analysis of a predator prey model with modified leslie gower and holling type ii schemes with stochastic perturbation abstract in this paper we consider a predator prey model with modified leslie gower and holling type ii schemes with stochastic perturbation we show there is a unique positive solution to the system with positive initial value and mainly investigate the long time behavior of the system condition for the system to be extinct is given and persistent condition is established at last numerical simulations are carried out to support our results

stationary distribution of a stochastic delayed sveir epidemic model with vaccination and saturation incidence abstract in this paper we develop and analyze a stochastic delayed sveir epidemic model with vaccination and saturation incidence by constructing a suitable stochastic lyapunov function we establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model the existence of a stationary distribution implies stochastic weak stability numerical simulations are introduced to illustrate the analytical result

a mode elimination technique to improve convergence of iteration methods for finding solitary waves we extend the key idea behind the generalized petviashvili method of t i lakoba j yang a generalized petviashvili iteration method for scalar and vector hamiltonian equations with arbitrary form of nonlinearity j comput phys this issue doi 10 1016 j jcp 2007 06 009 by proposing a novel technique based on a similar idea this technique systematically eliminates from the iteratively obtained solution a mode that is responsible either for the divergence or the slow convergence of the iterations we demonstrate theoretically and with examples that this mode elimination technique can be used both to obtain some nonfundamental solitary waves and to considerably accelerate convergence of various iteration methods as a collateral result we compare the linearized iteration operators for the generalized petviashvili method and the well known imaginary time evolution method and explain how their different structures account for the differences in the convergence rates of these two methods

newton conjugate gradient methods for solitary wave computations in this paper the newton conjugate gradient methods are developed for solitary wave computations these methods are based on newton iterations coupled with conjugate gradient iterations to solve the resulting linear newton correction equation when the linearization operator is self adjoint the preconditioned conjugate gradient method is proposed to solve this linear equation if the linearization operator is non self adjoint the preconditioned biconjugate gradient method is proposed to solve the linear equation the resulting methods are applied to compute both the ground states and excited states in a large number of physical systems such as the two dimensional nls equations with and without periodic potentials the fifth order kdv equation and the fifth order kp equation numerical results show that these proposed methods are faster than the other leading numerical methods often by orders of magnitude in addition these methods are very robust and always converge in all the examples being tested furthermore they are very easy to implement it is also shown that the nonlinear conjugate gradient methods are not robust and inferior to the proposed methods

gap solitons and their linear stability in one dimensional periodic media an analytical theory utilizing exponential asymptotics is presented for one dimensional gap solitons that bifurcate from edges of bloch bands in the presence of a general periodic potential it is shown that two soliton families bifurcate out from every bloch band edge under self focusing or self defocusing nonlinearity and an asymptotic expression for the eigenvalues associated with the linear stability of these solitons is derived the locations of these solitons relative to the underlying potential are determined from a certain recurrence relation that contains information beyond all orders of the usual perturbation expansion in powers of the soliton amplitude moreover this same recurrence relation decides which of the two soliton families is unstable the analytical predictions for the stability eigenvalues are in excellent agreement with numerical results

dynamical analysis of a delayed ratio dependent prey predator model within fluctuating environment abstract in this paper we consider a two dimensional ratio dependent prey predator model involving discrete time delay within fluctuating environment firstly we discuss basic dynamical properties of non delayed and delayed model system in brief within deterministic environment next we construct the stochastic differential equation model and stochastic delay differential equation model to study the effect of environmental driving forces on the dynamical behaviour stochastic models are extension of deterministic models by perturbing two demographic parameters namely birth rate of prey population and death rate of predator population with white noise terms characterized by gaussian distribution having zero mean and unit spectral density we calculate population fluctuation intensity variance for prey and predator species by laplace transform methods for stochastic differential equation model and fourier transforms method for stochastic delay differential equation model numerical simulations are carried out to substantiate the analytical findings significant outcomes of our analytical findings and their interpretations from ecological point of view are provided in concluding section

qmr a quasi minimal residual method for non hermitian linear systems the biconjugate gradient bcg method is the natural generalization of the classical conjugate gradient algorithm for hermitian positive definite matrices to general non hermitian linear systems unfortunately the original bcg algorithm is susceptible to possible breakdowns and numerical instabilities in this paper we present a novel bcg like approach the quasi minimal residual qmr method which overcomes the problems of bcg an implementation of qmr based on a look ahead version of the nonsymmetric lanczos algorithm is proposed it is shown how bcg iterates can be recovered stably from the qmr process some further properties of the qmr approach are given and an error bound is presented finally numerical experiments are reported

