bifurcation analysis of a generalized gause model with prey harvesting and a generalized holling response function of type iii abstract in this paper we study a generalized gause model with prey harvesting and a generalized holling response function of type iii p x m x 2 a x 2 b x 1 the goal of our study is to give the bifurcation diagram of the model for this we need to study saddle node bifurcations hopf bifurcation of codimension 1 and 2 heteroclinic bifurcation and nilpotent saddle bifurcation of codimension 2 and 3 the nilpotent saddle of codimension 3 is the organizing center for the bifurcation diagram the hopf bifurcation is studied by means of a generalized lienard system and for b 0 we discuss the potential integrability of the system the nilpotent point of multiplicity 3 occurs with an invariant line and can have a codimension up to 4 but because it occurs with an invariant line the effective highest codimension is 3 we develop normal forms in which the invariant line is preserved for studying of the nilpotent saddle bifurcation for b 0 the reversibility of the nilpotent saddle is discussed we study the type of the heteroclinic loop and its cyclicity the phase portraits of the bifurcations diagram partially conjectured via the results obtained allow us to give a biological interpretation of the behavior of the two species

dynamical behavior of lotka volterra competition systems non autonomous bistable case and the effect of telegraph noise this article is concerned with the study of trajectory behavior of lotka volterra competition bistable systems and systems with telegraph noises we proved that for bistable systems there exists a unique solution bounded above and below by positive constants the oscillatory situation of systems with telegraph noises is pointed out

hopf bifurcation of a predator prey system with stage structure and harvesting abstract in this paper a two species predator prey system with stage structure and harvesting is investigated the existence of hopf bifurcations of the system is given and the stability and directions of hopf bifurcations are determined by applying the normal form theory and the center manifold theorem

bifurcation analysis of modified leslie gower predator prey model with michaelis menten type prey harvesting abstract in the present paper we discuss bifurcation analysis of a modified leslie gower prey predator model in the presence of nonlinear harvesting in prey we give a detailed mathematical analysis of the model to describe some significant results that may arise from the interaction of biological resources the model displays a complex dynamics in the prey predator plane the permanence stability and bifurcation saddle node bifurcation transcritical hopf andronov and bogdanov takens of this model are discussed we have analyzed the effect of prey harvesting and growth rate of predator on the proposed model by considering them as bifurcation parameters as they are important from the ecological point of view the local existence and stability of the limit cycle emerging through hopf bifurcation is given the emergence of homoclinic loops has been shown through simulation when the limit cycle arising though hopf bifurcation collides with a saddle point this work reflects that the feasible upper bound of the rate of harvesting for the coexistence of the species can be guaranteed numerical simulations using matlab are carried out to demonstrate the results obtained

rendezvous search on the line with indistinguishable players alpern introduced a problem in which two players are placed on the real line at a distance drawn from a bounded distribution f known to both they can move at maximum velocity one and wish to meet as soon as possible neither knows the direction of the other nor do they have a common notion of a positive direction on the line it is required to find the symmetric rendezvous value r s f which is the minimum expected meeting time achievable by players using the same mixed strategy this corresponds to the case where the players are indistinguishable they both take directions from a controller who does not know their names in this paper we give a mixed strategy which has an expected meeting time of 1 78d mu 2 where d is the maximum of f and mu its mean this leads to an upper bound r s f le 1 78d mu 2 on the symmetric rendezvous value which is better than the upper bound r s f le 2d mu 2 obtained by alpern

stochastic persistence and stationary distribution in a holling tanner type prey predator model abstract in this paper we study a stochastic predator prey model with beddington deangelis type functional response and logistic growth for predators the deterministic model is already well studied and we recall some important results here we construct the stochastic model from the deterministic model by introducing multiplicative noise terms into the growth equations of prey and predator populations for the stochastic model we show that the system admits unique positive global solution starting from the positive initial value then we prove that the system is strongly persistent in mean when the intensity of environmental forcing is less than some threshold magnitudes finally we show that the system has a stationary distribution under certain parametric restrictions numerical simulations are carried out to substantiate the analytical results

chaotic dynamics of a three species prey predator competition model with noise in ecology in this paper we investigate a three species ecosystem consisting of a prey a predator and a top predator the predator survives on the prey and the top predator survives on both the prey and the predator the mathematical model consists of non linear simultaneous differential equations all the eight equilibrium points of the model are identified and by using routh hurwitz criteria as well as lyapunov function we derive the criteria for local and global stabilities also the population intensities of fluctuations variances around the positive equilibrium due to noise are computed their stability is also analyzed with computer simulation using matlab some numerical simulations for justifying the theoretical analysis are also provided the main conclusions are supplied in conclusion

