two parameter bifurcations in a network of two neurons with multiple delays abstract we consider a network of two coupled neurons with delayed feedback we show that the connection topology of the network plays a fundamental role in classifying the rich dynamics and bifurcation phenomena regarding eigenvalues of the connection matrix as bifurcation parameters we obtain codimension 1 bifurcations including a fold bifurcation and a hopf bifurcation and codimension 2 bifurcations including fold hopf bifurcations and hopf hopf bifurcations we also give concrete formulae for the normal form coefficients derived via the center manifold reduction that give detailed information about the bifurcation and stability of various bifurcated solutions in particular we obtain stable or unstable equilibria periodic solutions quasi periodic solutions and sphere like surfaces of solutions we also show how to evaluate critical normal form coefficients from the original system of delay differential equations without computing the corresponding center manifolds

robust model based and model assisted predictors of the finite population total the prediction approach to finite population inference has received considerable attention in recent years under this approach the finite population is assumed to be a realization from a superpopulation described by a known probability model usually a linear model the prediction approach is often criticized for its lack of robustness against model misspecification in this article we revisit this important issue and introduce a new robust prediction approach in which the superpopulation model is chosen adaptively from the well known box cox class of probability distributions the richness of the box cox class ensures robustness in our model based prediction approach we explain how our robust model based predictor can be adjusted to handle zero observations for the study variable and to achieve the design unbiasedness and benchmarking properties we demonstrate the robustness of our proposed predictors using a monte carlo simulation study and a real life example

nonlinear prediction theory and the estimation of proportions in a finite population abstract the prediction approach to finite population inference is developed for a general nonlinear model an estimator of the finite population total and an estimator of its variance are derived and the asymptotic properties of both are obtained when the random variables in the model are independent the theory is applied to the problem of estimating the total number of units that have a specified characteristic an empirical study is presented which confirms that a nonlinear bernoulli model is potentially useful for that problem but also illustrates difficulties that may be encountered comparisons with the ratio and linear regression estimators are also included

hopf transcritical bifurcation in toxic phytoplankton zooplankton model with delay abstract in this paper a phytoplankton zooplankton model with toxic liberation delay is considered firstly the critical values of hopf bifurcation transcritical bifurcation and hopf transcritical bifurcation are given and to give more detailed information about the periodic oscillations the direction and stability of hopf bifurcation is studied by using the normal form theory and center manifold theorem then we give the detailed bifurcation set by calculating the universal unfoldings near the hopf transcritical bifurcation point finally we show that the plankton system may exhibit quasi periodic oscillations which are verified both theoretically and numerically and explain the experimental observed fluctuation phenomenon of plankton population

estimation of variance of the regression estimator abstract the regression estimator and the ratio estimator are commonly used in survey practice in the past more attention has been given to the ratio estimator because of its computational ease and applicability for general sampling designs the ratio estimator is appropriate for populations whose regression line passes close to the origin if the intercept of the regression line is significantly nonzero however it is much less efficient than the regression estimator deng 1984 in general apart from n 2 terms the mean squared error mse of the former is bigger than that of the latter cochran 1977 p 196 given the present computing capacity the computational advantage of the ratio estimator should be less of a concern and the regression estimator will gain wider popularity the main purpose of this article is to provide a theoretical and empirical comparison of several variance estimators for the regression estimator in simple random sampling without replacement the companion problem for the

time delay effects on coupled limit cycle oscillators at hopf bifurcation abstract we present a detailed study of the effect of time delay on the collective dynamics of coupled limit cycle oscillators at hopf bifurcation for a simple model consisting of just two oscillators with a time delayed coupling the bifurcation diagram obtained by numerical and analytical solutions shows significant changes in the stability boundaries of the amplitude death phase locked and incoherent regions a novel result is the occurrence of amplitude death even in the absence of a frequency mismatch between the two oscillators similar results are obtained for an array of n oscillators with a delayed mean field coupling and the regions of such amplitude death in the parameter space of the coupling strength and time delay are quantified some general analytic results for the n thermodynamic limit are also obtained and the implications of the time delay effects for physical applications are discussed

double hopf bifurcation for van der pol duffing oscillator with parametric delay feedback control the stability and bifurcation of a van der pol duffing oscillator with the delay feedback are investigated in which the strength of feedback control is a nonlinear function of delay a geometrical method in conjunction with an analytical method is developed to identify the critical values for stability switches and hopf bifurcations the hopf bifurcation curves and multi stable regions are obtained as two parameters vary some weak resonant and non resonant double hopf bifurcation phenomena are observed due to the vanishing of the real parts of two pairs of characteristic roots on the margins of the death island regions simultaneously by applying the center manifold theory the normal forms near the double hopf bifurcation points as well as classifications of local dynamics are analyzed furthermore some quasi periodic and chaotic motions are verified in both theoretical and numerical ways