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

an algorithmic introduction to numerical simulation of stochastic differential equations a practical and accessible introduction to numerical methods for stochastic differential equations is given the reader is assumed to be familiar with euler s method for deterministic differential equations and to have at least an intuitive feel for the concept of a random variable however no knowledge of advanced probability theory or stochastic processes is assumed the article is built around 10 matlab programs and the topics covered include stochastic integration the euler maruyama method milstein s method strong and weak convergence linear stability and the stochastic chain rule

energy dissipating flows for solving nonlinear eigenpair problems abstract this work is concerned with computing nonlinear eigenpairs which model solitary waves and various other physical phenomena we aim at solving nonlinear eigenvalue problems of the general form t u q u in our setting t is a variational derivative of a convex functional such as the laplacian operator with respect to the dirichlet energy q is an arbitrary bounded nonlinear operator and is an unknown real eigenvalue we introduce a flow that numerically generates an eigenpair solution by its steady state analysis for the general case is performed showing a monotone decrease in the convex functional throughout the flow when t is the laplacian operator a complete discretized version is presented and anlalyzed we implement our algorithm on korteweg and de vries kdv and nonlinear schrodinger nls equations in one and two dimensions the proposed approach is very general and can be applied to a large variety of models moreover it is highly robust to noise and to perturbations in the initial conditions compared to classical petiashvili based methods

the choice of variables in multivariate regression a non conjugate bayesian decision theory approach we consider the choice of explanatory variables in multivariate linear regression our approach balances prediction accuracy against costs attached to variables in a multivariate version of a decision theory approach pioneered by lindley 1968 we also employ a non conjugate proper prior distribution for the parameters of the regression model extending the standard normal inverse wishart by adding a component of error which is unexplainable by any number of predictor variables thus avoiding the determinism identified by dawid 1988 simulated annealing and fast updating algorithms are used to search for good subsets when there are very many regressors the technique is illustrated on a near infrared spectroscopy example involving 39 observations and 300 explanatory variables this demonstrates the effectiveness of multivariate regression as opposed to separate univariate regressions it also emphasises that within a bayesian framework more variables than observations can be utilised

predicting multivariate responses in multiple linear regression we look at the problem of predicting several response variables from the same set of explanatory variables the question is how to take advantage of correlations between the response variables to improve predictive accuracy compared with the usual procedure of doing individual regressions of each response variable on the common set of predictor variables a new procedure is introduced called the curds and whey method its use can substantially reduce prediction errors when there are correlations between responses while maintaining accuracy even if the responses are uncorrelated in extensive simulations the new procedure is compared with several previously proposed methods for predicting multiple responses including partial least squares and exhibits superior accuracy one version can be easily implemented in the context of standard statistical packages

bayes model averaging with selection of regressors when a number of distinct models contend for use in prediction the choice of a single model can offer rather unstable predictions in regression stochastic search variable selection with bayesian model averaging offers a cure for this robustness issue but at the expense of requiring very many predictors here we look at bayes model averaging incorporating variable selection for prediction this offers similar mean square errors of prediction but with a vastly reduced predictor space this can greatly aid the interpretation of the model it also reduces the cost if measured variables have costs the development here uses decision theory in the context of the multivariate general linear model in passing this reduced predictor space bayes model averaging is contrasted with single model approximations a fast algorithm for updating regressions in the markov chain monte carlo searches for posterior inference is developed allowing many more variables than observations to be contemplated we discuss the merits of absolute rather than proportionate shrinkage in regression especially when there are more variables than observations the methodology is illustrated on a set of spectroscopic data used for measuring the amounts of different sugars in an aqueous solution