global analysis in a predator prey system with nonmonotonic functional response a predator prey system with nonmonotonic functional response is considered global qualitative and bifurcation analyses are combined to determine the global dynamics of the model the bifurcation a

closed form approximations to the reml estimator of a variance ratio or heritability in a mixed linear model in this article we estimate heritability or intraclass correlation in a mixed linear model having two sources of variation in most applications the commonly used restricted maximum likelihood reml estimator can only be obtained via an iterative approach in some cases the algorithm used to compute reml estimates may be slow or may even fail to converge we develop a set of closed form approximations to the reml estimator and the performance of these estimators is compared with that of the reml estimator we provide guidelines regarding how to choose the estimator that best approximates the reml estimator examples presented in the article suggest that the closed form estimators compete with and in some cases outperform the reml estimator

bounded solutions and wavefronts for discrete dynamics this paper deals with the second order nonlinear difference equation dd r k dd u k q kg u k 1 0 where r k and q k are positive real sequences defined on n cup 0 and the nonlinearity g r to r is nonnegative and nontrivial sufficient and necessary conditions are given for the existence of bounded solutions starting from a fixed initial condition u 0 the same dynamic with f instead of g such that uf u 0 for u not 0 was recently extensively investigated on the contrary our nonlinearity g is of a small appearance in the discrete case its introduction is motivated by the analysis of wavefront profiles in biological and chemical models the paper emphasizes the many different dynamical behaviors caused by such a g with respect to the equation involving function f some applications in the study of wavefronts complete this work

on the stability of non autonomous perturbed lotka volterra models the paper is devoted to an extended lotka volterra system of differential equations of predator prey model the extension is proposed with perturbation terms which are null for the positive equilibrium state in the original lotka volterra system the equilibrium state is not asymptotically stable due to the fact that perturbations are periodic in time the aim of the paper is to characterize a form of perturbation terms guaranteeing the asymptotic stability or instability of equilibrium state the reason of the proposed model is that for large time scale the lotka volterra model is too simple to be realistic in the paper the non autonomous perturbations do not change the equilibrium state but introduce functions of time as well as for additional perturbed terms as for the main part of the equations modified from lotka volterra model theorems are proposed in a renormalized form of the differential equations for time and the two variables the key point of the paper comes from the use of a liapunov function introduced in section 2 which allows to obtain conditions for the asymptotic stability section 3 and instability section 4 by using a cetaiev instability theorem following conditions on the renormalized coefficients in time of system 6 an appendix recalls the main results of the liapunov direct method for non autonomous binary systems of ordinary differential equations

improved bounds for the symmetric rendezvous value on the line a notorious open problem in the field of rendezvous search is to decide the rendezvous value of the symmetric rendezvous search problem on the line when the initial distance between the two players is two we show that the symmetric rendezvous value is within the interval 4 1520 4 2574 which considerably improves the previous best known result 3 9546 4 3931 to achieve the improved bounds we call upon results from absorbing markov chain theory and mathematical programming theory particularly fractional quadratic programming and semidefinite programming moreover we also establish some important properties of this problem which could be of independent interest and useful for resolving this problem completely finally we conjecture that the symmetric rendezvous value is asymptotically equal to 4 25 based on our numerical calculations

on analysis of variance in the mixed model an analysis of variance anova is defined to be a partition of the total sum of squares into independent terms which when suitably scaled are chisquared variables a partition of less than the total sum of squares but with these properties will often suffice and is referred to as a partial anova conditions for an anova and for partial anovas selected to contain only specific parameters are given implications for estimation of variance components from an anova are also discussed these results are largely an extension of work by graybill and hultquist 1961 with unbalanced data conditions for an anova and the number of terms in it both can depend on which effects in the model are fixed and which are random this is not taken into account by those procedures for partitioning a sum of squares which distinguish between random and fixed effects only in the calculation of expected mean squares several examples are given

