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

cortical thickness analysis in autism with heat kernel smoothing we present a novel data smoothing and analysis framework for cortical thickness data defined on the brain cortical manifold gaussian kernel smoothing which weights neighboring observations according to their 3d euclidean distance has been widely used in 3d brain images to increase the signal to noise ratio when the observations lie on a convoluted brain surface however it is more natural to assign the weights based on the geodesic distance along the surface we therefore develop a framework for geodesic distance based kernel smoothing and statistical analysis on the cortical manifolds as an illustration we apply our methods in detecting the regions of abnormal cortical thickness in 16 high functioning autistic children via random field based multiple comparison correction that utilizes the new smoothing technique

ideal spatial adaptation by wavelet shrinkage summary with ideal spatial adaptation an oracle furnishes information about how best to adapt a spatially variable estimator whether piecewise constant piecewise polynomial variable knot spline or variable bandwidth kernel to the unknown function estimation with the aid of an oracle offers dramatic advantages over traditional linear estimation by nonadaptive kernels however it is a priori unclear whether such performance can be obtained by a procedure relying on the data alone we describe a new principle for spatially adaptive estimation selective wavelet reconstruction we show that variable knot spline fits and piecewise polynomial fits when equipped with an oracle to select the knots are not dramatically more powerful than selective wavelet reconstruction with an oracle we develop a practical spatially adaptive method riskshrink which works by shrinkage of empirical wavelet coefficients riskshrink mimics the performance of an oracle for selective wavelet reconstruction as well as it is possible to do so a new inequality in multivariate normal decision theory which we call the oracle inequality shows that attained performance differs from ideal performance by at most a factor of approximately 2 log n where n is the sample size moreover no estimator can give a better guarantee than this within the class of spatially adaptive procedures riskshrink is essentially optimal relying only on the data it comes within a factor log 2 n of the performance of piecewise polynomial and variableknot spline methods equipped with an oracle in contrast it is unknown how or if piecewise polynomial methods could be made to function this well when denied access to an oracle and forced to rely on data alone

cortical thickness analysis examined through power analysis and a population simulation we have previously developed a procedure for measuring the thickness of cerebral cortex over the whole brain using 3 d mri data and a fully automated surface extraction asp algorithm this paper examines the precision of this algorithm its optimal performance parameters and the sensitivity of the method to subtle focal changes in cortical thickness the precision of cortical thickness measurements was studied using a simulated population study and single subject reproducibility metrics cortical thickness was shown to be a reliable method reaching a sensitivity probability of a true positive of 0 93 six different cortical thickness metrics were compared the simplest and most precise method measures the distance between corresponding vertices from the white matter to the gray matter surface given two groups of 25 subjects a 0 6 mm 15 change in thickness can be recovered after blurring with a 3 d gaussian kernel full width half max 30 mm smoothing across the 2 d surface manifold also improves precision in this experiment the optimal kernel size was 30 mm

effect of weak prey in leslie gower predator prey model a leslie gower prey predator model incorporating partial prey protection is proposed prey densities are divided into two groups strong and weak the special dynamic of each group is considered the condition of existence and uniqueness of the equilibrium point in the positive octant is determined and by constructing a suitable lyapunov function it is shown that the unique equilibrium point is stable in the positive octant the effects of strong prey becoming weak prey is studied and it is shown that it has no influence on the persistent property of the system and can enhance the co existence of the prey predator

optimal harvesting control problem for linear periodic age dependent population dynamics in this paper we investigate an optimal harvesting problem for linear periodic age dependent population dynamics namely we consider the lotka mckendrick model with periodic vital rates and a periodic forcing term that sustains oscillations by mazur s theorem we demonstrate existence of solutions of the optimal control problem oh and by the conception of normal cone we also obtain the first order necessary conditions of optimality for problem oh finally under suitable assumptions we give uniqueness of solutions of the optimal control problem oh our results extend some known criteria

dynamics of a nonlocal multi type sis epidemic model with seasonality abstract in this paper we propose and study a multi type sis nonlocal epidemic model with seasonality we first establish the existence of the spreading speed c and the non existence of periodic traveling waves with wave speed c c then we prove the existence and asymptotic behavior of the periodic traveling fronts with speed c c finally the existence of the critical periodic traveling wave fronts is established by using a limiting argument to overcome the difficulty of lack of compactness of solution maps of the nonlocal system with respect to compact open topology we show that the solution sequence is pre compact in l loc r 2 r m

