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

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

bifurcation analysis in van der pol s oscillator with delayed feedback in this paper a classical van der pol s equation with generally delayed feedback is considered it is shown that there are bogdanov takens bifurcation triple zero and hopf zero singularities by analyzing the distribution of the roots of the associated characteristic equation in the situation that the zero is as a simple eigenvalue the normal forms of the reduced equations are obtained by the center manifold theory and normal form method for functional differential equation and hence the stability of the fixed point is determined and transcritical and pitchfork bifurcations are found

multiple bifurcations in a delayed predator prey system with nonmonotonic functional response abstract a delayed predator prey system with nonmonotonic functional response is studied by using the normal form theory of retarded functional differential equations developed by faria and magalhaes the bifurcation analysis of the model indicates that there is a bogdanov takens singularity for any time delay value a versal unfolding of the model at the bogdanov takens singularity is obtained on the other hand it is shown that small delay changes the stability of the equilibrium of the model for some parameters and the system can exhibit hopf bifurcation as the time delay passes through some critical values

on errors in variables for binary regression models summary we consider binary regression models when some of the predictors are measured with error for normal measurement errors structural maximum likelihood estimates are considered we show that if the measurement error is large the usual estimate of the probability of the event in question can be substantially in error especially for high risk groups in the situation of large measurement error we investigate a conditional maximum likelihood estimator and its properties

identifying important results from multiple statistical tests when many statistical tests are performed simultaneously the overall chance of a type i error incorrect rejection of a true null hypothesis can substantially exceed the nominal error rate used in each individual test numerous techniques exist to adjust results of individual tests to control this problem in general these techniques apply a more stringent criterion of statistical significance a smaller p value to each individual test than normally needed to maintain the experimentwise type i error with an analysis that seeks to identify results for further research however such a conservative technique may not be appropriate we present a new approach that uses a mixture of several distributions to model the set of p values or of test statistics one component models the results consistent with a failure to reject the null hypothesis while the other distribution s in the mixture represent results inconsistent with the null hypothesis these latter results may not achieve statistical significance based on a conventional p value we illustrate the use of the method on national mortality data and on several data sets analysed previously

bifurcations stability and monotonicity properties of a delayed neural network model abstract a delay differential equation modelling an artificial neural network with two neurons is investigated a linear stability analysis provides parameter values yielding asymptotic stability of the stationary solutions these can lose stability through either a pitchfork or a hopf bifurcation which is shown to be supercritical at appropriate parameter values an interaction takes place between the pitchfork and hopf bifurcations conditions are also given for the set of initial conditions that converge to a stable stationary solution to be open and dense in the functional phase space analytic results are illustrated with numerical simulations

three and higher dimensional autonomous formations rigidity persistence and structural persistence in this paper we generalize the notion of persistence which has been originally introduced for two dimensional formations to r d for d 3 seeking to provide a theoretical framework for real world applications which often are in three dimensional space as opposed to the plane persistence captures the desirable property that a formation moves as a cohesive whole when certain agents maintain their distances from certain other agents we verify that many of the properties of rigid and or persistent formations established in r 2 are also valid for higher dimensions analysing the closed subgraphs and directed paths in persistent graphs we derive some further properties of persistent formations we also provide an easily checkable necessary condition for persistence we then turn our attention to consider some practical issues raised in multi agent formation control in three dimensional space we display a new phenomenon not present in r 2 whereby subsets of agents can behave in a problematic way when this behaviour is precluded we say that the graph depicting the multi agent formation has structural persistence in real deployment of controlled multi agent systems formations with underlying structurally persistent graphs are of interest we analyse the characteristics of structurally persistent graphs and provide a streamlined test for structural persistence we study the connections between the allocation of degrees of freedom dofs across agents and the characteristics of persistence and or structural persistence of a directed graph we also show how to transfer dofs among agents when the formation changes with new agent s added to preserve persistence and or structural persistence

lp theory for the multidimensional aggregation equation we consider well posedness of the aggregation equation tu div uv 0 v k u with initial data in input amssym cal p 2 rm bbb r d rm cap l p bbb r d in dimensions 2 and higher we consider radially symmetric kernels where the singularity at the origin is of order x 2 d and prove local well posedness in input amssym cal p 2 bbb r d rm cap l p bbb r d for sufficiently large p ps in the special case of k x x the exponent ps d d 1 is sharp for local well posedness in that solutions can instantaneously concentrate mass for initial data in input amssym cal p 2 bbb r d rm cap l p bbb r d with p ps we also give an osgood condition on the potential k x that guarantees global existence and uniqueness in input amssym cal p 2 bbb r d rm cap l p bbb r d 2010 wiley periodicals inc