confidence intervals for a variance ratio or for heritability in an unbalanced mixed linear model a procedure is presented for constructing an exact confidence interval for the ratio of the two variance components in a possibly unbalanced mixed linear model that contains a single set of m random effects this procedure can be used in animal and plant breeding problems to obtain an exact confidence interval for a heritability the confidence interval can be defined in terms of the output of a least squares analysis it can be computed by a graphical or iterative technique requiring the diagonalization of an m x m matrix or alternatively the inversion of a number of m x m matrices confidence intervals that are approximate can be obtained with much less computational burden using either of two approaches the various confidence interval procedures can be extended to some problems in which the mixed linear model contains more than one set of random effects corresponding to each interval procedure is a significance test and one or more estimators

topological degree in the generalized gause prey predator model abstract we consider a generalized gause prey predator model with t periodic continuous coefficients in the case where the poincare map p over time t is well defined the result of the paper can be explained as follows we locate a subset u of r 2 such that the topological degree d i p u equals to 1 the novelty of the paper is that the later is done under only continuity and some monotonicity assumptions for the coefficients of the model a suitable integral operator is used in place of the poincare map to cope with possible nonuniqueness of solutions the paper therefore provides a new framework for studying the generalized gause model with functional differential perturbations and multi valued ingredients

competing subcommunities of mutualist and a generalized kamke theorem a model of a biological community of species is considered the community consists of two competing subcommunities each of which has the property that each pair of species of the subcommunity interact in a mutually beneficial or noninterfering manner sufficient conditions are given that the two subcommunities can coexist the coexistence state being a stable equilibrium the domains of attraction of stable equilibria are considered the sharpest results are for the special case of lotka volterra systems mathematically the fundamental tool is a generalized kamke theorem

dynamics of a class of nonautonomous semi ratio dependent predator prey systems with functional responses abstract in this paper we investigate the dynamics of a class of the so called semi ratio dependent predator prey interaction models with functional responses based on systems of nonautonomous differential equations with time dependent parameters the functional responses are classified into five types and typical examples of each type are provided then we establish sufficient criteria for the boundedness of solutions the permanence of system and the existence uniqueness and globally asymptotic stability of positive periodic solution and positive almost periodic solution some conclusive discussion is presented at the end of this paper

optimal symmetric rendezvous search on three locations in the symmetric rendezvous search game played on n locations two players are initially placed at two distinct locations the game is played in discrete steps at each of which each player can either stay where he is or move to a different location the players share no common labelling of the locations we wish to find a strategy such that if both players follow it independently then the expected number of steps until they are in the same location is minimized informal versions of the rendezvous problem have received considerable attention in the popular press the problem was proposed by alpern in 1976 alpern s 1976 hide and seek games seminar at the institut fur hohere studien vienna and it has proved notoriously difficult to analyse in this paper we prove a 20 year old conjecture that the following strategy is optimal for the game on three locations in each block of two steps stay where you are or search the other two locations in random order doing these with probabilities 1 3 and 2 3 respectively this is now the first nontrivial symmetric rendezvous game of any type to be fully solved

rendezvous search on the line with more than two players suppose n blind speed one players are placed by a random permutation onto the integers 1 to n and each is pointed randomly to the right or left what is the least expected time required form m n of them to meet together at a single point if they must all use the same strategy we call this time the symmetric rendezvous value rn ms otherwise the asymmetric value rn ma we show that r3 2a 47 48 and that rn ns is asymptotic to n 2 these results respectively extend those for two players given by alpern and gal alpern s s gal 1995 rendezvous search on the line with distinguishable players siam j control optim 33 1270 1276 and anderson and essegaier anderson e j s essegaier 1995 rendezvous search on the line with indistinguishable players siam j control optim 33 1637 1642

the concept of force in population dynamics abstract the area of population dynamics has a rich history of the development and analysis of models of biological and social phenomena using ordinary differential equations this paper describes a method for understanding the influence one variable exerts on another in such models as a force with the relative effects of these forces providing a narrative explanation of the curvature in variable behaviour using the stock flow form of a model a symbolic notation is developed that identifies the forces with the causal pathways of the model s feedback loops a force is measured by its impact defined as the ratio of acceleration to rate of change computed by differentiation along its associated pathway between variables different phases of force dominance are determined to enhance the standard stability analysis of the models providing an explanation of model behaviour in newtonian mechanical terms the concepts developed are applied to well known models from mathematical biology the spruce budworm model where force dominance identifies scenarios that give clarity to intervention points and the lotka volterra predator prey model where the analysis highlights the importance of dissipative forces in achieving stability conclusions are drawn on the explanatory power of this approach with suggestions made for future work