oscillator death in coupled functional differential equations near hopf bifurcation abstract the stability of the equilibrium solution is analyzed for coupled systems of retarded functional differential equations near a supercritical hopf bifurcation necessary and sufficient conditions are derived for asymptotic stability under general coupling conditions it is shown that the largest eigenvalue of the graph laplacian completely characterizes the effect of the connection topology on the stability of diffusively and symmetrically coupled identical systems in particular all bipartite graphs have identical stability characteristics regardless of their size furthermore bipartite graphs and large complete graphs provide respectively lower and upper bounds for the parametric stability regions for arbitrary connection topologies generalizations are given for networks with asymmetric coupling the results characterize the connection topology as a mechanism for the death of coupled oscillators near hopf bifurcation

conditional coverage properties of finite population confidence intervals abstract standardized errors t v 1 2 were calculated for both ratio and regression estimators in each of 10 000 simple random samples of n 32 from each of six populations using four different variance estimators graphs show how the percentage of intervals t 1 96 v 1 2 that fail to contain t changes as a function of the average value of the auxiliary variable in the sample they reveal that a intervals using the variance estimators from standard linear regression theory were hopelessly unreliable b intervals using the conventional finite population variance estimators showed a striking excess of failures in badly balanced samples and c none of the four variance estimators produced satisfactory confidence intervals in populations arising from badly skewed prediction models

a stabilized finite point method for analysis of fluid mechanics problems in this paper a meshless procedure termed the finite point method for solving convection diffusion and fluid flow type problems is presented the method is based on the use of a weighted least square interpolation procedure together with point collocation for evaluating the approximation integrals special emphasis is given to the stabilization of the convective terms and the neumann boundary condition which has been found to be essential to obtain accurate results some examples of application to diffusive and convective transport and compressible flow problems using quadratic fp interpolations are presented

the weighted residual technique for estimating the variance of the general regression estimator of the finite population total summary the paper deals with design based estimation of the variance of the general regression estimator of the finite population total the usual taylor linearization variance estimator is an expression in the design weighted regression residuals in many applications the resulting expression is counterintuitive from a model based standpoint the improved variance estimator in this paper attaches another simple weight called g weight to each individual residual this new variance estimator i gives valid design based confidence intervals ii is nearly unbiased uiider a suitably chosen regression model and iii works well for conditional inference examples are given

on the asymptotic distribution of ratio and regression estimators we give a formal derivation of the asymptotic normality of ratio and regression estimators of a finite population total for simple random sampling and for sampling with probability proportional to aggregate size the results are all well known and widely used of course but a rigorous development spelling out relatively simple sufficient conditions under which the standard results are valid does not seem to be available at present

hopf pitchfork bifurcation in van der pol s oscillator with nonlinear delayed feedback abstract first we identify the critical values for hopf pitchfork bifurcation second we derive the normal forms up to third order and their unfolding with original parameters in the system near the bifurcation point by the normal form method and center manifold theory then we give a complete bifurcation diagram for original parameters of the system and obtain complete classifications of dynamics for the system furthermore we find some interesting phenomena such as the coexistence of two asymptotically stable states two stable periodic orbits and two attractive quasi periodic motions which are verified both theoretically and numerically

precision estimation in sample survey inference a criterion for choice between variance estimators summary we advocate the mean squared error of predicted squared error as a universal criterion for the choice between variance estimators in sample survey inference the predictive nature of the measure rewards variance estimators adapted to the amount of information in the actual sample this makes the new measure more satisfactory than the simpler mean squared error of the variance estimator the criterion turns out to be the same for design based as for model based inference and may also be used for comparison between the design and model based theoretical variances the theory is exemplified for the ratio estimator by a study of six variance estimators suggested in the literature these calculations are primarily made under a proportional regression model but consideration is also paid to model robustness three of the six estimators are shown to be inferior to the three others which are approximately equivalent

