accurate and efficient power calculations for 2 x m tables in unmatched case control designs the aim of this article was to derive an approximation of the distribution of pearson s statistic for 2 x m contingency tables to calculate power for case control studies accurately and efficiently in terms of computer time we first prove that rather than a non central chi square distribution pearson s statistic is asymptotically equivalent with the sum of squares of m independent normal random variables whose variances are typically different under the alternative hypothesis based on this asymptotically equivalent ae we derive a cost effective approximation ce numerical results show that ce was almost as precise as ae but computationally more efficient although somewhat less costly in terms of cpu time we show that a commonly used approximation using the non central chi square distribution can be very inaccurate and overestimate power in some scenarios and underestimate it in others simulations and exact distributions on the other hand are accurate but computationally very intensive compared to our ce the ce reached its lowest accuracy under the null hypothesis where it has a chi square distribution with m 1 degree of freedom this suggests that ce can be used to calculate power for tables where researchers would feel comfortable using pearson s chi square test

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

divergence criterion for generic planar systems the divergence criterion has been shown to be helpful in distinguishing between sub and supercritical hopf bifurcations but its applicability is limited to systems whose divergence is sign definite a step by step computational procedure which allows one to extend the applicability of the divergence criterion is derived by altering the system to an equivalent one with sign definite divergence the procedure is based on multiplying the original vector field by a positive quadratic function in a neighborhood of the bifurcating rest point this procedure is then applied to several examples of planar systems that exhibit the hopf bifurcation specifically it is demonstrated that only supercritical bifurcations occur in a system modeling specific immune responses with handling time it is also shown that the fitzhugh nagumo equations and the chemostat equations with substrate inhibition and linear yield coefficient may exhibit both sub and supercritical hopf bifurcations in both cases simple analytic cri

choice of test for association in small sample unordered r x c tables pearson s chi squared the likelihood ratio and fisher freeman halton s test statistics are often used to test the association of unordered r x c tables asymptotical exact conditional or exact conditional with mid p adjustment methods are commonly used to compute the p value we have compared test power and significance level for these test statistics and p value calculations in small sample r x c tables mostly 3 x 2 and some with both r and c are greater than 2 after extensive simulations in general we recommend using an exact conditional mid p test with pearson s chi squared or fisher freeman halton s statistic which usually is the most powerful test yet preserve the approximate significance level moreover we recommend that the asymptotic pearson s chi squared or other asymptotic tests not be used for small sample r x c tables

dynamics of a predator prey model we describe the bifurcation diagram of limit cycles that appear in the first realistic quadrant of the predator prey model proposed by r m may stability and complexity in model ecosystems princeton university press princeton nj 1974 in particular we give a qualitative description of the bifurcation curve when two limit cycles collapse on a semistable limit cycle and disappear moreover we show that locally asymptotic stability of a positive equilibrium point does not imply global stability for this class of predator prey models

multiparametric bifurcation analysis of a basic two stage population model in this paper we investigate long term dynamics of the most basic model for stage structured populations in which the per capita transition from the juvenile into the adult class is density dependent the model is represented by an autonomous system of two nonlinear differential equations with four parameters for a single population we find that the interaction of intra adult competition and intra juvenile competition gives rise to multiple attractors one of which can be oscillatory a detailed numerical study reveals a rich bifurcation structure for this two dimensional system originating from a degenerate bogdanov takens bt bifurcation point when one parameter is kept constant depending on the value of this fixed parameter the corresponding triple critical equilibrium has either an elliptic sector or it is a topological focus which is demonstrated by the numerical normal form analysis it is shown that the canonical unfolding of the codimension three bt point reveals the underlying dynamics of

abelian integrals in unfoldings of codimension 3 singularities with nilpotent linear parts abstract this paper is concerned with the upper bound of the number of limit cycles in unfolding of codimension 3 planar singularities with nilpotent linear parts after making a central rescaling the problem reduces to a perturbation problem of a one parameter family of quadratic reversible systems as the parameter a 1 1 0 is rational except the case a 2 3 based on the chebyshev criterion for abelian integrals and a rationalizing transformation the problem could be solved theoretically to illustrate our approaches two particular cases corresponding to nilpotent codimension 3 saddle and elliptic case respectively are proved where the upper bound of the number of limit cycles is two