conjugate gradient method for finding fundamental solitary waves abstract the conjugate gradient method cgm is known to be the fastest generic iterative method for solving linear systems with symmetric sign definite matrices in this paper we modify this method so that it can find fundamental solitary waves of nonlinear hamiltonian equations the main obstacle that such a modified cgm overcomes is that the operator of the equation linearized about a solitary wave is not sign definite instead it has a finite number of eigenvalues on the opposite side of zero than the rest of its spectrum we present versions of the modified cgm that can find solitary waves with prescribed values of either the propagation constant or power we also extend these methods to handle multi component nonlinear wave equations convergence conditions of the proposed methods are given and their practical implications are discussed we demonstrate that our modified cgms converge much faster than say petviashvili s or similar methods especially when the latter converge slowly

unique stationary distribution and ergodicity of a stochastic logistic model with distributed delay abstract dynamics of a stochastic logistic model with distributed delay are considered we first transfer a scalar stochastic logistic model with strong kernel or weak kernel into an equivalent stochastic system through the linear chain technique then we obtain the sufficient and necessary conditions for extinction and persistence of the species with probability one moreover in the case of persistence we prove that there exists a unique stationary distribution by the markov semigroups theory the results show that the stronger white noise results in the extinction of the species and the weaker white noise guarantees the existence of a unique stationary distribution though for the deterministic model with strong kernel or weak kernel the average delay may induce the existence of a group of small amplitude periodic solutions

convergence of petviashvili s iteration method for numerical approximation of stationary solutions of nonlinear wave equations we analyze a heuristic numerical method suggested by v i petviashvili in 1976 for approximation of stationary solutions of nonlinear wave equations the method is used to construct numerically the solitary wave solutions such as solitons lumps and vortices in a space of one and higher dimensions assuming that the stationary solution exists we find conditions when the iteration method converges to the stationary solution and when the rate of convergence is the fastest the theory is illustrated with examples of physical interest such as generalized korteweg de vries benjamin ono zakharov kuznetsov kadomtsev petviashvili and klein gordon equations

better subset regression using the nonnegative garrote a new method called the nonnegative nn garrote is proposed for doing subset regression it both shrinks and zeroes coefficients in tests on real and simulated data it produces lower prediction error than ordinary subset selection it is also compared to ridge regression if the regression equations generated by a procedure do not change drastically with small changes in the data the procedure is called stable subset selection is unstable ridge is very stable and the nn garrote is intermediate simulation results illustrate the effects of instability on prediction error

bayesian wavelet regression on curves with application to a spectroscopic calibration problem motivated by calibration problems in near infrared nir spectroscopy we consider the linear regression setting in which the many predictor variables arise from sampling an essentially continuous curve at equally spaced points and there may be multiple predictands we tackle this regression problem by calculating the wavelet transforms of the discretized curves then applying a bayesian variable selection method using mixture priors to the multivariate regression of predictands on wavelet coefficients for prediction purposes we average over a set of likely models applied to a particular problem in nir spectroscopy this approach was able to find subsets of the wavelet coefficients with overall better predictive performance than the more usual approaches in the application the available predictors are measurements of the nir reflectance spectrum of biscuit dough pieces at 256 equally spaced wavelengths the aim is to predict the composition i e the fat flour sugar and water content of the doug

petviashvili type methods for traveling wave computations i analysis of convergence in this paper a family of fixed point algorithms for the numerical resolution of some systems of nonlinear equations is designed and analyzed the family introduced here generalizes the petviashvili method and can be applied to the numerical generation of traveling waves in some nonlinear dispersive systems conditions for the local convergence are derived and numerical comparisons between different elements of the family are carried out

optimizing schrodinger functionals using sobolev gradients applications to quantum mechanics and nonlinear optics in this paper we study the application of the sobolev gradients technique to the problem of minimizing several schrodinger functionals related to timely and difficult nonlinear problems in quantum mechanics and nonlinear optics we show that these gradients act as preconditioners over traditional choices of descent directions in minimization methods and show a computationally inexpensive way to obtain them using a discrete fourier basis and a fast fourier transform we show that the sobolev preconditioning provides a great convergence improvement over traditional techniques for finding solutions with minimal energy as well as stationary states and suggest a generalization of the method using arbitrary linear operators