hopf transcritical bifurcation in retarded functional differential equations abstract firstly we analyze a codimension two unfolding for the hopf transcritical bifurcation and give complete bifurcation diagrams and phase portraits in particular we express explicitly the heteroclinic bifurcation curve and obtain conditions under which the secondary bifurcation periodic solutions and the heteroclinic orbit are stable secondly we show how to reduce general retarded functional differential equation with perturbation parameters near the critical point of the hopf transcritical bifurcation to a 3 dimensional ordinary differential equation which is restricted on the center manifold up to the third order with unfolding parameters and further reduce it to a 2 dimensional amplitude system where these unfolding parameters can be expressed by those original perturbation parameters finally we apply the general results to the van der pol s equation with delayed feedback and obtain the existence of stable or unstable equilibria periodic solutions and quasi periodic solutions

a note on bayesian least squares inference for finite population models abstract this note presents some distribution free results for incorporating prior information in finite population models the formulas given are based on modifications of existing bayesian least squares estimation results and require only the specification of first and second moments of the distributions involved

prediction models and unequal probability sampling summary prediction models are used to study the horvitz thompson estimator in probabilityproportional to size sampling and six estimators of its variance the variance estimators include the horvitz thompson yates grundy and jackknife statistics as well as two bias robust estimators from prediction theory an empirical study confirms prediction theory s implications about these estimators

optimal sampling and estimation strategies under the linear model in some cases model based and model assisted inferences can lead to very different estimators these two paradigms are not so different if we search for an optimal strategy rather than just an optimal estimator a strategy being a pair composed of a sampling design and an estimator we show that under a linear model the optimal model assisted strategy consists of a balanced sampling design with inclusion probabilities that are proportional to the standard deviations of the errors of the model and the horvitz thompson estimator if the heteroscedasticity of the model is fully explainable by the auxiliary variables then this strategy is also optimal in a model based sense moreover under balanced sampling and with inclusion probabilities that are proportional to the standard deviation of the model the best linear unbiased estimator and the horvitz thompson estimator are equal finally it is possible to construct a single estimator for both the design and model variance the inference can thus be valid under the sampling design and under the model

variance estimation under two phase sampling with application to imputation for missing data summary ratio estimation under two phase simple random sampling is studied a new linearisation variance estimator that makes more complete use of the sample data than a standard one is proposed a jackknife variance estimator and its linearised version are also obtained unconditional and conditional repeated sampling properties of these variance estimators are studied through simulation applications to mass imputation under two phase sampling and deterministic imputation for missing data are also given

normal forms for retarded functional differential equations and applications to bogdanov takens singularity abstract the paper addresses for retarded functional differential equations fdes the computation of normal forms associated with the flow on a finite dimensional invariant manifold tangent to invariant spaces for the infinitesimal generator of the linearized equation at a singularity a phase space appropriate to the computation of these normal forms is introduced and adequate nonresonance conditions for the computation of the normal forms are derived as an application the general situation of bogdanov takens singularity and its versal unfolding for scalar retarded fdes with nondegeneracy at second order is considered both in the general case and in the case of differential delay equations of the form t x t x t 1

conditional properties of some estimators in stratified sampling abstract the prediction properties of the stratified expansion estimator the separate and combined ratio estimators and the separate and combined regression estimators are studied under a model appropriate to a population stratified on a size variable several estimators of variance for each total estimator are considered including standard ones from probability sampling theory alternative choices derived from a superpopulation model and the jackknife the theory is tested in an empirical study using a real population earlier studies of the ratio and regression estimators under simple random sampling plans have illustrated that conditional properties of those estimators and of the linearization variance estimators that are often used with them can be much different and less desirable than unconditional properties whether similar results hold for stratified samples and estimators has been the subject of some debate this article illustrates both theoretically and empirically that the use of stratifi

double hopf bifurcation and quasi periodic attractors in delay coupled limit cycle oscillators abstract we investigate the double hopf bifurcation at zero equilibrium point firstly we give the critical values of hopf and double hopf bifurcations secondly we implement the normal form method and the center manifold theory for delay coupled limit cycle oscillators and derive the universal unfolding and a complete bifurcation diagram of the system thirdly many interesting phenomena such as attractive periodic motion and three dimensional invariant torus are observed using numerical simulation finally the normal forms of several strong resonant cases are listed

estimating a finite population mean from unequal probability samples abstract two approaches to estimating a finite population mean from unequal probability samples are contrasted in the prediction approach a model is specified for the population values and is used to predict the nonsampled values in the generalized regression approach the horvitz thompson estimator of the population mean is modified to allow the introduction of covariate information sarndal 1980 generalized regression estimates have the desirable property of asymptotic design consistency which is not always enjoyed by estimates in the prediction class however it is suggested that the prediction approach is the more principled method of estimation if asymptotic design consistency is a desirable property in a given application then only models that yield asymptotically design consistent prediction estimates should be used two classes of models with this property are suggested namely fixed and random effects models that allow a separate intercept for subclasses of the population indexed by the pr