on deriving the inverse of a sum of matrices available expressions are reviewed and new ones derived for the inverse of the sum of two matrices one of them being nonsingular particular attention is given to text bf a text bf ubv 1 where textbf a is nonsingular and textbf u b and textbf v may be rectangular generalized inverses of textbf a textbf ubv are also considered several statistical applications are discussed

stability analysis of interconnected systems with possibly unstable subsystems abstract a direct method is presented for stability analysis of nonlinear interconnected dynamical systems a new scalar lyapunov function is considered as weighted sum of individual lyapunov functions for each free subsystem and individual scalar functions related separately to each connection sufficient conditions are obtained for asymptotic stability of the equilibrium state by testing the definity of two constant square matrices whose dimension is equal to the number of subsystems this method can assure stability of systems with possible unstable subsystems a simple numerical example is included to illustrate this theory

periodic solutions for a delayed predator prey system with stage structured predator on time scales in this paper a modified delayed predator prey system with stage structure for predator is proposed and studied which generalizes and incorporates as special cases some known models with the help of continuation theorem based on the gaines and mawhin coincidence degree theory we investigate the existence of periodic solutions for the proposed delayed predator prey system with stage structured predator and two kinds of functional responses called holling iii functional response and beddington deangelis functional response on time scales in particular when the time scale is chosen as the set of the real numbers or the integers the existence of the periodic solutions of the corresponding continuous time and discrete time models follows

persistence of periodic patterns for perturbed biological oscillators abstract we apply the perturbation method and the implicit function theorem to study the persistence of periodic patterns for two perturbed general biological oscillators one weakly coupled ordinary differential equation and one reaction diffusion system the proof relies also on the formal adjoint equation theory and the lyapunov schmidt method for the perturbed reaction diffusion model spatial temporal patterns such as rotating waves are shown to exist numerical simulations are presented to illustrate our analytical results

global attractivity in a periodic chemostat with general uptake functions a system of ode s is considered as a model of two populations competing for a nutrient where nutrient inputs and chemostat washouts are periodic as well general nutrient uptake functions which may also be time dependent and periodic are considered criteria are derived for there to exist a globally attracting positive periodic solution and a theorem on global monotonicity of attracting solutions between different systems is proved

fiducial intervals for variance components in an unbalanced two component normal mixed linear model in this article we propose a new method for constructing confidence intervals for 2 2 and the intraclass correlation 2 2 e2 in a two component mixed effects linear model this method is based on an extension of r a fisher s fiducial argument we conducted a simulation study to compare the resulting interval estimates with other competing confidence interval procedures from the literature our results demonstrate that the proposed fiducial intervals have satisfactory performance in terms of coverage probability as well as shorter average confidence interval lengths overall we also prove that these fiducial intervals have asymptotically exact frequentist coverage probability the computations for the proposed procedures are illustrated using real data examples

dynamics of a general prey predator model with prey stage structure and diffusive effects in this paper we propose and study the dynamics of a diffusive prey predator model with general functional response and stage structure for the prey firstly we consider the asymptotical stability of equilibrium points and hopf bifurcation for the reduced ode system secondly the existence and uniform boundedness of global solutions and stability of equilibrium points for the corresponding reaction diffusion system are discussed finally we establish the existence and the nonexistence of nonconstant positive steady states of this reaction diffusion system which indicates the effect of large diffusivity our results shows the importance of the diffusion rate of the predator species i e d 3 the large diffusion rate of the predator alone will help the generation of patterns however a large diffusion rate of the immature prey species or a large diffusion rate of the mature prey species can lead to the nonexistence of spatial patterns

qualitative analysis of a stochastic ratio dependent predator prey system a stochastic ratio dependent predator prey model is investigated in this paper by the comparison theorem of stochastic equations and ito s formula we obtain the global existence of a positive unique solution of the ratio dependent model besides a condition for species to be extinct is given and a persistent condition is established we also conclude that both the prey population and the ratio dependent function are stable in time average in the end numerical simulations are carried out to confirm our findings

