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

a new skewed link model for dichotomous quantal response data abstract the logit probit and student t links are widely used in modeling dichotomous quantal response data most of the commonly used link functions are symmetric except the complementary log log link however in some applications the overall fit can be significantly improved by the use of an asymmetric link in this article we propose a new skewed link model for analyzing binary response data with covariates introducing a skewed distribution for the underlying latent variable we develop a class of asymmetric link models for binary response data using a bayesian approach we first characterize the propriety of the posterior distributions using standard improper priors we further propose informative priors using historical data from a similar previous study we examine the proposed method through a large scale simulation study and use data from a prostate cancer study to demonstrate the use of historical data in bayesian model fitting and comparison of skewed link models

a class of joint models for multivariate longitudinal measurements and a binary event predicting binary events such as newborns with large birthweight is important for obstetricians in their attempt to reduce both maternal and fetal morbidity and mortality such predictions have been a challenge in obstetric practice where longitudinal ultrasound measurements taken at multiple gestational times during pregnancy may be useful for predicting various poor pregnancy outcomes the focus of this article is on developing a flexible class of joint models for the multivariate longitudinal ultrasound measurements that can be used for predicting a binary event at birth a skewed multivariate random effects model is proposed for the ultrasound measurements and the skewed generalized t link is assumed for the link function relating the binary event and the underlying longitudinal processes we consider a shared random effect to link the two processes together markov chain monte carlo sampling is used to carry out bayesian posterior computation several variations of the proposed model are considered and compared via the deviance information criterion the logarithm of pseudomarginal likelihood and with a training test set prediction paradigm the proposed methodology is illustrated with data from the nichd successive small for gestational age births study a large prospective fetal growth cohort conducted in norway and sweden

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

flexible generalized t link models for binary response data a critical issue in modelling binary response data is the choice of the links we introduce a new link based on the generalized t distribution there are two parameters in the generalized t link one parameter purely controls the heaviness of the tails of the link and the second parameter controls the scale of the link two major advantages are offered by the generalized t links first a symmetric generalized t link with an unknown shape parameter is much more identifiable than a student t link with unknown degrees of freedom and a known scale parameter secondly skewed generalized t links with both unknown shape and scale parameters provide much more flexible and improved skewed link regression models than the existing skewed links various theoretical properties and attractive features of the proposed links are examined and explored in detail an efficient markov chain monte carlo algorithm is developed for sampling from the posterior distribution the deviance information criterion measure is used for guiding the choice of links the proposed methodology is motivated and illustrated by prostate cancer data

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

markov chain monte carlo 10 years and still running although markov chain monte carlo mcmc techniques can be traced back to the early 1950s and are almost contemporary with independent monte carlo methods the use of these techniques has only really taken off in the past 10 years at least in mainstream statistics with the work of gelfand and smith 1990 and the rediscovery of metropolis s and hastings s papers the impact on the discipline is deep and durable because these methods have opened new horizons in the scale of the problems that one can deal with thus enhancing the position of statistics in most applied fields the mcmc revolution has in particular boosted bayesian statistics to new heights by providing a virtually universal tool for dealing with integration and optimization problems this can be seen in for instance the explosion of papers dealing with complex models hierarchical modelings nonparametric bayesian estimation and spatial statistics this trend has also created new synergies with mathematicians and probabilists as well as econometricians engineers ecologists astronomers and others for theoretical requests and practical implications of mcmc techniques it is impossible to provide here a complete perspective on mcmc methods and applications for this as well as for other references we refer the reader to the books by gilks richardson and spiegelhalter 1995 and robert and casella 1999 here we focus on four particular aspects of mcmc algorithms theoretical foundations practical implementation bayesian inference and prospects the web provides many relevant sites including the mcmc preprint server http www statslab cam ac uk r mcmc which offers a most useful window to the current research on mcmc wilson s site on perfect simulation http dimacs rutgers edu dbwilson exact h which keeps track of papers and applets on this topic and a site on convergence control techniques http www ensae fr crest statistique robert mcdiag even more recent developments allow for on line computations through applets like breyer s http www maths lancs ac uk breyer java html which impressively illustrates the behavior of different samplers for simple problems note also that the bugs and coda software are freely available at http www mrc bsu cam ac uk bu