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

avoiding collisions in flocks among the many models for flocking systems of interacting particles the one introduced by cucker and smale has attracted attention due to the fact that a convergence to flocking i e to a common velocity could be established depending on conditions on the initial state of the system in this note we extend this model by adding to it a repelling force between particles we show that for this modified model convergence to flocking is established along the same lines while in addition avoidance of collisions i e the respect of a minimal distance between particles is ensured

state transitions and the continuum limit for a 2d interacting self propelled particle system we study a class of swarming problems wherein particles evolve dynamically via pairwise interaction potentials and a velocity selection mechanism we find that the swarming system undergoes various changes of state as a function of the self propulsion and interaction potential parameters in this paper we utilize a procedure which connects a class of individual based models to their continuum formulations and determine criteria for the validity of the latter h stability of the interaction potential plays a fundamental role in determining both the validity of the continuum approximation and the nature of the aggregation state transitions we perform a linear stability analysis of the continuum model and compare the results to the simulations of the individual based one c 2007 elsevier b v all rights reserved

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

bifurcation analysis of a class of first order nonlinear delay differential equations with reflectional symmetry abstract we consider a general class of first order nonlinear delay differential equations ddes with reflectional symmetry and study completely the bifurcations of the trivial equilibrium under some generic conditions on the taylor coefficients of the dde our analysis reveals a hopf bifurcation curve terminating on a pitchfork bifurcation line at a codimension two takens bogdanov point in parameter space we compute the normal form coefficients of the reduced vector field on the centre manifold in terms of the taylor coefficients of the original dde and in contrast to many previous bifurcation analyses of ddes we also compute the unfolding parameters in terms of these coefficients for application purposes this is important since one can now identify the possible asymptotic dynamics of the dde near the bifurcation points by computing quantities which depend explicitly on the taylor coefficients of the original dde we illustrate these results using simple model systems relevant to the areas of neural networks and atmospheric physics and show that the results agree with numerical simulations

van der pol s oscillator under delayed feedback the effect of delayed feedback on oscillatory behaviour is investigated for the classical van der pol oscillator it is shown how the presence of delay can change the amplitude of limit cycle oscillations or suppress them altogether the result is compared to the conventional proportional and derivative feedback the derivative like effect of delay is also demonstrated in a modified equation where a delayed term provides the damping

observer design for tracking consensus in second order multi agent systems fractional order less than two this technical note studies the leader following tracking consensus problem of a class of multi agent systems where the dynamics of the leader is described by second order systems in order to track the states of the leader observers for the followers are designed by fractional order multi agent systems where the relative velocity information is unavailable it is interestingly found that the followers can track the leader with second order dynamics even if the fractional order is less than two by only using the position information of the local neighbors which is different from the existing results a novel fractional order observer is first proposed whose order is surprisingly less than the original leader system it is also shown that leader following consensus can be ensured if some carefully selected followers are informed and the relative position based protocols are appropriately designed with fractional order being between one and two a necessary and sufficient condition for the leader following consensus in multi agent systems without control input delay is proposed the results are then extended to the case with constant control input delay it is found that in both cases the real and imaginary parts of the eigenvalues of the augmented laplacian matrix of the topology play an important role in achieving consensus

self organization in systems of self propelled particles we investigate a discrete model consisting of self propelled particles that obey simple interaction rules we show that this model can self organize and exhibit coherent localized solutions in one and in two dimensions in one dimension the self organized solution is a localized flock of finite extent in which the density abruptly drops to zero at the edges in two dimensions we focus on the vortex solution in which the particles rotate around a common center and show that this solution can be obtained from random initial conditions even in the absence of a confining boundary furthermore we develop a continuum version of our discrete model and demonstrate that the agreement between the discrete and the continuum model is excellent

spontaneously ordered motion of self propelled particles we study a biologically inspired inherently non equilibrium model consisting of self propelled particles in the model particles move on a plane with a velocity of constant magnitude they locally interact with their neighbours by choosing at each timestep a velocity direction equal to the average direction of their neighbours thus in the limit of vanishing velocities the model becomes analogous to a monte carlo realization of the classical xy ferromagnet we show by large scale numerical simulations that unlike in the equilibrium xy model a long range ordered phase characterized by non vanishing net flow emerges in this system in a phase space domain bordered by a critical line along which the fluctuations of the order parameter diverge the corresponding phase diagram as a function of two parameters the amplitude of noise and the average density of the particles is calculated and is found to have the form we also find that scales as a function of the external bias h field or wind according to a power law in the ordered phase the system shows long range correlated fluctuations and 1 f noise

approximate quasi likelihood estimation in models with surrogate predictors abstract we consider quasi likelihood estimation with estimated parameters in the variance function when some of the predictors are measured with error we review and extend four approaches to estimation in this problem all of them based on small measurement error approximations a taxonomy of the data sets likely to be available in measurement error studies is developed an asymptotic theory based on this taxonomy is obtained and includes measurement error and berkson error models as special cases

