specialized runge kutta methods for index 2 differential algebraic equations we consider the numerical solution of systems of semi explicit index 2 differential algebraic equations daes by methods based on runge kutta rk coefficients for nonstiffly accurate rk coefficients such as gauss and radau ia coefficients the standard application of implicit rk methods is generally not superconvergent to reestablish superconvergence projected rk methods and partitioned rk methods have been proposed in this paper we propose a simple alternative which does not require any extra projection step and does not use any additional internal stage moreover symmetry of gauss methods is preserved the main idea is to replace the satisfaction of the constraints at the internal stages in the standard definition by enforcing specific linear combinations of the constraints at the numerical solution and at the internal stages to vanish we call these methods specialized runge kutta methods for index 2 daes srk dae2

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

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

pattern formation in a predator prey diffusion model with stage structure for the predator in this paper we study a neumann boundary value problem in a d dimensional box t d 0 d d 1 2 3 for the predator prey diffusion model u 1 t d 1 u 1 u 1 a u 1 u 2 u 3 u 2 t d 2 u 2 d 4 u 2 u 3 2 k u 1 u 3 u 2 u 3 t d 3 u 3 b u 2 m u 3 with predator stage structure by using the bootstrap technique guo and hwang 2010 and higher order energy estimates we provide a rigorous quantitative characterization for the nonlinear evolution of early spatiotemporal pattern formation on the unstable positive constant equilibrium as a consequence the nonlinear instability occurs

energy conserving runge kutta methods for the incompressible navier stokes equations energy conserving methods have recently gained popularity for the spatial discretization of the incompressible navier stokes equations in this paper implicit runge kutta methods are investigated which keep this property when integrating in time firstly a number of energy conserving runge kutta methods based on gauss radau and lobatto quadrature are constructed these methods are suitable for convection dominated problems such as turbulent flows because they do not introduce artificial diffusion and are stable for any time step secondly to obtain robust time integration methods that work also for stiff problems the energy conserving methods are extended to a new class of additive runge kutta methods which combine energy conservation with l stability in this class the radau iia b method has the best properties results for a number of test cases on two stage methods indicate that for pure convection problems the additive radau iia b method is competitive with the gauss methods however for stiff problems such as convection dominated flows with thin boundary layers both the higher order gauss and radau iia b method suffer from order reduction overall the gauss methods are the preferred method for energy conserving time integration of the incompressible navier stokes equations

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

optimal control of harvest and bifurcation of a prey predator model with stage structure abstract this paper describes a prey predator model with stage structure for prey the adult prey and predator populations are harvested in the proposed system the dynamic behavior of the model system is discussed it is observed that singularity induced bifurcation phenomenon is appeared when variation of the economic interest of harvesting is taken into account state feedback controller is incorporated to stabilize the model system in case of positive economic interest harvesting of prey and predator population are used as controls to develop a dynamic framework to investigate the optimal utilization of the resource sustainability properties of the stock and the resource rent earned from the resource the pontryagin s maximum principle is used to characterize the optimal controls the optimality system is derived and then solved numerically using an iterative method with runge kutta fourth order scheme simulation results show that the optimal control scheme can achieve sustainable ecosystem

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

stability and bifurcation analysis of a stage structured predator prey model with time delay abstract in this paper we proposed and analyzed a prey predator system with stage structured for the predator population a time delay is incorporated due to the gestation for the matured predator all the possible non negative equilibria are obtained and their local as well as global behavior are studied choosing delay as a bifurcation parameter the existence of the hopf bifurcation of the system has been investigated moreover we use the normal form method and the center manifold theorem to examine the direction of the hopf bifurcation and the nature of the bifurcating periodic solution some numerical simulations are given to support the analytical results some interesting conclusions are obtained from our analysis and it is given at the end of the paper