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

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

generalized logistic models abstract a class of models indexed by two shape parameters is introduced both to extend the scope of the standard logistic model to asymmetric probability curves and improve the fit in the noncentral probability regions one parameter subclasses can be used to examine symmetric or asymmetric deviations from the logistic model the delta algorithm is adapted to obtain maximum likelihood estimates of the parameters a review is made of other proposed generalizations the standard linear logistic model is widely used for modeling the dependence of binary data on explanatory variables its success is due to its broad applicability simplicity of form and ease of interpretation this model works well for many common applications however it assumes that the expected probability curve is skew symmetric about and that the shape of is the cumulative distribution function of the logistic distribution symmetric data with a shallower or steeper slope of ascent may not be fitted well by this model

a particle algorithm for sequential bayesian parameter estimation and model selection we describe a particle algorithm for the sequential bayesian estimation of unknown static parameters the algorithm combines sequential importance sampling sis and markov chain monte carlo mcmc to achieve computational efficiency and stability in its most general form the algorithm has three components i sis ii a rejuvenation test and iii mcmc measurements are processed sequentially with an artificial time line if there is no natural one associated with the measurements by sis which is computationally inexpensive after each measurement is processed the rejuvenation test checks whether the resulting sis particles have to be rejuvenated when indicated by the test the particles are completely rejuvenated by mcmc which removes errors that accumulate from sis due to the finite number of particles thus ensuring stability whenever possible the sis particles can be used to advantage in the mcmc there is flexibility in the choice of the rejuvenation test as well as the mcmc method with potential to increase the usefulness of the algorithm in particular by using reversible jump mcnic with multiple models the algorithm can perform simultaneous model selection and parameter estimation in this paper we use a rejuvenation test based on a kullback leibler distance that is easy to compute and our choice of mcnic is independent metropolis hastings with a gaussian proposal density with these choices we illustrate the use of the algorithm in two signal processing applications passive source localization with angle of arrival and simultaneous weak signal detection and parameter estimation involving both simulated and real data the results demonstrate the algorithm s stability its built in protection against model overfitting and tolerance to model mismatch

bayesian measures of model complexity and fit summary we consider the problem of comparing complex hierarchical models in which the number of parameters is not clearly defined using an information theoretic argument we derive a measure pd for the effective number of parameters in a model as the difference between the posterior mean of the deviance and the deviance at the posterior means of the parameters of interest in general pd approximately corresponds to the trace of the product of fisher s information and the posterior covariance which in normal models is the trace of the hat matrix projecting observations onto fitted values its properties in exponential families are explored the posterior mean deviance is suggested as a bayesian measure of fit or adequacy and the contributions of individual observations to the fit and complexity can give rise to a diagnostic plot of deviance residuals against leverages adding pd to the posterior mean deviance gives a deviance information criterion for comparing models which is related to other information criteria and has an approximate decision theoretic justification the procedure is illustrated in some examples and comparisons are drawn with alternative bayesian and classical proposals throughout it is emphasized that the quantities required are trivial to compute in a markov chain monte carlo analysis

a sequential particle filter method for static models summary particle filter methods are complex inference procedures which combine importance sampling and monte carlo schemes in order to explore consistently a sequence of multiple distributions of interest we show that such methods can also offer an efficient estimation

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

bayesian sequential parameter estimation by cognitive radar with multiantenna arrays in this paper we consider the problem of bayesian sequential parameter estimation of extended targets for cognitive radar with multi antenna arrays using adaptive waveforms the target is modeled as a complex gaussian random process using iterative waveform transmission the cognitive radar estimates the target s characteristic parameters and updates its probabilistic model based on new measurements the adaptive waveform is designed by minimizing the conditional entropy from the posterior density of the model parameters we analyze the performance of the developed bayesian sequential estimation algorithm and derive expressions for the signal to noise ratio gain the asymp totical posterior cramer rao bound and the mutual information gain the analysis and numerical simulations demonstrate that the adaptive sequential bayesian estimator yields accelerated convergence of the estimate towards its true value and a smaller estimation error compared with the conventional bayesian esti mator that uses fixed waveform transmission under gaussian or non gaussian noise