oscillations in a van der pol equation with delayed argument we consider the van der pol equation d2dt2u t eddtu t eu2 t r ddtu t r u t 0 with the delayed time r where r and e are real parameters with e 0 small and 0 r 2 and prove the existence and stability of a periodic solution with period near 2 and amplitude near 2 cosr with these properties this solution is unique up to translations in time

distributed leader follower flocking control for multi agent dynamical systems with time varying velocities abstract using tools from algebraic graph theory and nonsmooth analysis in combination with ideas of collective potential functions velocity consensus and navigation feedback a distributed leader follower flocking algorithm for multi agent dynamical systems with time varying velocities is developed where each agent is governed by second order dynamics the distributed leader follower algorithm considers the case in which the group has one virtual leader with time varying velocity for each agent i this algorithm consists of four terms the first term is the self nonlinear dynamics which determines the final time varying velocity the second term is determined by the gradient of the collective potential between agent i and all of its neighbors the third term is the velocity consensus term and the fourth term is the navigation feedback from the leader to avoid an impractical assumption that the informed agents sense all the states of the leader the new designed distributed algorithm is developed by making use of observer based pinning navigation feedback in this case each informed agent only has partial information about the leader yet the velocity of the whole group can still converge to that of the leader and the centroid of those informed agents having the leader s position information follows the trajectory of the leader asymptotically finally simulation results are presented to demonstrate the validity and effectiveness of the theoretical analysis surprisingly it is found that the local minimum of the potential function may not form a commonly believed lattice

stability and bifurcation analysis in van der pol s oscillator with delayed feedback abstract the classical van der pol equation with delayed feedback and a modified equation where a delayed term provides the damping are considered linear stability of the equations is investigated by analyzing the associated characteristic equations it is found that there exist the stability switches when delay varies and the hopf bifurcation occurs when the delay passes through a sequence of critical values the bifurcation diagram is drawn in e k plane and the stability and direction of the hopf bifurcation are determined by applying the normal form theory and the center manifold theorem

analysis of an m m 1 driven fluid queue with multiple exponential vacations the main purpose of the current paper is to study a fluid queue model driven by an m m 1 queue with multiple exponential vacations we drive an explicit expression for the stationary distribution of the buffer content in terms of modified bessel function of first kind by employing generating function methodology several concrete examples are considered to illustrate the variation of the proposed model with respect to vacations

nonresonant hopf hopf bifurcation and a chaotic attractor in neutral functional differential equations abstract an algorithm for calculating the third order normal form of a nonresonant hopf hopf singularity in a neutral functional differential equation nfde is established the van der pol equation with extended delay feedback is investigated as an nfde of second order the existence of hopf hopf bifurcation is studied and the unfolding near these critical points is given by applying this algorithm periodic solutions and quasi periodic solutions are found with the aid of the bifurcation diagram and corresponding numerical illustrations are presented with the breaking down of the 3 torus a chaotic attractor appears in this nfde of second order following the ruelle takens newhouse scenario which usually arises for an ordinary differential equation of order at least 4 this transition is shown via both theoretical and numerical approaches

two step estimation of models between latent classes and external variables we consider models which combine latent class measurement models for categorical latent variables with structural regression models for the relationships between the latent classes and observed explanatory and response variables we propose a two step method of estimating such models in its first step the measurement model is estimated alone and in the second step the parameters of this measurement model are held fixed when the structural model is estimated simulation studies and applied examples suggest that the two step method is an attractive alternative to existing one step and three step methods we derive estimated standard errors for the two step estimates of the structural model which account for the uncertainty from both steps of the estimation and show how the method can be implemented in existing software for latent variable modelling

instrumental variable estimation in generalized linear measurement error models abstract instrumental variable estimation in generalized linear measurement error models are studied for models with canonical link functions unbiased estimating equations are derived the maximum likelihood estimator for the normal theory structural linear instrumental variable model is shown to be a solution to the estimating equations derived herein logistic regression is studied in detail an example is given and a simulation study described for the logistic model based on the framingham heart study data

regression among factor scores structural equation models with latent variables are sometimes estimated using an intuitive three step approach here denoted factor score regression consider a structural equation model composed of an explanatory latent variable and a response latent variable related by a structural parameter of scientific interest in this simple example estimation of the structural parameter proceeds as follows first common factor models areseparately estimated for each latent variable second factor scores areseparately assigned to each latent variable based on the estimates third ordinary linear regression analysis is performed among the factor scores producing an estimate for the structural parameter we investigate the asymptotic and finite sample performance of different factor score regression methods for structural equation models with latent variables it is demonstrated that the conventional approach to factor score regression performs very badly revised factor score regression using regression factor scores for the explanatory latent variables and bartlett scores for the response latent variables produces consistent estimators for all parameters