the rendezvous search problem the author considers the problem faced by two people who are placed randomly in a known search region and move about at unit speed to find each other in the least expected time this time is called the rendezvous value of the region it is shown how symmetries in the search region may hinder the process by preventing coordination based on concepts such as north or clockwise a general formulation of the rendezvous search problem is given for a compact metric space endowed with a group of isometrics which represents the spatial uncertainties of the players these concepts are illustrated by considering upper bounds for various rendezvous values for the circle and an arbitrary metric network the discrete rendezvous problem on a cycle graph for players restricted to symmetric markovian strategies is then solved finally the author considers the problem faced by two people on an infinite line who each know the distribution of the distance but not the direction to each other

analysis of autonomous lotka volterra competition systems with random perturbation abstract this paper discusses a randomized n species lotka volterra competition system we show that this system is stable in time average under certain conditions furthermore there is a stationary distribution of this system if extra conditions are satisfied also we give the extinction condition of this system finally numerical simulations are carried out to support our results

dynamics of age structured predator prey population models a predator prey model is investigated in which the prey population is assumed to have age structure and is governed by the mckendrick von foerster partial differential equation and the predator population is described by the classical volterra lotka ordinary differential equation quite general hypotheses are assumed for the mortality function the fertility function and the functional responses of predation existence and stability of three biologically meaningful equilibria corresponding to extinction of both species persistence of one species prey and coexistence of two species are studied a particular example and some numerical results are given

rendezvous search on the line with distinguishable players two players are placed on the real line at a distance d with a distribution f known to both neither knows the direction of the other nor do they have a common notion of a positive direction on the line we seek the least expected rendezvous time r r left f right in which they can meet given maximum speeds of one we consider the cases where f is a bounded point discrete or finite mean distribution we obtain upper bounds or exact values for r and in one case an optimality condition for search strategies a connection with beck s linear search problem is established

neimark sacker bifurcations in a non standard numerical scheme for a class of positivity preserving odes we discuss the nature of neimark sacker bifurcations occurring in a non standard numerical scheme for a class of positivity preserving systems of ordinary differential equations odes which undergoes a corresponding hopf bifurcation extending previous work alexander moghadas 2005a electron j diff eqn conf 12 9 19 it is shown that the type of neimark sacker bifurcation supercritical or subcritical may be affected by the integration time step the general form of the scheme in the vicinity of a fixed point is given from which the expression for the first lyapunov coefficient for two dimensional systems valid for arbitrary time step is explicitly derived the analysis shows that this coefficient undergoes an o shift with respect to the corresponding coefficient of the original ode this could lead to a type of bifurcation which differs from the corresponding hopf bifurcation in the ode due to changes in the sign of the first lyapunov coefficient as varies this is especially problematic in the vicinity of certain types of degenerate hopf bifurcation at which this coefficient may vanish we also present a general method to eliminate the possible o shift in the bifurcation parameter of the scheme however the first lyapunov coefficient may still be subjected to an o shift leading to a possibly erroneous type of bifurcation examples are given to illustrate the theoretical results of the paper with applications to mathematical biology

dynamics of a stochastic holling tanner predator prey model abstract in the paper we study a stochastic holling tanner predator prey system first by constructing a suitable stochastic lyapunov function we establish sufficient conditions for the existence of a unique ergodic stationary distribution of the positive solutions to the system after that sufficient causes for extinction of the predator population is obtained meanwhile we also obtain the threshold between persistence and extinction of the predator population at last some examples and numerical simulations are provided to illustrate our theoretical results

limit cycles for two families of cubic systems abstract in this paper we study the number of limit cycles of two families of cubic systems introduced in previous papers to model real phenomena the first one is motivated by a model of star formation histories in giant spiral galaxies and the second one comes from a model of volterra type to prove our results we develop a new criterion on the non existence of periodic orbits and we extend a well known criterion on the uniqueness of limit cycles due to kuang and freedman both results allow to reduce the problem to the control of the sign of certain functions that are treated by algebraic tools moreover in both cases we prove that when the limit cycles exist they are non algebraic

periodic solutions and permanence for a delayed nonautonomous ratio dependent predator prey model with holling type functional response by using the continuation theorem of coincidence degree theory the existence of positive periodic solutions for a delayed ratio dependent predator prey model with holling type iii functional response x t x t a t b t t k t s x s ds c t x2 t y t m2y2 t x2 t y t y t e t x2 t m2y2 t x2 t d t is established where a t b t c t e t and d t are all positive periodic continuous functions with period 0 m 0 and k s is a measurable function with period is a nonnegative constant the permanence of the system is also considered in particular if k s 0 s where 0 s is the dirac delta function at s 0 our results show that the permanence of the above system is equivalent to the existence of positive periodic solution