cortical surface based analysis ii inflation flattening and a surface based coordinate system the surface of the human cerebral cortex is a highly folded sheet with the majority of its surface area buried within folds as such it is a difficult domain for computational as well as visualization purposes we have therefore designed a set of procedures for modifying the representation of the cortical surface to i inflate it so that activity buried inside sulci may be visualized ii cut and flatten an entire hemisphere and iii transform a hemisphere into a simple parameterizable surface such as a sphere for the purpose of establishing a surface based coordinate system r 1999 academic press

periodic neural activity induced by network complexity we study a model for neural activity on the small world topology of watts and strogatz and on the scale free topology of barabasi and albert we find that the topology of the network connections may spontaneously induce periodic neural activity contrasting with nonperiodic neural activities exhibited by regular topologies periodic activity exists only for relatively small networks and occurs with higher probability when the rewiring probability is larger the average length of the periods increases with the square root of the network size

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

asymptotic speeds of spread and traveling waves for integral equations and delayed reaction diffusion models abstract the theory of asymptotic speeds of spread and monotone traveling waves is generalized to a large class of scalar nonlinear integral equations and is applied to some time delayed reaction and diffusion population models

determining the optimal level of smoothing in cortical thickness analysis a hierarchical approach based on sequential statistical thresholding article i nfo the extent of smoothing applied to cortical thickness maps critically influences sensitivity anatomical precision and resolution of statistical change detection theoretically it could be optimized by increasing the trade off between vertex wise sensitivity and specificity across several levels of smoothing but to date neither parametric nor nonparametric methods are able to control the error at the vertex level if the null hypothesis is rejected after smoothing of cortical thickness maps to overcome these drawbacks we applied sequential statistical thresholding based on a simple hierarchical model this methodology aims at controlling erroneous detections firstly at the level of clusters over smoothed statistical maps and secondly at the vertex level over unsmoothed statistical maps by applying an adaptive false discovery rate fdr procedure to clusters previously detected the superior performance of the proposed methodology over other conventional procedures was demonstrated in simulation studies as expected only the hierarchical method yielded a predictable false discovery proportion near the predefined fdr q value for any smoothing level at the same time as being as sensitive as the others at the optimal setting it was therefore the only method able to approximate the optimal size of spatial smoothing when the true change was assumed unknown the hierarchical method was further validated in a cross sectional study comparing moderate alzheimer s disease ad patients with healthy elderly subjects results suggest that the extent of cortical thinning reported in previous ad studies might be artificially inflated by the choice of inadequate smoothing in these cases interpretation should be based on the location of local maxima of suprathreshold regions rather than on the spatial extent of the detected signal in the statistical parametric map

perturbations from an elliptic hamiltonian of degree four abstract the paper deals with lienard equations of the form x y y p x yq x with p and q polynomials of degree respectively 3 and 2 attention goes to perturbations of the hamiltonian vector field with an elliptic hamiltonian of degree 4 exhibiting a cuspidal loop it is proven that the least upper bound for the number of zeros of the related elliptic integral is four and this upper bound is a sharp one this permits to prove the existence of lienard equations of type 3 2 with at least four limit cycles the paper also contains a complete result on the respective number of small and large limit cycles

modeling and analysis in a prey predator system with commercial harvesting and double time delays both maturation delay for prey and gestation delay for predator are considered positivity of solutions and uniform persistence of system are investigated combined dynamic effects of double time delays and economic interest are studied existence and control for singularity induced bifurcation are investigated local stability analysis and properties of hopf bifurcation are studied a differential algebraic prey predator system with commercial harvesting on predator is proposed where maturation delay for prey and gestation delay for predator are considered since commercial harvesting is dynamically influenced by variation of economic interest we will investigate combined dynamic effects of double time delays and economic interest on population dynamics positivity of solutions and uniform persistence of system are studied in the absence of time delay by taking economic interest as bifurcation parameter existence of singularity induced bifurcation is investigated based on differential algebraic system theory state feedback controllers are designed to eliminate singularity induced bifurcation and stabilize the proposed system around corresponding interior equilibrium in the presence of double time delays by analyzing associated characteristic transcendental equation it is found that interior equilibrium loses local stability when double time delays cross corresponding critical values according to hopf bifurcation theorem for functional differential equation existence of hopf bifurcation is investigated as local stability switches based on normal form theory and center manifold theorem directions of hopf bifurcation and stability of the bifurcating periodic solutions are studied numerical simulations are carried out to show consistency with theoretical analysis