improved regression calibration the likelihood for generalized linear models with covariate measurement error cannot in general be expressed in closed form which makes maximum likelihood estimation taxing a popular alternative is regression calibration which is computationally efficient at the cost of inconsistent estimation we propose an improved regression calibration approach a general pseudo maximum likelihood estimation method based on a conveniently decomposed form of the likelihood it is both consistent and computationally efficient and produces point estimates and estimated standard errors which are practically identical to those obtained by maximum likelihood simulations suggest that improved regression calibration which is easy to implement in standard software works well in a range of situations

generalized multilevel structural equation modeling a unifying framework for generalized multilevel structural equation modeling is introduced the models in the framework called generalized linear latent and mixed models gllamm combine features of generalized linear mixed models glmm and structural equation models sem and consist of a response model and a structural model for the latent variables the response model generalizes glmms to incorporate factor structures in addition to random intercepts and coefficients as in glmms the data can have an arbitrary number of levels and can be highly unbalanced with different numbers of lower level units in the higher level units and missing data a wide range of response processes can be modeled including ordered and unordered categorical responses counts and responses of mixed types the structural model is similar to the structural part of a sem except that it may include latent and observed variables varying at different levels for example unit level latent variables factors or random coefficients can be regressed on cluster level latent variables special cases of this framework are explored and data from the british social attitudes survey are used for illustration maximum likelihood estimation and empirical bayes latent score prediction within the gllamm framework can be performed using adaptive quadrature in gllamm a freely available program running in stata

limit cycle oscillators subject to a delayed feedback the coexistence of two stable limit cycles exhibiting different periods is examined for a nonlinear oscillator subject to a delayed feedback for the case of a weakly nonlinear oscillator we discuss the validity of a previously determined phase equation for the case of a strongly nonlinear oscillator we derive a phase equation and analyze its bifurcation diagram our analysis is motivated by previous experimental studies of chemical oscillators controlled by a delayed feedback

estimation by data augmentation in regression models with continuous and discrete covariates measured with error estimation methods are considered for regression models which have both misclassified discrete covariates and continuous covariates measured with error adjusted parameter estimates are obtained using the method of data augmentation where the true values of the covariates measured with error are regarded as missing data validation data on the covariates are assumed to be available the distinction between internal and external validation data is emphasized and its effects on the analysis are examined the method is illustrated with simulated data 1997 by john wiley sons ltd

likelihood analysis for probit regression with measurement errors summary likelihood analysis is proposed for a probit regression model when one of the explanatory variables is measured with error and replicate measurements of that variable are available on some of the subjects the distribution of the measurement error and of the unknown explanatory variable conditional on the known variables are both taken to be normal the maximum likelihood estimates can be computed exactly with the em algorithm likelihood ratio tests and confidence intervals can be computed with a laplace approximation

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

fluid model driven by an m g 1 queue with multiple exponential vacations abstract this paper studies a fluid model driven by an m g 1 queue with multiple exponential vacations by introducing various vacation strategies to the fluid model we can provide greater flexibility for the design and control of input rate and output rate the laplace transform of the steady state distribution of the buffer content is expressed through the minimal positive solution to a crucial equation then the performance measure mean buffer content which is independent of the vacation parameter is obtained finally with some numerical examples the parameter effect on the mean buffer content is presented

optimal multi agent coordination under tree formation constraints this paper presents a framework for studying the centralized optimal multi agent coordination problem under tree formation constraints the geodesic equations characterizing the optimal coordinated motions are derived in a suitably chosen coordinate system for general tree formation constraints the solutions to these equations however may fail to be optimal once extended beyond certain points called the conjugate points due to the failure of the second order optimality condition for the particular class of star formations two methods for computing the conjugate points along a natural candidate solution are introduced using these methods we derive analytically the conjugate points as well as the better solutions once the candidate solution is extended beyond its first conjugate point the optimal centralized coordinated motions derived in this paper will yield a performance lower bound for those generated by decentralized algorithms