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 of a competition model with two stage structure a population model with stage structure which describes the competition of two species for space is considered the model is established under the assumptions that reproductive rates of two species are affected by competition and that the space occupied by one type of juveniles cannot be neglected estimates on the length of delays for which positive equilibrium of the model remains stable are given sufficient conditions are also derived that ensure global stability of positive equilibrium

permanence of a stage structured predator prey system a stage structured predator prey system stage structure for both predator and prey with discrete delay is studied in this paper by introducing a new lemma and applying the standard comparison theorem a set of novel criteria which ensure the permanence of the system is obtained our result supplements the main results of chen xie and li partial survival and extinction of a delayed predator prey model with stage structure applied mathematics and computation 219 8 2012 4157 4162

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

projected implicit runge kutta methods for differential algebraic equations in this paper a new class of numerical methods projected implicit runge kutta methods is introduced for the solution of index 2 hessenberg systems of initial and boundary value differential algebraic equations daes these types of systems arise in a variety of applications including the modeling of singular optimal control problems and parameter estimation for differential algebraic equations such as multibody systems the new methods appear to be particularly promising for the solution of dae boundary value problems where the need to maintain stability in the differential part of the system often necessitates the use of methods based on symmetric discretizations previously defined symmetric methods have severe limitations when applied to these problems including instability oscillation and loss of accuracy the new methods overcome these difficulties for linear problems we define an essential underlying boundary value ode and prove well conditioning of the differential or state space solutio

global dynamics and bifurcation in a stage structured prey predator fishery model with harvesting abstract this paper describes a prey predator model with stage structure for predator and selective harvesting effort on predator population the holling type ii functional response function is taken into consideration all the equilibria of the proposed system are determined and the behavior of the system is investigated near them local stability of the system is analyzed geometric approach is used to derive the sufficient conditions for global stability of the system the occurrence of hopf bifurcation of the model system in the neighborhood of the co existing equilibrium point is shown through considering maximal relative increase of predation as bifurcation parameter fishing effort used to harvest predator population is considered as a control to develop a dynamic framework to investigate the optimal utilization of the resource sustainability properties of the stock and the resource rent earned from the resource pontryagin s maximum principle is used to characterize the optimal control the optimal system is derived and then solved numerically using an iterative method with runge kutta fourth order scheme simulation results show that the optimal control scheme can achieve sustainable ecosystem

periodic solutions of a nonautonomous predator prey system with stage structure and time delays a nonautonomous lotka volterra type predator prey 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 do not feed on prey and do not have the ability to reproduce by some comparison arguments we first discuss the permanence of the model by using the continuation theorem of coincidence degree theory sufficient conditions are derived for the existence of positive periodic solutions to the model by means of a suitable lyapunov functional sufficient conditions are obtained for the uniqueness and global stability of the positive periodic solutions to the model

persistence and periodicity of a delayed ratio dependent predator prey model with stage structure and prey dispersal a delayed periodic ratio dependent predator prey model with prey dispersal and stage structure for predator is investigated it is assumed that immature individuals and mature individuals of the predator species are divided by a fixed age and that immature predators don t have the ability to attack prey and that predator species is confined to one of the patches while the prey species can disperse between two patches we first discuss the uniform persistence and impermanence of the model by using gaines and mawhin s continuation theorem of coincidence degree theory a set of easily verifiable sufficient conditions are derived for the existence of positive periodic solutions of the proposed model numerical simulations are presented to illustrate the feasibility of our main results

asymptotic behavior of a stochastic non autonomous predator prey system with jumps in this paper a two species stochastic non autonomous food chain predator prey system with jumps is proposed and studied the asymptotic properties of the system are examined sufficient conditions for extinction non persistence in the mean weak persistence in the mean and weak persistence of the system are established results show that levy jumps are disadvantageous for the persistence of the populations furthermore we also show that the solution is stochastically ultimate bounded under certain conditions some examples together with numerical simulations are introduced to illustrate our main results