multiple focus and hopf bifurcations in a predator prey system with nonmonotonic functional response in this paper we develop a criterion to calculate the multiplicity of a multiple focus for general predator prey systems as applications of this criterion we calculate the largest multiplicity of a multiple focus in a predator prey system with nonmonotonic functional response p x frac x ax 2 bx 1 studied by zhu campbell and wolkowicz siam j appl math 63 2002 pp 636 682 and prove that the degenerate hopf bifurcation is of codimension two furthermore we show that there exist parameter values for which this system has a unique positive hyperbolic stable equilibrium and exactly two limit cycles the inner one unstable and outer one stable numerical simulations for the existence of the two limit cycles bifurcated from the multiple focus are also given in support of the criterion

the number of limit cycles of certain polynomial differential equations two dimensional differential systems are considered where p and q are polynomials the question of interest is the maximum possible numberof limit cycles of such systems in terms of the degree of p and q an algorithm is described for determining a so called focal basis this can be implemented on a computer estimates can then be obtained for the number of small amplitude limit cycles the technique is applied to certain cubic systems a class of examples with exactly five small amplitude limit cycles is constructed quadratic systems are also considered

bifurcation analysis of a predator prey system involving group defence a class of odes of generalized gause type modeling predator prey interaction is considered the prey are assumed to exhibit a phenomenon called group defence that is predation is decreased or even eliminated due to the ability of the prey to defend or disguise themselves as their numbers increase using the carrying capacity of the environment as the bifurcation parameter it is shown that the model undergoes a sequence of bifurcations that includes a homoclinic bifurcation as well as a hopf bifurcation conditions that hold even in the case of no group defence that ensure a subcritical hopf bifurcation and also the spontaneous appearance of a semistable periodic orbit that splits into a pair one stable and one unstable of periodic orbits are given ecological ramifications are considered unlike the classical model sufficient enrichment of the environment combined with group defence leads to extinction of the predator deterministically for almost all initial conditions providing strong support fo

uniqueness of periodic solutions of a nonautonomous density dependent predator prey system abstract in this present paper we investigate the uniqueness of periodic solutions of a nonautonomous density dependent and ratio dependent predator prey system where not only the prey density dependence but also the predator density dependence are considered such that the studied predator prey system conforms to the realistically biological environment we start with a sufficient condition for the permanence of the system and then construct a weaker sufficient condition by introducing a specific set denoted as based on this and the brouwer fixed point theorem we obtain the existence condition of positive periodic solutions moreover since the uniqueness of positive periodic solutions can be ensured by global attractiveness we alternatively introduce a sufficient condition for global attractiveness similarly we also provide a sufficient condition for the uniqueness of non negative periodic solutions

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

bifurcation analysis in a host generalist parasitoid model with holling ii functional response abstract in this paper we study a host generalist parasitoid model with holling ii functional response where the generalist parasitoids are introduced to control the invasion of the hosts it is shown that the model can undergo a sequence of bifurcations including cusp focus and elliptic types degenerate bogdanov takens bifurcations of codimension three and a degenerate hopf bifurcation of codimension at most two as the parameters vary and the model exhibits rich dynamics such as the existence of multiple coexistent steady states multiple coexistent periodic orbits homoclinic orbits etc moreover there exists a critical value for the carrying capacity of generalist parasitoids such that i when the carrying capacity of the generalist parasitoids is smaller than the critical value the invading hosts can always persist despite of the predation by the generalist parasitoids i e the generalist parasitoids cannot control the invasion of hosts ii when the carrying capacity of the generalist parasitoids is larger than the critical value the invading hosts either tend to extinction or persist in the form of multiple coexistent steady states or multiple coexistent periodic orbits depending on the initial populations i e whether the invasion can be stopped and reversed by the generalist parasitoids depends on the initial populations iii in both cases the generalist parasitoids always persist numerical simulations are presented to illustrate the theoretical results

nilpotent singularities and dynamics in an sir type of compartmental model with hospital resources abstract an sir type of compartmental model with a standard incidence rate and a nonlinear recovery rate was formulated to study the impact of available resources of public health system especially the number of hospital beds cusp focus and elliptic type of nilpotent singularities of codimension 3 are discovered and analyzed in this three dimensional model complex dynamics of disease transmission including multi steady states and multi periodicity are revealed by bifurcation analysis large amplitude oscillations found in our model provide a more reasonable explanation for disease recurrence with clinical data our studies have practical implications for the prevention and control of infectious diseases