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

the m m 1 queue with a production inventory system and lost sales abstract in this paper we study an m m 1 queue with an attached production inventory system customers arrive in the system according to a poisson process and a single server serves the customers the service times are assumed to be i i d exponential random variables the customers leave the system with exactly one item from the inventory at his service completion epoch if there is no inventory item all arriving customers are lost the stocks are replenished by 1 an external order under r q policy or 2 an internal production the internal production process is assumed to be a poisson process we first derive the stationary joint distribution of the queue length and the on hand inventory in product form using the joint distribution we introduce long run performance measures and a cost model then we show numerical examples which minimize the long run cost per unit time

correction of logistic regression relative risk estimates and confidence intervals for systematic within person measurement error errors in the measurement of exposure that are independent of disease status tend to bias relative risk estimates and other measures of effect in epidemiologic studies toward the null value two methods are provided to correct relative risk estimates obtained from logistic regression models for measurement errors in continuous exposures within cohort studies that may be due to either random unbiased within person variation or to systematic errors for individual subjects these methods require a separate validation study to estimate the regression coefficient lambda relating the surrogate measure to true exposure in the linear approximation method the true logistic regression coefficient beta is estimated by beta lambda where beta is the observed logistic regression coefficient based on the surrogate measure in the likelihood approximation method a second order taylor series expansion is used to approximate the logistic function enabling closed form likelihood estimation of beta confidence intervals for the corrected relative risks are provided that include a component representing error in the estimation of lambda based on simulation studies both methods perform well for true odds ratios up to 3 0 for higher odds ratios the likelihood approximation method was superior with respect to both bias and coverage probability an example is provided based on data from a prospective study of dietary fat intake and risk of breast cancer and a validation study of the questionnaire used to assess dietary fat intake

formulation of the normal form of turing hopf bifurcation in partial functional differential equations abstract turing hopf bifurcation is considered as an important mechanism for generating complex spatio temporal patterns in dynamical systems in this work the normal form up to the third order for the hopf steady state bifurcation which includes the turing hopf bifurcation of a general system of partial functional differential equations pfdes in a bounded spatial region of any dimension is derived based on the center manifold and the normal form theories of pfdes the explicit formula for the coefficients in the normal form of hopf steady state bifurcation are presented concisely in a matrix form which makes it more convenient in not only symbolic derivation but also numerical implementation this provides an approach of showing the existence and stability of stationary and time periodic solutions with spatial heterogeneity the derived formulas are also applicable to partial differential equations and functional differential equations

conditional independence models for epidemiological studies with covariate measurement error we construct a unifying representation of the structure of measurement error problems with particular reference to situations commonly encountered in epidemiological studies and outline how estimation of the parameters of interest can be carried out in a bayesian framework using gibbs sampling we show how this approach can be implemented for designs involving continuous measurement errors assessed through a validation substudy and discuss our results on simulated data

asymptotically optimal decentralized control for large population stochastic multiagent systems the interaction of interest coupled decision makers and the uncertainty of individual behavior are prominent characteristics of multiagent systems mas how to break through the framework of conventional control theory which aims at single decision maker and single decision objective and to extend the methodology and tools in the stochastic adaptive control theory to analyze mas are of great significance in this paper a preliminary exploration is made in this direction and the decentralized control problem is considered for large population stochastic mas with coupled cost functions different from the deterministic discounted costs in the existing differential game models a time averaged stochastic cost function is adopted for each agent the decentralized control law is constructed based on the state aggregation method and tracking like quadratic optimal control by using probability limit theory the stability and optimality of the closed loop system are analyzed the main contributions of this paper include the following points 1 the concepts of asymptotic nash equilibrium in probability and almost surely respectively are introduced and the relationship between these concepts is illuminated which provide necessary tools for analyzing the optimality of the decentralized control laws 2 the closed loop system is shown to be almost surely uniformly stable and bounded independently of the number of agents n 3 the population state average psa is shown to converge to the infinite population mean ipm trajectory in the sense of both l2 norm and time average almost surely as n increases to infinity 4 the decentralized control law is designed and shown to be almost surely asymptotically optimal the cost of each agent based on local measurements converges to that based on global measurements almost surely as n increases to infinity

saddle node hopf bifurcation in a modified leslie gower predator prey model with time delay and prey harvesting abstract from the saddle node hopf bifurcation point of view this paper considers a modified leslie gower predator prey model with time delay and the michaelis menten type prey harvesting firstly we discuss the stability of the equilibria obtain the critical conditions for the saddle node hopf bifurcation and give the completion bifurcation set by calculating the universal unfoldings near the saddle node hopf bifurcation point by using the normal form theory and center manifold theorem then we derive the parameter conditions for the existence of monostable coexistence equilibrium and the parameter regions in which both the prey extinction and the coexistence equilibrium or coexistence periodic or quasi periodic solutions are simultaneously stabilized we also investigate the heteroclinic bifurcation and describe the phenomenon that the periodic behavior disappears as through the heteroclinic bifurcation finally some numerical simulations are performed to support our analytic results

