear to be all monotone regardless of the state dependent time delay this is an interesting property since many findings are frequently reported that delay causes a loss of monotonicity with the front developing a prominent hump in some other delay models

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

permanence and stability of a stage structured predator prey model abstract a predator prey model with a stage structure for the predator which improves the assumption that each individual predator has the same ability to capture prey 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 we obtain conditions that determine the permanence of the populations and the extinction of the populations furthermore we establish necessary and sufficient conditions for the local stability of the positive equilibrium of the model by exploiting the monotonicity of one equation of the model we obtain conditions for the global attractivity of the positive equilibrium which allow for long delay as long as the predator birth rate is large or the death rate of immature predators is small by constructing liapunov functionals we also obtain conditions under which the positive equilibrium is globally stable when the delay is small

an equivalence between sparse approximation and support vector machines in the first part of this paper we show a similarity between the principle of structural risk minimization principle srm vapnik 1982 and the idea of sparse approximation as defined in chen donoho and saunders 1995 and olshausen and field 1996 then we focus on two specific approximate implementations of srm and sparse approximation which have been used to solve the problem of function approximation for srm we consider the support vector machine technique proposed by v vapnik and his team at at t bell labs and for sparse approximation we consider a modification of the basis pursuit de noising algorithm proposed by chen donoho and saunders 1995 we show that under certain conditions these two techniques are equivalent they give the same solution and they require the solution of the same quadratic programming problem

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

potential based reduced newton algorithm for nonlinear multiphase flow in porous media we present a phase based potential ordering that is an extension of the cascade ordering introduced by appleyard and cheshire john r appleyard ian m cheshire the cascade method for accelerated convergence in implicit simulators in european petroleum conference 1982 pp 113 122 the proposed ordering is valid for both two phase and three phase flow and it can handle countercurrent flow due to gravity and or capillarity we show how this ordering can be used to reduce the nonlinear algebraic system that arises from the fully implicit method fim into one with only pressure dependence the potential based reduced newton algorithm is then obtained by applying newton s method to this reduced order system numerical evidence shows that our potential based reduced newton solver is able to converge for time steps that are much larger than what the standard newton s method can handle in addition whenever standard newton converges so does the reduced newton algorithm and the number of global nonlinear iterations required for convergence is significantly reduced compared with the standard newton s method

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

a sparsity driven kernel machine based on minimizing a generalization error bound a new sparsity driven kernel classifier is presented based on the minimization of a recently derived data dependent generalization error bound the objective function consists of the usual hinge loss function penalizing training errors and a concave penalty function of the expansion coefficients the problem of minimizing the non convex bound is addressed by a successive linearization approach whereby the problem is transformed into a sequence of linear programs the algorithm produced comparable error rates to the standard support vector machine but significantly reduced the number of support vectors and the concomitant classification time

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

unconditionally convergent nonlinear solver for hyperbolic conservation laws with s shaped flux functions this paper addresses the convergence properties of implicit numerical solution algorithms for nonlinear hyperbolic transport problems it is shown that the newton raphson nr method converges for any time step size if the flux function is convex concave or linear which is in general the case for cfd problems in some problems e g multiphase flow in porous media the nonlinear flux function is s shaped not uniformly convex or concave as a result a standard nr iteration can diverge for large time steps even if an implicit discretization scheme is used to solve the nonlinear system of equations in practice when such convergence difficulties are encountered the current time step is cut previous iterations are discarded a smaller time step size is tried and the nr process is repeated the criteria for time step cutting and selection are usually based on heuristics that limit the allowable change in the solution over a time step and or nr iteration here we propose a simple modification to the nr iteration scheme for conservation laws with s shaped flux functions that converges for any time step size the new scheme allows one to choose the time step size based on accuracy consideration only without worrying about the convergence behavior of the nonlinear solver the proposed method can be implemented in an existing simulator e g for co 2 sequestration or reservoir flow modeling quite easily the numerical analysis is confirmed with simulation studies using various test cases of nonlinear multiphase transport in porous media the analysis and numerical experiments demonstrate that the modified scheme allows for the use of arbitrarily large time steps for this class of problems