bifurcations and complex dynamics of an sir model with the impact of the number of hospital beds abstract in this paper we establish an sir model with a standard incidence rate and a nonlinear recovery rate formulated to consider the impact of available resource of the public health system especially the number of hospital beds for the three dimensional model with total population regulated by both demographics and diseases incidence we prove that the model can undergo backward bifurcation saddle node bifurcation hopf bifurcation and cusp type of bogdanov takens bifurcation of codimension 3 we present the bifurcation diagram near the cusp type of bogdanov takens bifurcation point of codimension 3 and give epidemiological interpretation of the complex dynamical behaviors of endemic due to the variation of the number of hospital beds this study suggests that maintaining enough number of hospital beds is crucial for the control of the infectious diseases

a quasi exact test for comparing two binomial proportions the use of the fisher exact test for comparing two independent binomial proportions has spawned an extensive controversy in the statistical literature many critics have faulted this test for being highly conservative partly in response to such criticism some statisticians have suggested the use of a modified non randomized version of this test namely the mid p value test this paper examines the actual type i error rates of this test for both one sided and two sided tests and for a wide range of sample sizes we show that the actual levels of significance of the mid p test tend to be closer to the nominal level as compared with various classical tests the computational effort required for the mid p test is no more than that needed for the fisher exact test further the basis for its modification is a natural adjustment for discreteness thus the test easily generalizes to r c contingency tables and other discrete data problems

global dynamics of a predator prey model abstract this paper deals with the dynamics of a predator prey model with hassell varley holling functional response first we show that the predator coexists with prey if and only if predator s growth ability is greater than its death rate second using a blow up technique we prove that the origin equilibrium point is repelling and extinction of both predator and prey populations is impossible third the local and global stability of the positive steady state coincide when the predator interference is large finally for a typical biological case we show instability of the positive equilibrium implies global stability of the limit cycle numerical simulations are carried out for a hypothetical set of parameter values to substantiate our analytical findings

exact inference for categorical data recent advances and continuing controversies methods for exact small sample analyses with categorical data have been increasingly well developed in recent years a variety of exact methods exist primarily using the approach that eliminates unknown parameters by conditioning on their sufficient statistics in addition a variety of algorithms now exist for implementing the methods this paper briefly summarizes the exact approaches and describes recent developments controversy continues about the appropriateness of some exact methods primarily relating to their conservative nature because of discreteness this issue is examined for two simple problems in which discreteness can be severe interval estimation of a proportion and the odds ratio in general adjusted exact methods based on the mid p value seem a reasonable way of reducing the severity of this problem

recommended tests for association in 2 2 tables summary the asymptotic pearson s chi squared test and fisher s exact test have long been the most used for testing association in 2 2 tables unconditional tests preserve the significance level and generally are more powerful than fisher s exact test for moderate to small samples but previously were disadvantaged by being computationally demanding this disadvantage is now moot as software to facilitate unconditional tests has been available for years moreover fisher s exact test with mid p adjustment gives about the same results as an unconditional test consequently several better tests are available and the choice of a test should depend only on its merits for the application involved unconditional tests and the mid p approach ought to be used more than they now are the traditional fisher s exact test should practically never be used copyright q 2009 john wiley sons ltd

multiple bifurcation in a predator prey system with nonmonotonic predator response a model of a predator prey system showing group defence on the part of the prey is formulated and reduced to a three parameter family of quartic polynomial systems of equations mathematically this system contains the volterra lotka system and yields numerous kinds of bifurcation phenomena including a codimension two singularity of cusp type in a neighbourhood of which the quartic system realises every phase portrait possible under small smooth perturbation biologically the nonmonotonic behaviour of the predator response function allows existence of a second singularity in the first quadrant so that the system exhibits an enrichment paradox and for certain choices of parameters coexistence of stable oscillation and a stable equilibrium

recommended tests and confidence intervals for paired binomial proportions we describe evaluate and recommend statistical methods for the analysis of paired binomial proportions a total of 24 methods are considered the best tests for association include the asymptotic mcnemar test and the mcnemar mid p test for the difference between proportions we recommend two simple confidence intervals with closed form expressions and the asymptotic score interval the asymptotic score interval is also recommended for the ratio of proportions as is an interval with closed form expression based on combining two wilson score intervals for the single proportion for the odds ratio we recommend a transformation of the wilson score interval and a transformation of the clopper pearson mid p interval we illustrate the practical application of the methods using data from a recently published study of airway reactivity in children before and after stem cell transplantation and a matched case control study of the association between floppy eyelid syndrome and obstructive sleep apnea hypopnea syndrome