distributed nonlinear control of mobile autonomous multi agents abstract this paper studies the distributed nonlinear control of mobile autonomous agents with variable and directed topology a new distributed nonlinear design scheme is presented for multi agent systems modeled by double integrators with the new design the outputs of the controlled agents asymptotically converge to each other as long as a mild connectivity condition is satisfied moreover the velocity derivative of the output of each agent can be restricted to be within any specified neighborhood of the origin which is of practical interest for systems under such physical constraint the new design is still valid if one of the agents is a leader and the control objective is to achieve leader following as an illustration of the generality and effectiveness of the presented methodology the formation control of a group of unicycle mobile robots with nonholonomic constraints is revisited instead of assuming the point robot model the unicycle model is transformed into two double integrators by dynamic feedback linearization and the proposed distributed nonlinear design method is used to overcome the singularity problem caused by the nonholonomic constraint by properly restricting the velocities simulation results are included to illustrate the theoretical results

qualitative analysis in a delayed van der pol oscillator abstract the main purpose of this manuscript is to introduce and compare two methods for discussing the nature of hopf bifurcation namely a research method combining the normal form theory and the center manifold theorem and the other method of multiple scales taking a delayed van der pol oscillator as an example the local stability as well as the occurrence of hopf bifurcation are explored via choosing time delay as the bifurcation parameter on the basis of two different methods respectively the characters of hopf bifurcation which includes the direction of hopf bifurcation as well as the stability of bifurcating periodic solutions are analyzed finally numerical simulations supporting the theoretical findings are given and it is observed that the results of two methods are consistent

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

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

distributed circular formation stabilization for dynamic unicycles this paper investigates the problem of designing distributed control laws making a group of dynamic unicycles converge to a common circle of prespecified radius whose center is stationary but dependent on the initial conditions and travel around the circle in a desired direction the vehicles are required to converge to a formation on the circle expressed by desired separations and ordering of the unicycles the information exchange between unicycles is modelled by a directed graph which is assumed to have a spanning tree a hierarchical approach is proposed which simplifies the control design by decoupling the problem of making the unicycles converge to a common circle from the problem of stabilizing the formation

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

on a planar system modelling a neuron network with memory abstract we consider a delay differential equation modelling a network of two neurons with memory the situations without self connections and two delays and with self connections and two equal delays are addressed in terms of local stability and bifurcation analysis in the first case the dynamical behavior is studied by taking one of the delays as the bifurcating parameter namely the hopf bifurcation whose existence was proven in former works occurs as the delay crosses some critical values and is completely described conditions ensuring the stability of the periodic cycles are given when self connections are present hopf and pitchfork bifurcations co exist and the equation describing the flow on the center manifold is derived

some contributions to efficient statistics in structural models specification and estimation of moment structures current practice in structural modeling of observed continuous random variables is limited to representation systems for first and second moments e g means and covariances and to distribution theory based on multivariate normality in psychometrics the multinormality assumption is often incorrect so that statistical tests on parameters or model goodness of fit will frequently be incorrect as well it is shown that higher order product moments yield important structural information when the distribution of variables is arbitrary structural representations are developed for generalizations of the bentler weeks joreskog keesling wiley and factor analytic models some asymptotically distribution free efficient estimators for such arbitrary structural models are developed limited information estimators are obtained as well the special case of elliptical distributions that allow nonzero but equal kurtoses for variables is discussed in some detail the argument is made that multivariate normal theory for covariance structure models should be abandoned in favor of elliptical theory which is only slightly more difficult to apply in practice but specializes to the traditional case when normality holds many open research areas are described

brief paper second order consensus in multi agent dynamical systems with sampled position data this paper studies second order consensus in multi agent dynamical systems with sampled position data a distributed linear consensus protocol with second order dynamics is designed where both the current and some sampled past position data are utilized it is found that second order consensus in such a multi agent system cannot be reached without any sampled position data under the given protocol while it can be achieved by appropriately choosing the sampling period a necessary and sufficient condition for reaching consensus of the system in this setting is established based on which consensus regions are then characterized it is shown that if all the eigenvalues of the laplacian matrix are real then second order consensus in the multi agent system can be reached for any sampling period except at some critical points depending on the spectrum of the laplacian matrix however if there exists at least one eigenvalue of the laplacian matrix with a nonzero imaginary part second order consensus cannot be reached for sufficiently small or sufficiently large sampling periods in such cases one nevertheless may be able to find some disconnected stable consensus regions determined by choosing appropriate sampling periods finally simulation examples are given to verify and illustrate the theoretical analysis

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

stability and bifurcation analysis of micro electromechanical nonlinear coupling system with delay abstract in this paper we study dynamics in delayed micro electromechanical nonlinear coupling system with particular attention focused on hopf and hopf pitchfork bifurcations based on the distribution of eigenvalues we prove that a sequence of hopf and hopf pitchfork bifurcations occur at the trivial equilibrium as the delay increases and obtain the critical values of two types of bifurcations next by applying the multiple time scales method the normal forms near the hopf and hopf pitchfork bifurcations critical points are derived finally bifurcation analysis and numerical simulations are presented to demonstrate the application of the theoretical results we show the regions near above bifurcation critical points in which the micro electromechanical nonlinear coupling system exists stable fixed point or stable periodic solution detailed numerical analysis using matlab extends the local bifurcation analysis to a global picture and stable windows are observed as we change control parameters namely the stable fixed point and stable periodic solution can exist in large regions of unfolding parameters as the unfolding parameters increase away from the critical value