accelerating propagation in a recursive system arising from seasonal population models with nonlocal dispersal abstract the system of interest is defined by iterations of the poincare map of a time periodic population model with symmetric nonlocal dispersal and periodic time delay under the kpp type setting we show that the system admits the spreading speed c 0 that coincides with the minimal speed of traveling waves where c if the nonlocal dispersal kernel j is exponentially bounded and c if j is exponentially unbounded further the latter case gives rises to an accelerating propagation that the level set of solutions with compactly supported initial values locate in between two exponential functions in time

effect of harvesting delay and diffusion in a generalist predator prey model in compared with specialist predators which feed almost exclusively on a specific species of prey generalist predators feed on many types of species consequently their dynamics is not coupled to the dynamics of a specific prey population and the generalist predators has itself growth function which be extended a well known logistic growth term we develop a generalist predator prey model with diffusion and study the effect of harvesting and delay under neumann conditions the stability of the equilibria is firstly investigated and the existence of traveling wave solutions is then established by constructing a pair of upper lower solutions and using the cross iteration method and schauder s fixed point theorem

optimal harvesting of a stochastic delay tri trophic food chain model with levy jumps abstract in this paper the optimal harvesting of a stochastic delay tri trophic food chain model with levy jumps is considered we introduce two kinds of environmental perturbations in this model one is called white noise which is continuous and is described by a stochastic integral with respect to the standard brownian motion and the other one is jumping noise which is modeled by a levy process under some mild assumptions the critical values between extinction and persistent in the mean of each species are established the sufficient and necessary criteria for the existence of optimal harvesting policy are established and the optimal harvesting effort and the maximum of sustainable yield are also obtained we utilize the ergodic method to discuss the optimal harvesting problem the results show that white noises and levy noises significantly affect the optimal harvesting policy while time delays is harmless for the optimal harvesting strategy in some cases at last some numerical examples are introduced to show the validity of our results

travelling wave solutions for a nonlocal dispersal hiv infection dynamical model abstract this paper is devoted to developing a nonlocal dispersal hiv infection dynamical model the existence of travelling wave solutions is investigated by employing schauder s fixed point theorem that is we study the existence of travelling wave solutions for r 0 1 and each wave speed c c in addition the boundary asymptotic behaviour of travelling wave solutions at is obtained by constructing suitable lyapunov functions and employing lebesgue dominated convergence theorem by employing a limiting argument we investigate the existence of travelling wave solutions for r 0 1 and c c the main difficulties are that the semiflow generated by the model does not have the order preserving property and the solutions lack of regularity

on a non selective harvesting prey predator model with hassell varley type functional response in this paper a nonautonomous delayed prey predator model with non selective harvesting and hassell varley type functional response is investigated some sufficient conditions are obtained for the existence of positive periodic solutions to the system using the continuation theorem of coincidence degree theory moreover the obtained results are different from the previous works numerous are conducted to illustrate the feasibility of the obtained results

global attractivity of nonautonomous stage structured population models with dispersal and harvest the nonautonomous stage structured single species dispersal model with harvesting of mature individuals in an n patch environment is considered in which the individual members of the population have a life history that takes them through two stages immature and mature by using the theory of monotone and concave operators to functional differential equations we establish conditions under which this population dynamical system admits a positive periodic solution which attracts all positive solutions

optimal harvesting policy for general stochastic logistic population model abstract we consider some optimal harvesting policies for a general stochastic logistic population model for two management objectives that are maximum sustainable yield and the maximum retained profits the optimal harvesting policies are obtained meanwhile the optimal harvest effort the maximum of expectation of sustainable yield or retained profits and the corresponding variance are given

global asymptotical stability of a n 1 dimensional leslie gower predator prey model abstract by constructing suitable lyapunov function we obtain the global asymptotical stability of n 1 dimensional leslie gower predator prey models it is shown that the prey refuge and the proportional harvesting have no influence on the global asymptotical stability of the system but they can change the position of the unique interior equilibrium finally mathematic analysis shows that if we choose and control the harvesting efforts e e i appropriately we can not only harvest the biological resources and achieve the economic interest but also protect the biological resources

traveling waves in a delayed sir epidemic model with nonlinear incidence we study the traveling waves of a diffusive sir epidemic model with a general nonlinear incidence we obtain the threshold dynamics for spatial spread of the disease we show that c is the minimum wave speed for the existence of traveling wave solutions we establish the existence and non existence of traveling wave solutions for a diffusive sir model with a general nonlinear incidence the existence proof is shown by introducing an auxiliary system applying schauder s fixed point theorem and then a limiting argument the nonexistence proof is obtained by two sided laplace transform when the speed is less than the critical velocity numerical simulations support the theoretical results we also point out the effects of the delay and the diffusion rate of the infective individuals on the spreading speed