canard cycles for predator prey systems with holling types of functional response abstract by using the singular perturbation theory developed by dumortier and roussarie and recent work of de maesschalck and dumortier we study the canard phenomenon for predator prey systems with response functions of holling types we first develop a formula for computing the slow divergence integrals by using the formula we prove that for the systems with the response function of holling types iii and iv the cyclicity of any limit periodic set is at most two that is at most two families of hyperbolic limit cycles or at most one family of limit cycles with multiplicity two can bifurcate from the limit periodic set by small perturbations we also indicate the regions in parameter space where the corresponding limit periodic set has cyclicity at most one or at most two

asymptotic behavior of solutions of a periodic diffusion system this paper deals with a periodic reaction diffusion system of plankton allelopathy under homogeneous neumann boundary conditions based on the result of ahmad and lazer we show some estimates and nonexistence results for the positive solutions of the system furthermore we investigate the asymptotic behavior of the solutions of the system that is one species dies out and the other exists as time t tends to infinity

explicit transversality conditions and local bifurcation diagrams for bogdanov takens bifurcation on center manifolds abstract this application oriented study is concerned with the derivation of parameter dependent normal forms for the codimension two bogdanov takens bifurcation of n dimensional m parameterized systems on the basis of the homological method in the case of an enduring equilibrium simple formulas are obtained for the transformation of parameters enabling the formulation of explicit transversality conditions and bifurcation diagrams to at most the second order moreover in z 2 symmetric systems the calculation can be further limited within certain subspaces in the general case existing results are re derived and a revision necessary for determining the bifurcation diagrams to the second order is then provided these results facilitate the derivation of normal forms check of transversality and depiction of bifurcation diagrams for the bogdanov takens bifurcation

bifurcation analysis of a plant herbivore model with toxin determined functional response a system of ordinary differential equations is considered which models the plant herbivore interactions mediated by a toxin determined functional response the new functional response is a modification of the traditional holling type ii functional response by explicitly including a reduction in the consumption of plants by the herbivore due to chemical defenses a detailed bifurcation analysis of the system reveals a rich array of possible behaviors including cyclical dynamics through hopf bifurcations and homoclinic bifurcation the results are obtained not only analytically but also confirmed and extended numerically 2007 published by elsevier inc

dynamics of a diffusion reaction prey predator model with delay in prey effects of delay and spatial components abstract we study the complex dynamics of a monod haldane type predator prey interaction model that incorporates 1 a constant time delay in the prey growth and 2 diffusion in both prey and predator we provide the rigorous results of our system including the asymptotic stability of a positive equilibrium hopf bifurcation and the direction of hopf bifurcation and the stability of bifurcated periodic solutions we also perform numerical simulations on the effects of diffusion or and delay when the corresponding ode model has either a unique interior equilibrium with two interior attractors or two interior equilibria our theoretical and numerical results show that diffusion can either stabilize or destabilize the system large delay could destabilize the system and the combination of diffusion and delay could intensify the instability of the system moreover when the corresponding ode system has two interior equilibria diffusion or time delay in prey or both could lead to the extinction of predator our results may provide us useful biological insights on population managements for prey predator interaction systems

spatiotemporal dynamics in a delayed diffusive predator model in this paper we investigate the spatiotemporal dynamics of a delayed reaction diffusion leslie gower model based on the stability analysis we demonstrate that delayed feedback may generate hopf and turing instability under some conditions resulting in spatial patterns one of the most interesting findings is that the model exhibits complex pattern replication pure turing instability gives birth to spots spots stripes mixture stripes stripes holes mixture and holes patterns pure hopf instability to spiral wave pattern and hopf turing instability to chaotic wave pattern our results well extend the findings of spatiotemporal dynamics in the delayed reaction diffusion predator prey model and indicate that time delay play an important roles in pattern formation

global qualitative analysis of a quartic ecological model abstract in this paper we complete the global qualitative analysis of a quartic ecological model in particular studying global bifurcations of singular points and limit cycles we prove that the corresponding dynamical system has at most two limit cycles