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

correction to comparison of diversity combining techniques for rayleigh fading channels the authors comment that the probability density function pdf of the signal to noise ratio snr for third order selection combining sc3 given by eng kong and milstein see ibid vol 44 p 1117 29 1996 is incorrect a correction is given by presenting a more efficient method of deriving the generalized pdf of the snr essential in the analysis of nth order selection combining

partial survival and extinction of a delayed predator prey model with stage structure abstract in this paper we revisit the non persistent property of a stage structured predator prey system which was proposed by ma et al 2008 z h ma z z li s f wang t li f p zhang permanence of a predator prey system with stage structure and time delay appl math comput 201 2008 pp 65 71 by applying the standard comparison theorem some novel results concern with the extinction of the system and partial survival of the predator prey species respectively are obtained one of the interesting finding is that for this system the extinction of prey may not necessarily lead to extinction of predator

global attractivity of periodic solutions of population models abstract this paper studies periodic solutions of two types of population models with time delays and periodic coefficients the first represents one species growth with delayed recruitments and the second models a single species despersal among the n patches by developing the theory of monotone and concave operators to functional differential equations we establish conditions under which each model admits a positive periodic solution which attracts all positive solutions

a nonautonomous predator prey system with stage structure and double time delays in the present paper we study a nonautonomous predator prey model with stage structure and double time delays due to maturation time for both prey and predator we assume that the immature and mature individuals of each species are divided by a fixed age and the mature predator only attacks the immature prey based on some comparison arguments we discuss the permanence of the species by virtue of the continuation theorem of coincidence degree theory we prove the existence of positive periodic solution by means of constructing an appropriate lyapunov functional we obtain sufficient conditions for the uniqueness and the global stability of positive periodic solution two examples are given to illustrate the feasibility of our main results

dynamical properties of a stage structured three species model with intra guild predation this paper considers a stage structured three species model with intra guild predation igp first we show local and global stability of igp model it is known that introduction of igp in tritrophic food chain can destabilize the system so in order to ensure survival of all species for all future time we show a necessary and sufficient condition for permanence of igp model next we consider the igp model with a stage structure for predator the model uses time delay to express a maturation period and a through stage survival rate for the predator by using stability switch criteria which can provide practical guidelines that combine graphical information with analytical work we can show that the delay can stabilize the igp model

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 of stage structured population models in order to model populations which go through distinct stages such as laboratory insect populations it is necessary to take the age structure of the population into account the oscillations which have frequently been observed in the sizes of such populations cannot be explained by a model which ignores the effects of age structure while it is feasible to use a fully age structured model of mckendrickkvon foerster type 3 or an analogous size structured model 4 it is generally impossible to derive qualitative information about the behavior of solutions of such models accordingly models have been proposed which subdivide the lifetime of an individual into two stages larvae and adults with different dynamics in each stage such models may be formulated as systems of differentialdifference equations and several different types of systems of differentialdifference equations to model different types of larval competition have been proposed in s our purpose is to analyze the stability properties of the various models proposed in s using the standard method of determining equilibria linearizing about an equilibrium and locating the roots of the corresponding characteristic equation by an equilibrium of a system of differential difference equations we mean simply a constant solution thus equilibria are found by setting the right side of each equation equal to zero assuming that each equation of the system has been solved for the derivatives of the unknown functions in cases where every constant is a solution of one of the equations in a system it is necessary to replace that equation by an integrated form which incorporates the initial data in order to solve for equilibria the linearization of a system about an equilibrium is obtained by using the deviations of the unknown functions from equilibrium as new variables expanding by taylor s theorem and retaining only the linear terms the

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

semi lagrangian multistep exponential integrators for index 2 differential algebraic systems implicit explicit imex multistep methods are very useful for the time discretization of convection diffusion pde problems such as the burgers equations and the incompressible navier stokes equations in the latter as well as in pde models of plasma physics and of electromechanical systems semi discretization in space gives rise to differential algebraic dae system of equations often of index higher than 1 in this paper we propose a new class of exponential integrators for index 2 daes arising from the semi discretization of pdes with a dominating and typically nonlinear convection term this class of problems includes the incompressible navier stokes equations the integration methods are based on the backward differentiation formulae bdf and they can be applied without modifications in the semi lagrangian integration of convection diffusion problems the approach gives improved performance at low viscosity regimes