optimal harvesting of a stochastic mutualism model with levy jumps in this letter a stochastic mutualism model with levy jumps and harvesting is considered under some simple assumptions sufficient and necessary criteria for the existence of optimal harvesting policy are established the optimal harvesting effort and the maximum of sustainable yield are also obtained the effects of random noises on the optimal harvesting of the model are discussed and some numerical simulations are introduced to illustrate the main results

denoising functional mr images a comparison of wavelet denoising and gaussian smoothing we present a general wavelet based denoising scheme for functional magnetic resonance imaging fmri data and compare it to gaussian smoothing the traditional denoising method used in fmri analysis one dimensional wavelab thresholding routines were adapted to two dimensional 2 d images and applied to 2 d wavelet coefficients to test the effect of these methods on the signal to noise ratio snr we compared the snr of 2 d fmri images before and after denoising using both gaussian smoothing and wavelet based methods we simulated a fmri series with a time signal in an active spot and tested the methods on noisy copies of it the denoising methods were evaluated in two ways by the average temporal snr inside the original activated spot and by the shape of the spot detected by thresholding the temporal snr maps denoising methods that introduce much smoothness are better suited for low snrs but for images of reasonable quality they are not preferable because they introduce heavy deformations wavelet based denoising methods that introduce less smoothing preserve the sharpness of the images and retain the original shapes of active regions we also performed statistical parametric mapping on the denoised simulated time series as well as on a real fmri data set false discovery rate control was used to correct for multiple comparisons the results show that the methods that produce smooth images introduce more false positives the less smoothing wavelet based methods although generating more false negatives produce a smaller total number of errors than gaussian smoothing or wavelet based methods with a large smoothing effect

asymptotic patterns of a structured population diffusing in a two dimensional strip abstract in this paper we derive a population model for the growth of a single species on a two dimensional strip with neumann and robin boundary conditions we show that the dynamics of the mature population is governed by a reaction diffusion equation with delayed global interaction using the theory of asymptotic speed of spread and monotone traveling waves for monotone semiflows we obtain the spreading speed c the non existence of traveling waves with wave speed 0 c c and the existence of monotone traveling waves connecting the two equilibria for c c

asymptotic behavior and traveling wave solutions for parabolic functional differential equations on presente une generalisation de la theorie des equations kpp et de diffusion bistables non lineaires on montre que des solutions onde de propagation existent pour des equations fonctionnelles paraboliques non lineaires

hopf bifurcation analysis for a ratio dependent predator prey system with two delays and stage structure for the predator the ratio dependent theory is favored by researchers since it is more suitable for describing the relationship between predator and its prey in this paper a ratio dependent predator prey system with holling type ii functional response two time delays and stage structure for the predator is investigated firstly by choosing the two time delays as the bifurcation parameter the sufficient conditions for the local stability and the existence of hopf bifurcation with respect to both delays are established furthermore based on the normal form method and center manifold theorem explicit formulas are derived to determine the direction of hopf bifurcation and stability of the bifurcating periodic solution finally numerical simulations are given to verify the theoretical analysis

entire solutions for a multi type sis nonlocal epidemic model in r or z abstract in this paper we study entire solutions for a multi type sis nonlocal epidemic model in r or z the existence and asymptotic behavior of spatially independent solutions are first established some new entire solutions are then constructed by combining traveling wave fronts with different speeds and a spatially independent solution from the viewpoint of epidemiology the results provide some new spread ways of the epidemic

perturbations from an elliptic hamiltonian of degree four i saddle loop and two saddle cycle abstract the paper deals with lienard equations of the form x y y p x yq x with p and q polynomials of degree respectively 3 and 2 attention goes to perturbations of the hamiltonian vector fields with an elliptic hamiltonian of degree 4 and especially to the study of the related elliptic integrals besides some general results the paper contains a complete treatment of the saddle loop case and the two saddle cycle case it is proven that the related elliptic integrals have at most two zeros respectively one zero the multiplicity taken into account the bifurcation diagram of the zeros is also obtained

solving ratio dependent predator prey system with constant effort harvesting using adomian decomposition method abstract in this paper an algorithm based on adomian s decomposition method is developed to approximate the solution of the ratio dependent predator prey system with constant effort harvesting the convergence of the decomposition series is enhanced using pade approximation technique the qualitative analysis of the model reveals that constant effort prey harvesting may contribute to mutual extinction as a possible outcome of predator prey interaction some plots of the population of predator and prey versus time are presented to illustrate the performance and the accuracy of the algorithm the decomposition method has the advantage of being more concise for numerical purposes