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

markov chain monte carlo convergence diagnostics a comparative review abstract a critical issue for users of markov chain monte carlo mcmc methods in applications is how to determine when it is safe to stop sampling and use the samples to estimate characteristics of the distribution of interest research into methods of computing theoretical convergence bounds holds promise for the future but to date has yielded relatively little of practical use in applied work consequently most mcmc users address the convergence problem by applying diagnostic tools to the output produced by running their samplers after giving a brief overview of the area we provide an expository review of 13 convergence diagnostics describing the theoretical basis and practical implementation of each we then compare their performance in two simple models and conclude that all of the methods can fail to detect the sorts of convergence failure that they were designed to identify we thus recommend a combination of strategies aimed at evaluating and accelerating mcmc sampler convergence including ap

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

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

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

flexible link functions in nonparametric binary regression with gaussian process priors in many scientific fields it is a common practice to collect a sequence of 0 1 binary responses from a subject across time space or a collection of covariates researchers are interested in finding out how the expected binary outcome is related to covariates and aim at better prediction in the future 0 1 outcomes gaussian processes have been widely used to model nonlinear systems in particular to model the latent structure in a binary regression model allowing nonlinear functional relationship between covariates and the expectation of binary outcomes a critical issue in modeling binary response data is the appropriate choice of link functions commonly adopted link functions such as probit or logit links have fixed skewness and lack the flexibility to allow the data to determine the degree of the skewness to address this limitation we propose a flexible binary regression model which combines a generalized extreme value link function with a gaussian process prior on the latent structure bayesian computation is employed in model estimation posterior consistency of the resulting posterior distribution is demonstrated the flexibility and gains of the proposed model are illustrated through detailed simulation studies and two real data examples empirical results show that the proposed model outperforms a set of alternative models which only have either a gaussian process prior on the latent regression function or a dirichlet prior on the link function

using machine learning to predict catastrophes in dynamical systems nonlinear dynamical systems which include models of the earth s climate financial markets and complex ecosystems often undergo abrupt transitions that lead to radically different behavior the ability to predict such qualitative and potentially disruptive changes is an important problem with far reaching implications even with robust mathematical models predicting such critical transitions prior to their occurrence is extremely difficult in this work we propose a machine learning method to study the parameter space of a complex system where the dynamics is coarsely characterized using topological invariants we show that by using a nearest neighbor algorithm to sample the parameter space in a specific manner we are able to predict with high accuracy the locations of critical transitions in parameter space

robust statistical modeling using the t distribution abstract the t distribution provides a useful extension of the normal for statistical modeling of data sets involving errors with longer than normal tails an analytical strategy based on maximum likelihood for a general model with multivariate t errors is suggested and applied to a variety of problems including linear and nonlinear regression robust estimation of the mean and covariance matrix with missing data unbalanced multivariate repeated measures data multivariate modeling of pedigree data and multivariate nonlinear regression the degrees of freedom parameter of the t distribution provides a convenient dimension for achieving robust statistical inference with moderate increases in computational complexity for many models estimation of precision from asymptotic theory and the bootstrap is discussed and graphical methods for checking the appropriateness of the t distribution are presented

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

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

saturated particle filter almost sure convergence and improved resampling nonlinear stochastic dynamical systems are widely used to model physical processes in many practical applications the state variables are defined on a compact set of the state space i e they are bounded or saturated to estimate the states of systems with saturated variables the saturated particle filter spf has recently been developed this filter exploits the structure of the saturated system using a specific importance sampling distribution in this paper we investigate the asymptotic properties of the filter in particular its almost sure convergence to the true posterior pdf furthermore an improved spf is developed that uses a novel resampling procedure to overcome the practical shortcomings of the original spf we prove that this new filter also converges almost surely to the true posterior pdf both versions of the spf are presented in easy to implement algorithmic forms

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

dynamic conditional independence models and markov chain monte carlo methods abstract in dynamic statistical modeling situations observations arise sequentially causing the model to expand by progressive incorporation of new data items and new unknown parameters for example in clinical monitoring patients and data arrive sequentially and new patient specific parameters are introduced with each new patient markov chain monte carlo mcmc might be used for continuous updating of the evolving posterior distribution but would need to be restarted from scratch at each expansion stage thus mcmc methods are often too slow for real time inference in dynamic contexts by combining mcmc with importance resampling we show how real time sequential updating of posterior distributions can be effected the proposed dynamic sampling algorithms use posterior samples from previous updating stages and exploit conditional independence between groups of parameters to allow samples of parameters no longer of interest to be discarded such as when a patient dies or is discharged we apply the