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

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

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

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

nonlinear analysis of multiphase transport in porous media in the presence of viscous buoyancy and capillary forces nonlinear convergence problems in numerical reservoir simulation can lead to unacceptably large computational time and are often the main impediment to performing simulation studies of large scale problems we analyze the nonlinearity of the discrete transport mass conservation equation for immiscible incompressible two phase flow in porous media in the presence of viscous buoyancy and capillary forces although simulation problems are multi dimensional with large numbers of cells and variables we find that the essence of the nonlinear behavior can be understood by studying the discretized numerical flux function for the interface between two cells the numerical flux is expressed in terms of the saturations of the two cells discontinuities in the first order derivative of the flux function referred to as kinks and inflection lines are identified as the cause of convergence difficulty these critical features kinks and inflections change the curvature of the numerical flux function abruptly and can lead to overshoots oscillations or divergence in newton iterations based on our understanding of the nonlinearity a nonlinear solver is developed referred to as the numerical trust region ntr solver the solver is able to guide the newton iterations safely and efficiently through the different saturation trust regions delineated by the kinks and inflections specifically overshoots and oscillations that often lead to convergence failure are avoided numerical examples demonstrate that our ntr solver has superior convergence performance compared with existing methods in particular convergence is achieved for a wide range of timestep sizes and courant friedrichs lewy cfl numbers spanning several orders of magnitude in addition a discretization scheme is proposed for handling heterogeneities in capillary pressure saturation relationship the scheme has less degree of nonlinearity compared with the standard single point phase based upstream weighting scheme leading to an improved nonlinear convergence performance especially when used together with our ntr solver our proposed numerical solution strategy that is based on the numerical flux and handles capillarity extends the previous work by jenny et al 2009 6 and wang and tchelepi 2013 7 significantly the nonlinearity of multiphase transport in porous media is analyzed the analysis considers viscous buoyancy and capillary forces the critical features that cause nonlinear convergence failures are identified a nonlinear solver that converges without oscillations and divergence is developed the solver converges faster than existing methods and allows large timesteps

a reaction diffusion model for a single species with age structure i travelling wavefronts on unbounded domains in this paper we derive the equation for a single species population with two age classes and a fixed maturation period living in a spatially unbounded environment we show that if the mature deat

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

a new method for sparsity control in support vector classification and regression abstract a new method of implementing support vector learning algorithms for classification and regression is presented which deals with problems of over defined solutions and excessive complexity classification problems are solved with a minimum number of support vectors irrespective of the degree of overlap in the training data support vector regression can deliver a sparse solution without requiring vapnik s e insensitive zone this paper generalises sparsity control for both support vector classification and regression the novelty in this work is in the method of achieving a sparse support vector set which forms a minimal basis for the prediction function

the effect of state dependent delay and harvesting on a stage structured predator prey model we propose and analyze a stage structured predator prey model in which the time from birth to maturity is directly related to the number of individuals present individuals mature more quickly when there are fewer of them around the state dependent time delay is taken to be an increasing differentiable bounded function in this research we study the dynamics of our model analytically we present results on positivity and boundedness of all populations criteria for the existence of all equilibria and uniqueness of a positive equilibrium are given in order to observe the effect of state dependent maturation delay local stability analysis around all equilibria of the proposed model is discussed due to variation of maturation delay also global stability of trivial and the boundary equilibria is investigated using liapunov functional and lasalle invariant principle to investigate the effect of state dependent maturation delay and the harvesting effort of all species we carried out numerical simulations

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

on the spatial dynamics of vaccination a spatial sirs v model abstract in this paper we analyze the effects of vaccination from a spatial perspective we propose a spatial deterministic sirs v model which considers a non linear system of partial differential equations with explicit attrition and diffusion terms for the vaccination process the model allows us to simulate numerically the spatial and temporal dynamics of an epidemic considering different spatial strategies for the vaccination policy in particular in our first example we analyze the classical sirs v evolution with the addition of movements due to diffusion while in the second one we focus on modeling one ring vaccination policy we expect this model can improve spatial predictions of sir vaccination models by taking into account the spatial dimension of the problem

global stability of a stage structured predator prey model with prey dispersal a delayed lotka volterra type predator prey model with stage structure for predator and prey dispersal in two patch environments is investigated it is assumed that immature individuals and mature individuals of predator species are divided by a fixed age and that immature predators do not feed on prey and do not have the ability to reproduce on the other hand it is assumed that the prey species can disperse between one patch with a low level of food and without predation and one patch with a higher level of food but with predation by means of two different kinds of lyapunov functionals sufficient conditions are derived respectively for the global asymptotic stability of a positive equilibrium of the model by analyzing the characteristic equation criterion is established for the local stability of the positive equilibrium numerical simulations are presented to illustrate 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

analysis of a model representing stage structured population growth with state dependent time delay a stage structured model of population growth is proposed where the time to ma turity is itself state dependent it is shown that under appropriate assumptions all solutions are positive and bounded criteria for the existence of positive equilibria and further conditions for the uniqueness of the equilibria are given the stability of the equilibria are also discussed in addition an attracting region is determined for solutions such that this region collapses to the unique positive equilibrium in the state independent case