new conformal mapping for adaptive resolving of the complex singularities of stokes wave a new highly efficient method is developed for computation of travelling periodic waves stokes waves on the free surface of deep water a convergence of numerical approximation is determined by the complex singularities above the free surface for the analytical continuation of the travelling wave into the complex plane an auxiliary conformal mapping is introduced which moves singularities away from the free surface thus dramatically speeding up numerical convergence by adapting the numerical grid for resolving singularities while being consistent with the fluid dynamics the efficiency of that conformal mapping is demonstrated for the stokes wave approaching the limiting stokes wave the wave of the greatest height which significantly expands the family of numerically accessible solutions it allows us to provide a detailed study of the oscillatory approach of these solutions to the limiting wave generalizations of the conformal mapping to resolve multiple singularities are also introduced

a statistical view of some chemometrics regression tools chemometrics is a field of chemistry that studies the application of statistical methods to chemical data analysis in addition to borrowing many techniques from the statistics and engineering literatures chemometrics itself has given rise to several new data analytical methods this article examines two methods commonly used in chemometrics for predictive modeling partial least squares and principal components regression from a statistical perspective the goal is to try to understand their apparent successes and in what situations they can be expected to work well and to compare them with other statistical methods intended for those situations these methods include ordinary least squares variable subset selection and ridge regression

applications of second order cone programming in a second order cone program socp a linear function is minimized over the intersection of an affine set and the product of second order quadratic cones socps are nonlinear convex problems that include linear and convex quadratic programs as special cases but are less general than semidefinite programs sdps several efficient primaldual interior point methods for socp have been developed in the last few years after reviewing the basic theory of socps we describe general families of problems that tan be recast as socps these include robust linear programming and robust leastsquares problems problems involving sums or maxima of norms or with convex hyperbolic constraints we discuss a variety of engineering applications such as filter design antenna array weight design truss design and grasping forte optimization in robotics we describe an efficient primaldual interior point method for solving socps which shares many of the features of primaldual interior point methods for linear program

persistence and global stability in a delayed leslie gower type three species food chain abstract our investigation concerns the three dimensional delayed continuous time dynamical system which models a predator prey food chain this model is based on the holling type ii and a leslie gower modified functional response this model can be considered as a first step towards a tritrophic model of leslie gower and holling tanner type with inverse trophic relation and time delay that is when a certain species that is usually eaten can consume immature predators it is proved that the system is uniformly persistent under some appropriate conditions by constructing a proper lyapunov function we obtain a sufficient condition for global stability of the positive equilibrium

global exponential stability for stochastic coupled systems on networks with markovian switching abstract this paper investigates the global exponential stability of stochastic coupled systems on networks with markovian switching scsnms sufficient conditions are established to guarantee p th moment exponential stability and almost surely exponential stability of the scsnms by using concepts from graph theory and m matrix into lyapunov method consequently the upper boundaries of the p th moment lyapunov exponent and the sample lyapunov exponent are given finally to illustrate the capabilities of the stability principle easy verifiable sufficient conditions of global exponential stability for a stochastic coupled oscillator on network with markovian switching are obtained

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

deleted residuals the qr factored newton iteration and other methods for formally overdetermined determinate discretizations of nonlinear eigenproblems for solitary cnoidal and shock waves abstract solitary waves cnoidal waves and shock waves can be computed by solving a nonlinear eigenvalue problem which in discretized form is a system of nonlinear algebraic equations unfortunately many such systems are singular because the solution is not unique until one or more additional constraints are imposed for example if the waves are translationally invariant and u x is a solution then so also is u x for arbitrary to obtain a unique solution one must impose an additional condition to reduce the one parameter family of solutions by constraining we describe five methods for coping with such singular systems i reformulation of the problem ii deleting residuals iii keller s bordered matrix scheme iv qr factored overdetermined newton iteration and v pseudoinverse newton iteration we illustrate these ideas using the cnoidal waves of the korteweg de vries equation the traveling shocks of the korteweg de vries burgers equation and the weakly nonlocal solitary waves of the nonlinear equatorial beta plane equations finite difference fourier and rational chebyshev pseudospectral methods and spectrally upgraded finite differences are applied reformulation and deleting residuals are the cheapest strategies but the qr factored newton iteration is needed for the shock waves which lack the symmetry of the other two wave species