homoclinic bifurcation of prey predator model with impulsive state feedback control abstract in this paper homoclinic bifurcations of a prey predator system with state impulse are investigated firstly the existence of order 1 homoclinic cycle of system 1 2 with 0 is investigated secondly choosing q as a control parameter the sufficient conditions of existence and stability of order 1 periodic solution of system 1 2 with 0 are obtained by means of the geometry theory of semi continuous dynamic systems thirdly on the basis of the theory of rotated vector fields homoclinic bifurcation of system 1 2 about parameter are also studied finally some simulations are provided to prove the main results the methods used in this paper are intuitive to prove the existence of order 1 homoclinic cycle and homoclinic bifurcations

simultaneous confidence intervals for functions of variance components in random models abstract interval estimation of certain functions of variance components is of interest to research workers in all fields of applications in which the variance component model is used confidence intervals for linear functions and ratios of variance components have been proposed by several authors for the most part these intervals are approximate with unknown exact probabilities associated with their coverage in this article a technique is given for the construction of simultaneous confidence intervals for the values of all continuous functions of the variance components in a balanced general random linear model these confidence intervals are conservative that is the actual confidence level cannot be less than any preset value the proposed technique is easy to apply as it only requires the optimization of a given continuous function of the variance components over a bounded region several examples of continuous functions are considered including linear functions and ratios of variance components

dynamical and numerical analyses of a generalized food chain model this paper focuses on the qualitative and quantitative analysis of a generalized three species food chain model the conditions for the existence and stability of the boundary and positive equilibria of the model are established by constructing an appropriate bifurcation function it is shown that the model undergoes a hopf bifurcation from the positive equilibrium for certain parameter values the root of this bifurcation function gives the bifurcation value a robust non standard numerical method is constructed and used to obtain the solution of the model numerical simulations using this method show that the hopf bifurcation is supercritical with a stable limit cycle in the positive octant

existence of a polycycle in non lipschitz gause type predator prey models abstract we study gause type predator prey models when the interaction between predator and prey is not locally lipschitz continuous in the absence of one of them we shall show that in this case there appears a polycycle which affects the existence of limit cycles for the system we apply the results to study the existence of limit cycles for a classical gause system

exact confidence sets for variance components in unbalanced mixed linear models we present a general procedure for obtaining an exact confidence set for the variance components in a mixed linear model the procedure can be viewed as a generalization of the anova method used with balanced models our procedure uses as pivotal quantities quadratic forms that are distributed independently as chi squared variables these quadratic forms are constructed with reference to spaces that are orthogonal with respect to the covariance matrix of the observation vector which is a function of the variance components for balanced models these pivotal quantities simplify to multiples of the sums of squares used in the anova method an exact confidence set for the vector of ratios of the effect variances to the error variance is also presented based on the same collection of quadratic forms computing formulas for calculating approximations to these confidence sets are presented and the results of their application to several two way data sets are given

singular perturbations of the holling i predator prey system with a focus abstract we study the occurrence of limit cyles in a model for two species predator prey interaction referred to as holling i this model is based on the phenomenological fitting of the so called functional response function to observed data in nature by a continuous piecewise differentiable function of the original models presented by holling it is the only model for which the possible asymptotic behaviour of the prey and predator densities has not been determined yet we extend the work of liu who showed that for certain values of parameters of the holling i system at least two nested limit cycles will occur surrounding a focus his case corresponds to a bifurcation problem where limit cycles are created from a system with a continuum of singularities i e a singular perturbation problem with slow fast solutions we prove that exactly two hyperbolic limit cycles occur after perturbation

positive periodic solutions in a non selective harvesting predator prey model with multiple delays abstract this paper is concerned with a predator prey model with hassell varley type functional response non selective harvesting and multiple delays some new sufficient conditions are obtained for the existence of positive periodic solutions by applying the coincidence degree theorem in addition the results are delay dependent which is different from the previous work finally simulations illustrate the effectiveness of our results