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

covariate measurement error in generalized linear models summary the em algorithm is used to obtain estimators of regression coefficients for generalized linear models with canonical link when normally distributed covariates are masked by normally distributed measurement errors by casting the true covariates as missing data the em procedure suggests an iterative scheme in which each cycle consists of an e step requiring the computation of approximate first and second conditional moments of the true covariates given the observed data followed by an m step in which regression parameters are updated by iteratively reweighted least squares based on these approximations the proposed procedure is compared numerically with the exact maximum likelihood solution obtained by using gaussian quadrature instead of the approximations in the e step of the em algorithm and with alternative estimators for simple logistic regression with measurement error the results for the proposed procedure are encouraging a procedure is proposed in this paper for estimating regression coefficients in generalized linear models when one or more of the covariates is measured with error this work is related to the paper by carroll et al 1984 in which maximum likelihood estimates are considered for the structural logistic regression model these authors provide estimates for the computationally simpler probit regression model and suggest that the structural logistic regression can be done in principle this paper follows up on that suggestion but differs in detail from similar work by armstrong 1985 other procedures with related aims have been suggested by stefanski carroll 1985 wolter fuller 1982 and prentice 1982 for a quick introduction to the proposed method it is convenient to display the naive estimator which ignores measurement error in its standard computational form if yi is an observed response variable and xi is the observed covariate then for the model which equates the canonical parameter of the distribution of yi to xtf3 the maximum likelihood estimator of f3 can be obtained by iteratively reweighted least squares the estimate of f3 after s 1 cycles is given by

double hopf bifurcation in a container crane model with delayed position feedback in this paper we study dynamics in a container crane model with delayed position feedback with particular attention focused on non resonant double hopf bifurcation by using multiple time scales and center manifold reduction methods we obtain the equivalent normal forms near a double hopf critical point in this neutral delayed differential system moreover bifurcations are classified in a two dimensional parameter space near the critical point numerical simulations are presented to demonstrate the applicability of the theoretical results

oscillation sliding in a modified van der pol duffing electronic oscillator abstract some periodic behaviour exhibited by a modified van der pol duffing electronic oscillator near a degenerate hopf pitchfork bifurcation have been studied numerical continuation of these periodic orbits leads to the appearance of interesting phenomena after varying one of the characteristics of the oscillator oscillation sliding between two periodic regimes is detected in the region where oscillation sliding is present quasiperiodic oscillations invariant torus breakdown of the torus and the corresponding resonant periodic orbits are also found

effects of time delayed position feedback on a van der pol duffing oscillator abstract the mechanism for the action of time delay in a non autonomous system is investigated in this paper the original mathematical model under consideration is a van der pol duffing oscillator with excitation a delayed system is obtained by adding both linear and nonlinear time delayed position feedbacks to the original system functional analysis is used to change the delayed system into a functional differential equation fde the time delay is taken as a variable parameter to investigate its effect on the dynamics of the system such as the stability and bifurcation of an equilibrium point phase locked periodic and phase shifting solution period doubling quasi periodic motion and chaos a periodic solution expressed in the closed form with the aid of the center manifold and averaging theorem is found to be in good agreement with that obtained by numerical simulation two routes to chaos are found namely period doubling bifurcation and torus breaking the results obtained in this paper show that time delay may be used as a simple but efficient switch to control motions of a system either from order motion to chaos or from chaotic motion to order for different applications

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

state agreement for continuous time coupled nonlinear systems two related problems are treated in continuous time first the state agreement problem is studied for coupled nonlinear differential equations the vector fields can switch within a finite family associated to each vector field is a directed graph based in a natural way on the interaction structure of the subsystems generalizing the work of moreau under the assumption that the vector fields satisfy a certain subtangentiality condition it is proved that asymptotic state agreement is achieved if and only if the dynamic interaction digraph has the property of being sufficiently connected over time the proof uses nonsmooth analysis second the rendezvous problem for kinematic point mass mobile robots is studied when the robots fields of view have a fixed radius the circumcenter control law of ando e ieee trans robotics automation 15 1999 pp 818 828 is shown to solve the problem the rendezvous problem is a kind of state agreement problem but the interaction structure is state dependent

pseudo maximum likelihood estimation the asymptotic distribution gong and samaniego 1981 define pseudo maximum likelihood estimation and derive the asymptotic distribution of the resulting estimates this note gives a simpler and more elegant expression for the asymptotic variance of a pseudo maximum likelihood estimate