stability and further analytical bifurcation behaviors of moran ricker model with delayed density dependent birth rate regulation abstract in this paper we consider moran ricker model with delayed density dependent birth rate presented by neverova et al 2016 it is well known that normal form of a dynamical system is easier to work with while it has the same qualitative properties as those of the original one firstly existence and local stability analysis of the model fixed points are addressed then normal form theory and perturbation method are applied to investigate different types of bifurcations included in the model it is demonstrated the presence of transcritical flip and neimark sacker bifurcations in the model in addition it is proved that the model has a chaotic behavior in the sense of marotto finally numerical simulations are provided to verify our analytic results compared with those obtained in neverova et al 2016 and explore further rich dynamics of the model as well

on alleged gains in power from lower p values the various suggestions that have been made to increase the power of fisher s test for 2 2 tables are shown to give no real increases one sided tests are examined in detail but two sided test problems are also considered the need for flexibility in use of p values is stressed

bifurcations in a predator prey system of leslie type with generalized holling type iii functional response abstract we consider a predator prey system of leslie type with generalized holling type iii functional response p x m x 2 a x 2 b x 1 by allowing b to be negative b 2 a p x is monotonic for b 0 and nonmonotonic for b 0 when x 0 the model has two non hyperbolic positive equilibria one is a multiple focus of multiplicity one and the other is a cusp of codimension 2 for some values of parameters and a degenerate bogdanov takens singularity focus or center case of codimension 3 for other values of parameters when there exist a multiple focus of multiplicity one and a cusp of codimension 2 we show that the model exhibits subcritical hopf bifurcation and bogdanov takens bifurcation simultaneously in the corresponding small neighborhoods of the two degenerate equilibria respectively different phase portraits of the model are obtained by computer numerical simulations which demonstrate that the model can have i a stable limit cycle enclosing two non hyperbolic positive equilibria ii a stable limit cycle enclosing an unstable homoclinic loop iii two limit cycles enclosing a hyperbolic positive equilibrium iv one stable limit cycle enclosing three hyperbolic positive equilibria or v the coexistence of three stable states two stable equilibria and a stable limit cycle when the model has a bogdanov takens singularity of codimension 3 we prove that the model exhibits degenerate focus type bogdanov takens bifurcation of codimension 3 these results not only demonstrate that the dynamics of this model when b 2 a are much more complex and far richer than the case when b 0 but also provide new bifurcation phenomena for predator prey systems

bifurcations of invariant tori in predator prey models with seasonal prey harvesting in this paper we study bifurcations in predator prey systems with seasonal prey harvesting first when the seasonal harvesting reduces to constant yield it is shown that various kinds of bifurcat

predator prey systems with a general non monotonic functional response abstract in this paper we study a predator prey model with a general non monotonic functional response we first demonstrate that the non monotonicity can be explained by a tradeoff argument using game theory we then study the reduced morse smale portrait of the general system that is all the possible stable phase portraits without limit cycles we show that under suitable conditions the system admits at least one limit cycle

power comparison of two sided exact tests for association in 2 x 2 contingency tables using standard mid p and randomized test versions exact pearson s chi square likelihood ratio lr and fisher s tests are obtained from the conditional distribution of its test statistic given the row and column sums of the contingency table the power and obtained significance level of the standard mid p and randomized versions of these tests are compared for two sided tests in 2 x 2 tables using binomial and multinomial sampling the mid p type i error probabilities seldom exceed the nominal significance level the mid p and randomized test versions have approximately the same power and higher power than the standard test version the power of the pearson s chi square lr and fisher s test differ and they differ in approximately the same way for standard mid p and randomized test versions for any given set of parameters there is no general ranking between the three tests in many cases pearson s chi square and fisher s tests have almost equal power and higher power than lr in a few cases perhaps characterized by poorly balanced designs lr performs best fisher s test seems to be slightly more robust even if the design is poor

dynamical analysis of fractional order modified logistic model in this paper we study a fractional differential equation model of the single species multiplicative allee effect first we study the stability of equilibrium points further we give some sufficient conditions ensuring the existence and uniqueness of integral solution in the last section we perform several numerical simulations to validate our analytical findings

exponential extinction of a stochastic predator prey model with allee effect abstract in this paper we study a stochastic predator prey model with beddington deangelis functional response and allee effect whose coefficients are dependent on expectations we prove that there is a unique global positive solution to the system with the positive initial value moreover sufficient conditions for exponential extinction are established