stability and bifurcation analysis on a ratio dependent predator prey model with time delay a ratio dependent predator prey model with time delay due to the gestation of the predator is investigated by analyzing the corresponding characteristic equations the local stability of a positive equilibrium and a semi trivial boundary equilibrium is discussed respectively further it is proved that the system undergoes a hopf bifurcation at the positive equilibrium using the normal form theory and the center manifold reduction explicit formulae are derived to determine the direction of bifurcations and the stability and other properties of bifurcating periodic solutions by means of an iteration technique sufficient conditions are obtained for the global attractiveness of the positive equilibrium by comparison arguments the global stability of the semi trivial equilibrium is also addressed numerical simulations are carried out to illustrate the main results

permanence and stability in non autonomous predator prey lotka volterra systems with feedback controls the main purpose of this article is considering whether or not the feedback controls have an influence on a non autonomous predator prey lotka volterra type system general criteria on permanence are established which is described by an integral form and independent of some feedback controls by constructing suitable lyapunov functionals a set of easily verifiable sufficient conditions are derived for the global stability of any positive solution to the model

optimal trade off between speed and acuity when searching for a small object a searcher seeks to find a stationary hider located at some point h not necessarily a node on a given network q the searcher can move along the network from a given starting point at unit speed but to actually find the hider she must pass it while moving at a fixed slower speed which may depend on the arc in this bimodal search game the payoff is the first time the searcher passes the hider while moving at her slow speed this game models the search for a small or well hidden object e g a contact lens improvised explosive device predator search for camouflaged prey we define a bimodal chinese postman tour as a tour of minimum time i which traverses every point of every arc at least once in the slow mode for trees and weakly eulerian networks networks containing a number of disjoint eulerian cycles connected in a tree like fashion the value of the bimodal search game is i 2 for trees the optimal hider strategy has full support on the network this differs from traditional search games where it is optimal for him to hide only at leaf nodes we then consider the notion of a lucky searcher who can also detect the hider with a positive probability q even when passing him at her fast speed this paper has particular importance for demining problems

the basins of attraction in a modified may holling tanner predator prey model with allee affect abstract i analyse a modified may holling tanner predator prey model considering an allee effect in the prey and alternative food sources for predator additionally the predation functional response or predation consumption rate is linear the extended model exhibits rich dynamics and we prove the existence of separatrices in the phase plane separating basins of attraction related to oscillation co existence and extinction of the predator prey population we also show the existence of a homoclinic curve that degenerates to form a limit cycle and discuss numerous potential bifurcations such as saddle node hopf and bogdanov takens bifurcations we use simulations to illustrate the behaviour of the model

exponential convergence and instability of solutions of uncertain dynamical systems abstract in the present paper we investigate exponential convergence and instability of finite dimensional dynamical systems determined by uncertain ordinary differential equations our approach is based on the constructive use of matrix valued lyapunov functions examples are given which illustrate the improvement of the proposed conditions

dynamic analysis of fractional order singular holling type ii predator prey system abstract in this paper a fractional order singular fos predator prey model with holling type ii functional response has been introduced and the mathematical behavior of the model from the aspect of local stability is investigated through the fractional calculus and economic theory a new and more realistic predator prey model has been extended and the solvability condition is presented besides numerical simulations are considered to illustrate the effectiveness of the numerical method and confirm the theoretical results to explore the impacts of fractional order and economic interest on the presented system in biological context it is found that the presence of fractional order in the differential model can improve the stability of the solutions and enrich the dynamics of system in addition singular models exhibit more complicated dynamics rather than standard models especially the bifurcation phenomena which can reveal the instability mechanism of systems

finite element approximation of spatially extended predator prey interactions with the holling type ii functional response we study the numerical approximation of the solutions of a class of nonlinear reaction diffusion systems modelling predator prey interactions where the local growth of prey is logistic and the predator displays the holling type ii functional response the fully discrete scheme results from a finite element discretisation in space with lumped mass and a semi implicit discretisation in time we establish a priori estimates and error bounds for the semi discrete and fully discrete finite element approximations numerical results illustrating the theoretical results and spatiotemporal phenomena are presented in one and two space dimensions the class of problems studied in this paper are real experimental systems where the parameters are associated with real kinetics expressed in nondimensional form the theoretical techniques were adapted from a previous study of an idealised reaction diffusion system garvie and blowey in eur j appl math 16 5 621 646 2005

persistence in dynamical systems soit un espace metrique localement compact de metrique d et soit e un sous ensemble clos de a frontiere e et interieur e on suppose que l on a un flot continu 7b f defini sur e tel que e est invariant par 7b f on considere la notion de persistance et on donne un critere de persistance