amplitude response of coupled oscillators abstract we investigate the interaction of a pair of weakly nonlinear oscillators eg each near a hopf bifurcation when the coupling strength is comparable to the attraction of the limit cycles changes in amplitude cannot then be ignored and there are new phenomena we show that even for simple forms of these equations there are parameter regimes in which the interaction causes the system to stop oscillating and the rest state at zero stabilized by the interaction is the only stable solution when the uncoupled oscillators have a local frequency that is independent of amplitude zero shear and the coupling is scalar we give a complete description of the behavior we then analyze more complicated equations to show the effects of amplitude dependent frequency in the uncoupled equations nonzero shear and nonscalar coupling for example when there is shear there can be bistability between a phase locked solution and an unlocked drift solution in which the oscillators go at different average frequencies there can also be bistability between a phase locked solution and an equilibrium nonoscillatory solution the equations for the zero shear case have a pair of degenerate bifurcation points and the new phenomena in the nonzero shear case arise from a partial unfolding of these singularities when the coupling is nonscalar there are a variety of new behaviors including bistability of an in phase and an anti phase solution for two identical oscillators parameters for which only the anti phase solution is stable and phase trapping i e nonlocked solutions in which the oscillators still have the same average frequency it is shown that whether the coupling is diffusive or direct has many effects on the behavior of the system

the prediction approach to robust variance estimation in two stage cluster sampling abstract robust statistics are derived for estimating the error variance when a finite population total or a ratio of totals is estimated from a two stage cluster sample in which the first stage sampling fraction is small the analysis is based on prediction superpopulation models that allow for very general correlation structure within clusters results are obtained for when all cluster sizes are known and for when sizes are known only for sample clusters ratio regression and mean of ratios statistics are in the class of population total estimators considered

lagrangian formulations to solve free surface incompressible inviscid fluid flows abstract a particle method is presented for the solution of the incompressible inviscid fluid flow equation using a lagrangian formulation the interpolated function are those used in meshless approximations and the time integration is introduced in a semi implicit way by a fractional step method in this manner both classical stabilization terms used in incompressible euler equations are unnecessary numerical diffusion for convective terms are unnecessary due to the lagrangian formulation and stabilization of pressure due to the incompressibility constraint for equal order interpolations is eliminated using the fractional step method

stability analysis of swarms in this note we specify an individual based continuous time model for swarm aggregation in n dimensional space and study its stability properties we show that the individuals autonomous agents or biological creatures will form a cohesive swarm in a finite time moreover we obtain an explicit bound on the swarm size which depends only on the parameters of the swarm model

the finite population linear regression estimator and estimators of its variance an empirical study abstract the usual variance estimator for the linear regression estimator of a finite population total is examined under some prediction superpopulation models its bias is compared with that of the least squares variance estimator also described are three bias robust alternatives one of which is the jackknife variance estimator the theoretical results are supported by an empirical study in which simple and restricted random samples as well as some purposive nonrandom samples are drawn from six real populations the results illustrate the need for prediction models and the inadequacy of randomization per se in providing a theoretical framework for robust inferences

total and partial amplitude death in networks of diffusively coupled oscillators networks of weakly nonlinear oscillators are considered with diffusive and time delayed coupling averaging theory is used to determine parameter ranges for which the network experiences amplitude death whereby oscillations are quenched and the equilibrium solution has a large domain of attraction the amplitude death is shown to be a common phenomenon which can be observed regardless of the precise nature of the nonlinearities and under very general coupling conditions in addition when the network consists of dissimilar oscillators there exist parameter values for which only parts of the network are suppressed sufficient conditions are derived for total and partial amplitude death in arbitrary network topologies with general nonlinearities coupling coefficients and connection delays

does simple random sampling provide adequate balance une etude empirique montre que sous un echantillonnage aleatoire simple les intervalles de confiance du total peuvent avoir des probabilites de recouvrement conditionnelles qui sont imposantes de facon persistante lorsque la taille de l echantillon croit

some prediction properties of balanced half sample variance estimators in single stage sampling on introduit un modele de prediction et une classe d estimateurs qui inclut plusieurs estimateurs du ratio de la regression et autres on donne une approximation a l estimateur bhs balanced half sample