convex saturated particle filter in many systems the state variables are defined on a compact set of the state space to estimate the states of such systems the constrained particle filters have been used with some success the performance of the standard particle filters can be improved if the measurement information is used during the importance sampling of the filtering phase it has been shown that the particles obtained in such a way approximate the true state of the system more accurately the measurement is incorporated into the filtering algorithm through a user specified detection function which aims to detect the saturation as it occurs the algorithm derived from the aforementioned principle is called the saturated particle filter spf in our previous work we have derived a complete spf framework for the class of systems with one dimensional constraints in this paper we derive a novel convex spf that extends our method to multidimensional systems with convex constraints the effectiveness of the new method is demonstrated using an illustrative example

sequential imputations and bayesian missing data problems abstract for missing data problems tanner and wong have described a data augmentation procedure that approximates the actual posterior distribution of the parameter vector by a mixture of complete data posteriors their method of constructing the complete data sets is closely related to the gibbs sampler both required iterations and similar to the em algorithm convergence can be slow we introduce in this article an alternative procedure that involves imputing the missing data sequentially and computing appropriate importance sampling weights in many applications this new procedure works very well without the need for iterations sensitivity analysis influence analysis and updating with new data can be performed cheaply bayesian prediction and model selection can also be incorporated examples taken from a wide range of applications are used for illustration

transformations to linearity in binary regression a one parameter family of transformations for binary response probabilities is introduced the family is used to explore relationships between response and explanatory variables by assuming that the transformed probabilities depend linearly on the known variables and on unknown parameters reflecting the variables effect on response the family includes the logistic and one hit transformations which form the bases for two popular notions of no interaction between explanatory variables maximum likelihood methods are used to determine those transformations in the family that provide acceptable fits to data and the methods are illustrated with data from an animal cancer bioassay the paper concludes with a comparison of probabilistic and statistical properties of logistic and one hit transformations

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

bayesian analysis of binary and polychotomous response data abstract a vast literature in statistics biometrics and econometrics is concerned with the analysis of binary and polychotomous response data the classical approach fits a categorical response regression model using maximum likelihood and inferences about the model are based on the associated asymptotic theory the accuracy of classical confidence statements is questionable for small sample sizes in this article exact bayesian methods for modeling categorical response data are developed using the idea of data augmentation the general approach can be summarized as follows the probit regression model for binary outcomes is seen to have an underlying normal regression structure on latent continuous data values of the latent data can be simulated from suitable truncated normal distributions if the latent data are known then the posterior distribution of the parameters can be computed using standard results for normal linear models draws from this posterior are used to sample new latent data and t

analytical search for bifurcation surfaces in parameter space the method of resultants can be used to compute hopf bifurcations in ode systems we discuss this method from the applicant s point of view furthermore we show by theory and examples that the method may be extended to cover other bifurcation situations as well among them are the real hopf situation which plays an important role in the transition to shil nikov chaos as well as some higher codimension bifurcations such as takens bogdanov gavrilov guckenheimer and double hopf bifurcations the method yields an analytical test function that can be solved analytically or by computer algebra systems in contrast to common analytical techniques based on eigenvalue computation which can only be applied to systems of size n 4 the method is applicable for systems of intermediate size n 10 we illustrate the power of the method by discussing examples from different disciplines of science a lorenz like oscillator two coupled oscillators and a five species food chain

change point detection for recursive bayesian geoacoustic inversions in order to carry out geoacoustic inversion in low signal to noise ratio snr conditions extended duration observations coupled with source and or receiver motion may be necessary as a result change in the underlying model parameters due to time or space is anticipated in this paper an inversion method is proposed for cases when the model parameters change abruptly or slowly a model parameter change point detection method is developed to detect the change in the model parameters using the importance samples and corresponding weights that already are available from the recursive bayesian inversion if the model parameter change abruptly a change point will be detected and the inversion will restart with the pulse measurement after the changepoint if the model parameters change gradually the inversion based on constant model parameters may proceed until the accumulated model parameter mismatch is significant and triggers the detection of a change point these change point detections form the heu

the collapsed gibbs sampler in bayesian computations with applications to a gene regulation problem abstract this article describes a method of grouping and collapsing in using the gibbs sampler and proves from an operator theory viewpoint that the method is in general beneficial the norms of the forward operators associated with the corresponding nonreversible markov chains are used to discriminate among different simulation schemes when applied to bayesian missing data problems the idea of collapsing suggests skipping the steps of sampling parameter s values in standard data augmentation by doing this we obtain a predictive update version of the gibbs sampler a procedure of calculating the posterior odds ratio via the collapsed gibbs sampler when incomplete observations are involved is presented as an illustration of possible applications three examples along with a bayesian treatment for identifying common protein binding sites in unaligned dna sequences are provided