consequences of double allee effect on the number of limit cycles in a predator prey model the main goal of this work is to show a comparative analysis of simple continuous time predator prey models considering the allee effect affecting the prey population also known as depensation in fisheries sciences this phenomenon may be expressed by different mathematical forms yielding a distinct number of limit cycles surrounding a positive equilibrium point when two of these different formalizations are considered in the same system it is known that the volterra predation model using the most usual form to express the allee effect has a unique limit cycle in this work considering a more complex mathematical expression the existence of two limit cycles is proved by means of the lyapunov quantities we argue that the second equation explains the existence of two allee effects affecting the same population which could justify the difference observed between the models these results imply that the election of mathematical formulation can have consequences on the fit of the observed data thus leading to mistakes for ecologists we conclude that the oscillatory behaviors and overall dynamics depend strongly on the algebraic expression of the allee effect making difficult the proposition of general results nevertheless the techniques reviewed in this paper emerge as key tools to analyze the existence of limit cycles in the presence of multiple allee effects

optimality for a diffusive predator prey system in a spatially heterogeneous environment incorporating a prey refuge abstract in this paper we consider the optimal harvesting controls for a diffusive predator prey system which is formulated by prey refuge and modified leslie gower functional response the locally and globally asymptotic stability of unique positive constant steady state is discussed under homogeneous neumann boundary condition the nonexistence and existence of nonconstant steady states are obtained by leray schauder degree theory also the optimal harvesting strategies to get maximum sustainable yield msy and maximum economic yield mey are correspondingly given

three limit cycles in a leslie gower predator prey model with additive allee effect in this work a bidimensional continuous time differential equations system is analyzed which is derived of leslie type predator prey schemes by considering a nonmonotonic functional response and allee effect on population prey for the system obtained we describe the bifurcation diagram of limit cycles that appears in the first quadrant the only quadrant of interest for the sake of realism we show that under certain conditions over the parameters the system allows the existence of three limit cycles the first two cycles are infinitesimal ones generated by hopf bifurcation the third one arises from a homoclinic bifurcation furthermore we give conditions over the parameters such that the model allows long term extinction or survival of both populations in particular the presence of a weak allee effect does not imply extinction of populations necessarily for our model

local and global bifurcations in an sirs epidemic model this paper studies the existence and stability of the disease free equilibrium and endemic equilibria for the sirs epidemic model with the saturated incidence rate considering the factor of population dynamics such as the disease related the natural mortality and the constant recruitment of population analytical techniques are used to show for some parameter values the periodic solutions can arise through the hopf bifurcation which is important to carry different strategies for the controlling disease then the codimension two bifurcation i e bt bifurcation is investigated by using a global qualitative method and the curves of saddle node bifurcation hopf bifurcation and homoclinic bifurcation are obtained at the degenerate equilibrium moreover several numerical simulations are given to support the theoretical analysis

a michaelis menten type food chain model with strong allee effect on the prey dynamical behaviours of a tritrophic food chain model with strong allee effect in the prey are studied in this paper positivity and boundedness of the system are discussed some global results on extinction of the species are derived stability analysis of the equilibrium points is presented the effect of discrete time delay is studied where the delay may be regarded as the gestation period of the superpredator numerical simulations are carried out to validate our analytical findings implications of our analytical and numerical findings are discussed critically

new conditions on the existence and stability of periodic solution in lotka volterra s population system in this paper we revisit the famous periodic lotka volterra competitive system some new and interesting sufficient conditions are obtained to guarantee the existence and global asymptotic stability of the periodic solution in the lotka volterra competitive system our method is based on mawhin s coincidence degree matrix s spectral theory and some new estimation techniques for the priori bounds of unknown solutions to the equation lx lambda nx due to this new method our new results are much different from the known results in the previous literature finally some examples and their simulations show the feasibility of our results

bifurcation analysis of a predator prey system with nonmonotonic functional response we consider a predator prey system with nonmonotonic functional response p x frac mx ax 2 bx 1 by allowing b to be negative b 2 sqrt a p x is concave up for small values of x 0 a