bogdanov takens singularity in van der pol s oscillator with delayed feedback abstract in this paper we study the classical van der pol s equation with delayed feedback we investigate the bogdanov takens singularity and bifurcation occurring in the system with the variation of the original parameters by using the normal form method and predict the suitable choice in the feedback control in order to obtain the asymptotic stable state

all hexahedral element meshing generation of the dual mesh by recurrent subdivision abstract the domain geometry is defined by means of a closed all quadrilateral mesh the outer mesh imposes very strong restrictions on the possible connectivities between the inner hexahedral elements following the guidelines of the outer topology the inner one is almost entirely defined several ways may be decided for certain configurations some of them requiring special considerations in order to achieve a valid fem mesh the process is entirely performed by constructing the graph theoretical dual of the hexahedral mesh this means no metric information is handled until the final positioning and smoothing steps the essential steps of this scheme are described by means of examples

double hopf bifurcation of coupled dissipative stuart landau oscillators with delay in this paper the double hopf bifurcation of delay coupled dissipative stuart landau oscillators models are considered where the time delay is regarded as one of the parameters and the other is the natural frequency it is found that as the values of the two parameters vary a number of double hopf bifurcation points arise consequently it has been found that the system exhibits very rich complex dynamics some resonant and non resonant double hopf bifurcation phenomena can be observed some numerical simulations support our analysis result

emergent behavior in flocks we provide a model for both continuous and discrete time describing the evolution of a flock our model is parameterized by a constant beta capturing the rate of decay which in our model is polynomial of the influence between birds in the flock as they separate in space our main result shows that when beta 1 2 convergence of the flock to a common velocity is guaranteed while for betages1 2 convergence is guaranteed under some condition on the initial positions and velocities of the birds only

the meshless finite element method a meshless method is presented which has the advantages of the good meshless methods concerning the ease of introduction of node connectivity in a bounded time of order n and the condition that the shape functions depend only on the node positions furthermore the method proposed also shares several of the advantages of the finite element method such as a the simplicity of the shape functions in a large part of the domain b c0 continuity between elements which allows the treatment of material discontinuities and c ease of introduction of the boundary conditions copyright 2003 john wiley sons ltd

an empirical study of the ratio estimator and estimators of its variance abstract this paper reports results from an empirical study of the ratio estimator for a finite population total from each of six real populations 1 000 simple random samples 1 000 restricted random samples and three nonrandom samples of size 32 are drawn performance of the ratio estimator and of five estimators of its variance is compared with theoretical results generated using a prediction superpopulation models and b probability sampling distributions the results presented graphically show that theory based on prediction models can reveal relationships that are essential in making inferences but that are concealed in probability sampling analyses

normal forms of non resonance and weak resonance double hopf bifurcation in the retarded functional differential equations and applications the norm forms of the double hopf bifurcation for a general dde is established the van der pol duffing oscillator with delayed position and velocity feedback is investigated the dynamical classification near the double hopf bifurcation point is studied the stable periodic doubling solutions and unstable three dimensional torus are found in this paper we firstly present the general framework of calculation of normal forms of non resonance and weak resonance double hopf bifurcation for the general retarded functional differential equations by using the normal form theory of delay differential equations due to faria and magalh a es then the dynamical behavior of van der pol duffing oscillator with delayed position and velocity feedback is considered specifically the dynamical classification near the double hopf bifurcation point is investigated by analyzing the obtained normal form finally the numerical simulations support the theoretical results and present some interesting phenomena

polyhedrization of an arbitrary 3d point set abstract given a 3d point set the problem of defining the volume associated dividing it into a set of regions elements and defining a boundary surface is tackled several physical problems need to define volume domains boundary surfaces and approximating functions from a given point distribution this is for instance the case of particle methods in which all the information is the particle positions and there are not boundary surfaces definition until recently all the fem mesh generators were limited to the generation of simple elements as tetrahedral or hexahedral elements or triangular and quadrangular in 2d problems the reason of this limitation was the lack of any acceptable shape function to be used in other kind of geometrical elements nowadays there are several acceptable shape functions for a very large class of polyhedra these new shape functions together with a generalization of the delaunay tessellation presented in this paper gives an optimal marriage and a powerful tool to solve a large variety of physical problems by numerical methods the domain partition into polyhedra presented here is not a standard mesh generation the problem here is for a given node distribution to find a suitable boundary surface and a suitable mesh to be used in the solution of a physical problem by a numerical method to include new nodes or change their positions is not allowed