on errors in variables in binary regression berkson case abstract in binary regression the predictor variables may be measured with error the berkson case of the errors in variables problem is considered under which the values of the predictor variables are set by the experimenter but not achieved exactly a particular model for this case is considered with probit regression and normally distributed errors of observation the regression parameters for intercept and slope are to be estimated two estimators are studied the maximum likelihood estimator mle and a modification of it in a simulation study the modified mle is shown to improve on the mle in a situation with substantial measurement error quantal bioassay is an important field of application of the berkson case of the binary regression model in quantal bioassay there is a stimulus perhaps a carcinogen or poison with doses x to be determined by the experimenter to address questions on carcinogenicity or toxicity of the stimulus each experimental animal is assigned a dose of the stimulus

dynamics in a ratio dependent predator prey model with predator harvesting abstract the objective of this paper is to study systematically the dynamical properties of a ratio dependent predator prey model with nonzero constant rate predator harvesting it is shown that the model has at most two equilibria in the first quadrant and can exhibit numerous kinds of bifurcation phenomena including the bifurcation of cusp type of codimension 2 i e bogdanov takens bifurcation the subcritical and supercritical hopf bifurcations these results reveal far richer dynamics compared to the model with no harvesting and different dynamics compared to the model with nonzero constant rate prey harvesting in d xiao l jennings bifurcations of a ratio dependent predator prey system with constant rate harvesting siam appl math 65 2005 737 753 biologically it is shown that nonzero constant rate predator harvesting can prevent mutual extinction as a possible outcome of the predator prey interaction and remove the singularity of the origin which was regarded as pathological behavior for a ratio dependent predator prey model in p yodzis predator prey theory and management of multispecies fisheries ecological applications 4 2004 51 58

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

pseudo maximum likelihood estimation theory and applications abstract pseudo maximum likelihood estimation easily extends to k parameter models and is of interest in problems in which the likelihood surface is ill behaved in higher dimensions but well behaved in lower dimensions several signal plus noise or convolution models are examined which exhibit such behavior and satisfy the regularity conditions of the asymptotic theory for specific models a numerical comparison of asymptotic variances suggests that a psuedo maximum likelihood estimate of the signal parameter is uniformly more efficient than estimators that have been advanced by previous authors a number of other potential applications are noted

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

likelihood analysis for errors in variables regression with replicate measurements summary this paper advocates likelihood analysis for regression models with measurement errors in explanatory variables for data problems in which the relevant distributions can be adequately modelled although computationally difficult maximum likelihood estimates are more efficient than those based on first and second moment assumptions and likelihood ratio inferences can be substantially better than those based on asymptotic normality of estimates the em algorithm is presented as a straightforward approach for likelihood analysis of normal linear regression with normal explanatory variables and normal replicate measurements likelihood methods for regression analysis with explanatory variable measurement error have received little attention relative to methods based on first and second moment assumptions largely because of computational difficulties uncertainty about the robustness of likelihood methods and the belief that the simpler methods perform just as well in practice with improved computational tools for likelihood analysis as discussed for example by tanner 1993 it is worthwhile to reinvestigate these issues in particular the common belief that the simpler methods perform just as well as likelihood methods may be naive first the comparison is usually cast in terms of efficiency without regard to test and confidence interval validity likelihood ratio tests and confidence intervals can be substantially better than tests and confidence intervals based on estimates and standard errors of the commonly used method of moments approaches the sampling distributions of the estimators are very often skewed especially if the measurement errors are large furthermore knowledge about the relative efficiency of the moment methods comes from a small number of efficiency comparisons from simulations of isolated situations in papers promoting these simpler methods carroll rupert stefanski 1995 7 1 an important and often overlooked issue is that the moment methods may be especially inappropriate when the distribution of the true covariates is skewed pierce et al 1992 section 2 discusses computational approaches and difficulties associated with likelihood analysis in the measurement error problem generally section 3 illustrates the em algorithm dempster laird rubin 1977 for likelihood analysis of normal linear regression with a normally distributed explanatory variable measured with normally distributed error when there are replicate measurements for at least some of the cases sections 5 and 6

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

maximum likelihood estimation of limited and discrete dependent variable models with nested random effects abstract gauss hermite quadrature is often used to evaluate and maximize the likelihood for random component probit models unfortunately the estimates are biased for large cluster sizes and or intraclass correlations we show that adaptive quadrature largely overcomes these problems we then extend the adaptive quadrature approach to general random coefficient models with limited and discrete dependent variables the models can include several nested random effects intercepts and coefficients representing unobserved heterogeneity at different levels of a hierarchical dataset the required multivariate integrals are evaluated efficiently using spherical quadrature rules simulations show that adaptive quadrature performs well in a wide range of situations