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

global asymptotic stability of a ratio dependent predator prey system with diffusion this paper is concerned with a predator prey system with diffusion the global asymptotic stability of the unique positive constant equilibrium is obtained under certain conditions the method used here is the upper and lower solutions combined with the monotone iteration and constructing suitable lyapunov functions

dynamics of a density dependent stage structured predator prey system with beddington deangelis functional response abstract in this paper we study the dynamics of a stage structured predator prey system with beddington deangelis functional response where not only the prey density dependence but also the predator density dependence are considered such that the studied predator prey system conforms to the realistically biological environment first we derive a sufficient and necessary condition for the existence of a unique positive equilibrium by analyzing the corresponding locations of hyperbolic curves then we provide a sufficient condition to assure the local asymptotic stability of this positive equilibrium by constructing a lyapunov function afterward by iteratively making use of the comparison theorem we propose a sufficient condition to assure its global attractiveness finally by investigating types of the limit set instead of making use of the persistence theory we prove that the predator coexists with the prey permanently if and only if positive equilibria exist

uniqueness theorems of hermitian metrics of seminegative curvature on quotients of bounded symmetric domains in the theory of locally symmetric spaces of negative ricci curvature it has been a classical problem to study the extent to which the topology of the manifold determines the geometry and in the hermitian case the complex structure the rigidity theorem of mostow 26 asserts that for a compact locally symmetric riemannian manifold of negative ricci curvature the manifold is determined up to isometry and normalizing constants by its fundamental group among the class of such manifolds with the obvious exceptions involving compact riemann surfaces the same theorem for locally symmetric riemannian manifolds of finite volume and negative ricci curvature was proved by prasad 27 in case of rank 1 and included in the super rigidity theorem of margulis 13 in the case of rank 2 in the class of compact locally symmetric hermitian manifolds of negative ricci curvature calabi vesentini 5 and borel 3 proved vanishing theorems of certain cohomology groups which imply in particular that for x locally irreducible of complex dimension 2 there exists no non trivial deformation of x as a complex manifold in this direction siu 32 33 proved the strong rigidity of the kdhler manifold x in the sense that any compact kkhler manifold m homotopic to x is necessarily biholomorphic or conjugate biholomorphic to x if m is also locally symmetric by assumption then it follows from the uniqueness of kihler einstein metrics of negative ricci curvature yau 37 that the conjugate biholomorphism is in fact an isometry up to a normalizing constant it is thus natural to ask

power of testing proportions in small two sample studies when sample sizes are equal in planning experiments having two groups of equal but small size investigators face the uncertainty of power calculations that rely on asymptotic methods this paper presents a method for determining power for two sided tests i compare two randomization tests fisher s exact test fet and the mid p mid with the uncorrected chi square test chi results show power as a function of relative risk for these methods and assesses their relative power and type i error rates mid is shown to have intermediate power between chi which is the most powerful and fet the least powerful situations are shown in which chi and mid occasionally exceed the nominal level of alpha

hilbert s 16th problem for quadratic vector fields abstract we discuss here a systematic approach towards a positive answer to hilbert s 16th problem for quadratic systems namely the existence of a uniform bound for the number of limit cycles of a quadratic system the method is the following describe the limit periodic sets surrounding the origin in a family of quadratic vector fields and prove that they have finite cyclicity in this paper we give the list of all graphics and degenerate graphics that should be considered and describe their general features we also indicate how to find or where to find concrete examples of these limit periodic sets

pattern formation of a diffusive predator prey model with strong allee effect and nonconstant death rate abstract this paper is concerned with the pattern formation of a diffusive predator prey model with strong allee effect in the prey population and nonconstant death rate for the predator the necessary and sufficient conditions of turing instability are explicitly obtained by regarding the diffusion coefficient d 2 of the predator as bifurcation parameter we demonstrate that at the critical value of the bifurcation parameter d 2 a turing bifurcation occurs i e a pattern arises the conditions for the stability of the pattern are also derived in detail our results show that strong allee effect in our model plays a crucial role in the formation of stationary pattern which is a strong contrast to the case without strong allee effect

detection and computation of high codimension bifurcations in diffuse predator prey systems abstract in this paper we consider reaction diffusion model with modified leslie gower and holling type ii functional response and by varying simultaneously three model parameters our model exhibits different types of complex dynamics this allowed us to delimit several bifurcation surfaces with higher codimension corresponding to turing turing transcritical turing bogdanov taken turing hopf andronov turing saddle node moreover by varying at least three bifurcation parameters we show that small variations in the ratio of the diffusion coefficients can significantly alter bifurcation structure finally the paper ends with the emergence of spatio temporal patterns via numerical simulations these simultaneous parameter variations leaded to spatio temporal local and global bifurcations which are always catastrophic our results give new insights about how simultaneous changes in environmental and life history parameters drive different distribution dynamics of predator prey populations this only underscores the importance of including global bifurcations in the analysis of food chain models such results can be used to improve ecological decision making on species conservation