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

existence of positive periodic solution for nonautonomous predator prey system with diffusion and time delay a two species nonautonomous predator prey system with time delay and diffusion is investigated a sufficient condition of the existence of positive periodic solution is established for the system by using the continuation theorem of coincidence degree theory

asymptotic behavior of a predator prey system with diffusion and delays abstract in this paper the asymptotic behavior of solutions of a predator prey system is determined the model incorporates time delays due to gestation and assumes that the prey disperses between two patches of a heterogeneous environment with barriers between patches and that the predator disperses between the patches with no barrier conditions are established for the permanence of the populations and the global attractivity of a positive equilibrium

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

qualitative analysis of a prey predator model with stage structure for the predator in this paper we propose a diffusive prey predator model with stage structure for the predator we first analyze the stability of the nonnegative steady states for the reduced ode system and then study the same question for the corresponding reaction diffusion system with homogeneous neumann boundary conditions we find that a hopf bifurcation occurs in the ode system but no turing pattern happens in the reaction diffusion system however when a natural cross diffusion term is included in the model we can prove the emergence of stationary patterns i e nonconstant positive stationary solutions for this system moreover these stationary patterns do not exist in the considered parameter regime when there is no cross diffusion

almost periodic solution of the non autonomous two species competitive model with stage structure abstract sufficient conditions are obtained for the existence of a unique globally attractive strictly positive componentwise almost periodic solution of a non autonomous almost periodic competitive two species model with a stage structure in one species an example together with its numeric simulations shows the feasibility of our main results our result generalizes the main results of zeng et al g z zeng l s chen l h sun y liu permanence and the existence of the periodic solution of the non autonomous two species competitive model with stage structure adv complex syst 7 3 4 2004 385 393

global dynamics of a predator prey model with stage structure for the predator the global properties of a predator prey model with nonlinear functional response and stage structure for the predator are studied using lyapunov functions and lasalle s invariance principle it is found that under hypotheses which ensure the uniform persistence of the system and the existence of a unique positive steady state a feasible a priori lower bound condition on the abundance of the prey population ensures the global asymptotic stability of the positive steady state a condition which leads to the extinction of the predators is indicated we also obtain results on the existence and stability of periodic solutions in particular when 4 2 fails to hold and the unique positive steady state e becomes unstable the coexistence of prey and predator populations is ensured for initial populations not on the one dimensional stable manifold of e albeit with fluctuating population sizes

global stability in chemostat type competition models with nutrient recycling this note corrects some typos and errors in the paper s ruan and x z he siam j appl math 58 1998 pp 170 192

persistence and global stability of a ratio dependent predator prey model with stage structure a ratio dependent predator prey model with stage structure for prey is investigated first sufficient conditions are derived for the uniform persistence and impermanence of the model next by constructing appropriate lyapunov functions a set of easily verifiable sufficient conditions are obtained for the global asymptotic stability of nonnegative equilibria of the model numerical simulations are presented to illustrate the validity of our main results

global convergence of a reaction diffusion predator prey model with stage structure for the predator abstract a lotka volterra type reaction diffusion predator prey model with stage structure for the predator and time delay due to maturity is investigated by successively modifying the coupled lower upper solution pairs sufficient conditions independent of the effect of spatial diffusion are derived for the global convergence of positive solutions to the proposed problem

monotone semiflows generated by functional differential equations abstract this obtains sufficient condition for an autonomous functional differential equation to generate a strongly monotone semiflow on a suitable state space this allows the application to functional differential equations of very powerful recent results on strongly monotone semiflows due to hirsch and matano in addition a very striking relationship is established between such functional differential equations and corresponding ordinary differential equations an example involving a biochemical feedback loop is considered keywords stability steady states

reversible methods of runge kutta type for index 2 daes a new interpretation of runge kutta methods for differential algebraic equations daes of index 2 is presented where a step of the method is described in terms of a smooth map smooth also with respect to the stepsize this leads to a better understanding of the convergence behavior of runge kutta methods that are not stiffly accurate in particular our new framework allows for the unified study of two order improving techniques for symmetric runge kutta methods namely post projection and symmetric projection specially suited for solving reversible index 2 daes

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

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