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

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

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

generalised gibbs sampler and multigrid monte carlo for bayesian computation summary although monte carlo methods have frequently been applied with success indiscriminate use of markov chain monte carlo leads to unsatisfactory performances in numerous applications we present a generalised version of the gibbs sampler that is based on conditional moves along the traces of groups of transformations in the sample space we explore its connection with the multigrid monte carlo method and its use in designing more efficient samplers the generalised gibbs sampler provides a framework encompassing a class of recently proposed tricks such as parameter expansion and reparameterisation to illustrate we apply this new method to bayesian inference problems for nonlinear state space models ordinal data and stochastic differential equations with discrete observations

following a moving target monte carlo inference for dynamic bayesian models markov chain monte carlo mcmc sampling is a numerically intensive simulation technique which has greatly improved the practicality of bayesian inference and prediction however mcmc sampling is too slow to be of practical use in problems involving a large number of posterior target distributions as in dynamic modelling and predictive model selection alternative simulation techniques for tracking moving target distributions known as particle filters which combine importance sampling importance resampling and mcmc sampling tend to suffer from a progressive degeneration as the target sequence evolves we propose a new technique based on these same simulation methodologies which does not suffer from this progressive degeneration

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

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

use of the box cox transformation with binary response models abstract the power transformation is applied to the odds ratio to generalize the logistic model and to parameterize a certain type of lack of fit transformation of the design variable within the context of the dose response problem is also considered

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

linear frequency modulated signal detection using radon ambiguity transform a novel time frequency technique for linear frequency modulated lfm signal detection is proposed the design of the proposed detectors is based on the radon transform of the modulus square or the envelope amplitude of the ambiguity function af of the signal a practical assumption is made that the chirp rate is the only parameter of interest since the af of lfm signals will pass through the origin of the ambiguity plane the line integral of the radon transform is performed over all lines passing through the origin of the ambiguity plane the proposed detectors yield maxima over chirp rates of the lfm signals this reduces the two dimensional 2 d problem of the conventional wigner ville distribution wvd based detection or the radon wigner transform rwt based detector to a one dimensional 1 d problem and consequently reduces the computation load and keeps the feature of built in filtering related issues such as the finite length effect the resolution and the effect of noise are studied the result is a tool for lfm detection as well as the time varying filtering and adaptive kernel design for multicomponent lfm signals

reversible jump markov chain monte carlo computation and bayesian model determination markov chain monte carlo methods for bayesian computation have until recently been restricted to problems where the joint distribution of all variables has a density with respect to some fixed standard underlying measure they have therefore not been available for application to bayesian model determination where the dimensionality of the parameter vector is typically not fixed this paper proposes a new framework for the construction of reversible markov chain samplers that jump between parameter subspaces of differing dimensionality which is flexible and entirely constructive it should therefore have wide applicability in model determination problems the methodology is illustrated with applications to multiple change point analysis in one and two dimensions and to a bayesian comparison of binomial experiments

on two families of transformations to additivity for binary response data summary two families of power transformations for probabilities are introduced to model symmetric and asymmetric departures from the logistic model the aim is to provide in a comprehensive way a representation of alternative scales in terms of which to carry out the analysis of binary response data maximum likelihood methods are employed to estimate an appropriate transformation using glim tests for detection of symmetric and asymmetric departures are proposed

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

testing treatment effects in unconfounded studies under model misspecification logistic regression discretization and their combination logistic regression is commonly used to test for treatment effects in observational studies if the distribution of a continuous covariate differs between treated and control populations logistic regression yields an invalid hypothesis test even in an uncounfounded study if the link is not logistic this flaw is not corrected by the commonly used technique of discretizing the covariate into intervals a valid test can be obtained by discretization followed by regression adjustment within each interval

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

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