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

permanence of general stage structured consumer resource models much of the existing stage structured consumer resource models ignore the permanence in this paper we consider the permanence for a series of staged structured consumer resource models with the function response of so called prey dependence resource dependence type we show that the systems are permanent if and only if the adult consumer s recruitment rate at the peak of resource abundance is more than its death rate our results indicate that the large consumer s maturation time delay will directly lead to its extinction furthermore our arguments for the main results give a light for permanence in the general stage structured consumer resource systems

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

stability and traveling fronts in lotka volterra competition models with stage structure this paper is concerned with a delay differential equation model for the interaction between two species the adult members of which are in competition the competitive effects are of the lotka volterra kind and in the absence of competition it is assumed that each species evolves according to the predictions of a simple age structured model which reduces to a single equation for the total adult population for each of the two species the model incorporates a time delay which represents the time from birth to maturity of that species thus the time delays appear in the adult recruitment terms the dynamics of the model are determined and global stability results are established for each equilibrium the equilibria of the model involve the maturation delays the criteria for global convergence to each equilibrium are sharp and involve these delays a reaction diffusion extension of the model is also studied for the case when only the adult members of each species can diffuse we prove the existence of a

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

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 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

traveling wavefronts in diffusive and cooperative lotka volterra system with delays existence of traveling wave front solutions is established for diffusive and cooperative lotka volterra system with delays the result is an extension of an existing result for delayed logistic scaler equation to systems and is somewhat parallel to the existing result for diffusive and competitive lotka volterra systems without delay the approach used in this paper is the upper lower solution technique and the monotone iteration recently developed by wu and zou j dynam differential equations 13 2001 651 687 for delayed reaction diffusion systems without the so called quasimonotonicity 2002 elsevier science usa all rights reserved

permanence and existence of a positive periodic solution to a periodic stage structured system with infinite delay in this paper we consider a periodic non autonomous competitive stage structured system with infinite delay for the interaction between n species the adult members of which are in competition for each of the n species the model incorporates a time delay which represents the time from birth to maturity of that species infinite delay is introduced which denotes the influential effect of the entire past history of the system on the current competition interactions we first prove by using the comparison principle that if the growth rates are sufficiently large then the solutions are uniformly permanent then by using horn s fixed point theorem we show that the system with finite delay has a positive periodic solution as a consequence of this result we prove that even the system with infinite delay admits a positive periodic solution

extinction and permanence in nonautonomous competitive system with stage structure in this paper the n species nonautonomous stage structured competitive system is constructed and considered sufficient conditions for its extinction and permanence are obtained results here generalize and unify some previous ones moreover it is concluded that stage structure in this system is one of the important factors that effect the extinction and permanence of species

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

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

implicit hybrid upwind scheme for coupled multiphase flow and transport with buoyancy abstract numerical simulation of coupled multiphase flow and transport in porous media is used in many scientific and industrial applications such as groundwater management and oil recovery to solve the governing partial differential equations we focus on the fully implicit backward euler finite volume method fim in this numerical scheme large algebraic systems must be solved at each time step using newton s method this can be quite expensive especially for highly nonlinear problems with buoyancy in this work we present a new first order approximation of the flux in the fim leading to improved nonlinear convergence rate and radius this approximation is based on implicit hybrid upwinding and relies on separate treatments of the viscous and buoyancy parts of the numerical flux moreover in the viscous part the total velocity discretization is key as it controls the coupling between the elliptic flow problem and the hyperbolic multiphase transport problem to achieve robustness and efficiency we propose a differentiable total velocity discretization that adapts to the balance of forces at each interface we analyze the theoretical properties of the resulting numerical scheme and prove that saturations remain between physical bounds challenging two and three phase test cases illustrate that our numerical scheme brings a significant reduction in the number of nonlinear iterations compared to a finite volume discretization relying on the widely used phase per phase upstream weighting our numerical scheme therefore reduces the simulation cost while providing similar accuracy