simultaneous variable selection we propose a new method for selecting a common subset of explanatory variables where the aim is to model several response variables the idea is a natural extension of the lasso technique proposed by tibshirani 1996 and is based on the joint residual sum of squares while constraining the parameter estimates to lie within a suitable polyhedral region the properties of the resulting convex programming problem are analyzed for the special case of an orthonormal design for the general case we develop an efficient interior point algorithm the method is illustrated on a dataset with infrared spectrometry measurements on 14 qualitatively different but correlated responses using 770 wavelengths the aim is to select a subset of the wavelengths suitable for use as predictors for as many of the responses as possible

symmetry breaking of solitons in two dimensional complex potentials symmetry breaking is reported for continuous families of solitons in the nonlinear schrodinger equation with a two dimensional complex potential this symmetry breaking is forbidden in generic complex potentials however for a special class of partially parity time symmetric potentials it is allowed at the bifurcation point two branches of asymmetric solitons bifurcate out from the base branch of symmetry unbroken solitons stability of these solitons near the bifurcation point are also studied and two novel properties for the bifurcated asymmetric solitons are revealed one is that at the bifurcation point zero and simple imaginary linear stability eigenvalues of asymmetric solitons can move directly into the complex plane and create oscillatory instability the other is that the two bifurcated asymmetric solitons even though having identical powers and being related to each other by spatial mirror reflection can possess different types of unstable eigenvalues and thus exhibit nonreciprocal nonlinear evolutions under random noise perturbations

multivariate bayesian variable selection and prediction the multivariate regression model is considered with p regressors a latent vector with p binary entries serves to identify one of two types of regression coefficients those close to 0 and those not specializing our general distributional setting to the linear model with gaussian errors and using natural conjugate prior distributions we derive the marginal posterior distribution of the binary latent vector fast algorithms aid its direct computation and in high dimensions these are supplemented by a markov chain monte carlo approach to sampling from the known posterior distribution problems with hundreds of regressor variables become quite feasible we give a simple method of assigning the hyperparameters of the prior distribution the posterior predictive distribution is derived and the approach illustrated on compositional analysis of data involving three sugars with 160 near infra red absorbances as regressors

analysis of a stochastic predator prey system with modified leslie gower and holling type iv schemes abstract in this paper we investigate the dynamics of a stochastic predator prey system with modified leslie gower and holling type iv schemes we first show the existence and uniqueness of the global positive solution to the system with positive initial values in some case the stochastic boundedness and stochastic permanence are obtained then under some conditions we prove the persistence in mean and extinction of the stochastic system moreover under certain parametric restrictions we obtain that the system has a stationary distribution which is ergodic finally some numerical simulations are carried out to support our results

a stochastic sirs epidemic model with nonlinear incidence rate a stochastic sirs model with ratio dependent incidence rate is developed the global dynamics of the deterministic model is shown the stochastic dynamics of the sde model is given the existence of a unique stationary distribution of the sde model is displayed in this paper we investigate the global dynamics of a general sirs epidemic model with a ratio dependent incidence rate and its corresponding stochastic differential equation version for the deterministic model we show that the basic reproduction number r0 determines whether there is an endemic outbreak or not if r0 1 the disease persists for the stochastic model we show that its related reproduction number r0s can determine whether there is a unique disease free stationary distribution or a unique endemic stationary distribution in addition we provide analytic results regarding the stochastic boundedness and permanence extinction one of the most interesting findings is that random fluctuations introduced in our stochastic model can suppress disease outbreak which can provide us some useful control strategies to regulate disease dynamics

global stability analysis for stochastic coupled systems on networks this paper considers the global stability problem for some stochastic coupled systems on networks scsns we provide a systematic method for constructing a global lyapunov function for these scsns by using graph theory and the lyapunov second method consequently a new global stability principle which has a close relation to the topology property of the network is given as an application to the results we employ the principle to two well known coupled systems in physical and ecology and then some easy verified sufficient conditions which guarantee the global stability are obtained

a generalized petviashvili iteration method for scalar and vector hamiltonian equations with arbitrary form of nonlinearity the petviashvili s iteration method has been known as a rapidly converging numerical algorithm for obtaining fundamental solitary wave solutions of stationary scalar nonlinear wave equations with power law nonlinearity mu up 0 where m is a positive definite self adjoint operator and p const in this paper we propose a systematic generalization of this method to both scalar and vector hamiltonian equations with arbitrary form of nonlinearity and potential functions for scalar equations our generalized method requires only slightly more computational effort than the original petviashvili method