validating cluster size inference random field and permutation methods cluster size tests used in analyses of brain images can have more sensitivity compared to intensity based tests the random field rf theory has been widely used in implementation of such tests however the behavior of such tests is not well understood especially when the rf assumptions are in doubt in this paper we carried out a simulation study of cluster size tests under varying smoothness thresholds and degrees of freedom comparing rf performance to that of the permutation test which is known to be exact for gaussian images we find that the rf methods are generally conservative especially for low smoothness and low threshold for t images the rf tests are found to be conservative at lower thresholds and do not perform well unless the threshold is high and images are sufficiently smooth the permutation test performs well for any settings though the discreteness in cluster size must be accounted for we make specific recommendations on when permutation tests are to be preferred to rf tests

threshold free cluster enhancement addressing problems of smoothing threshold dependence and localisation in cluster inference many image enhancement and thresholding techniques make use of spatial neighbourhood information to boost belief in extended areas of signal the most common such approach in neuroimaging is cluster based thresholding which is often more sensitive than voxel wise thresholding however a limitation is the need to define the initial cluster forming threshold this threshold is arbitrary and yet its exact choice can have a large impact on the results particularly at the lower e g t z 4 cluster forming thresholds frequently used furthermore the amount of spatial pre smoothing is also arbitrary given that the expected signal extent is very rarely known in advance of the analysis in the light of such problems we propose a new method which attempts to keep the sensitivity benefits of cluster based thresholding and indeed the general concept of clusters of signal while avoiding or at least minimising these problems the method takes a raw statistic image and produces an output image in which the voxel wise values represent the amount of cluster like local spatial support the method is thus referred to as threshold free cluster enhancement tfce we present the tfce approach and discuss in detail roc based optimisation and comparisons with cluster based and voxel based thresholding we find that tfce gives generally better sensitivity than other methods over a wide range of test signal shapes and snr values we also show an example on a real imaging dataset suggesting that tfce does indeed provide not just improved sensitivity but richer and more interpretable output than cluster based thresholding

traveling wavefronts of a prey predator diffusion system with stage structure and harvesting from a biological point of view we consider a prey predator type free diffusion fishery model with stage structure and harvesting first we study the stability of the nonnegative constant equilibria in particular the effect of harvesting on the stability of equilibria is discussed and supported with numerical simulation then employing the upper and lower solution method we show that when the wave speed is large enough there exists a traveling wavefront connecting the zero solution to the positive equilibrium of the system numerical simulation is also carried out to illustrate the main result

delay induced traveling wave fronts in reaction diffusion equations of kpp fisher type this paper explores the impact of delay on the existence of traveling wave fronts in reaction diffusion equations of kpp fisher type for two such equations one being local and the other with nonlocal effect arising from the age structure of the population we show that delay can induce slow traveling wave fronts

a system with three limit cycles appearing in a hopf bifurcation and dying in a homoclinic bifurcation the cusp of order 4 abstract in this paper we give an example of a family of polynomial vector fields with three limit cycles appearing simultaneously on a hopf bifurcation h of order 3 and vanishing simultaneously in a homoclinic loop bifurcation hl of order 3 the region with three limit cycles is a topological 3 simplex the system is a generalization of bogdanov s system at the same time we give the bifurcation diagram for the universal unfolding of the cusp of order 4 this bifurcation diagram is a cone it contains a cone on the bifurcation diagram with the three limit cycles inside a 3 simplex region plus saddle node and cusp bifurcations of lower order

modelling and analysis of a harvested prey predator system incorporating a prey refuge the present paper deals with a prey predator model incorporating a prey refuge and independent harvesting in either species our study shows that using the harvesting efforts as controls it is possible to break the cyclic behaviour of the system and drive it to a required state the possibility of existence of bionomic equilibria has been considered the problem of optimal harvest policy is then solved by using pontryagin s maximal principle

traveling wavefronts for delayed reaction diffusion systems via a fixed point theorem abstract by using schauder s fixed point theorem we prove some existence results for traveling wavefronts of reaction diffusion systems with quasimonotonicity reactions more precisely we reduce the existence of traveling wavefronts to the existence of an admissible pair of supersolution and subsolution which are easy to construct in practice finally to illustrate our main results we study the existence of traveling wavefronts for a delayed predator prey model with diffusion as well as the reaction diffusion system with the well known belousov zhabotinskii reaction and the obtained results improve the existing ones

stochastic periodic solution for a perturbed non autonomous predator prey model with generalized nonlinear harvesting and impulses abstract in this paper stochastic non autonomous predator prey models with and without impulses are investigated the effects of generalized nonlinear harvesting for prey and predator populations are considered for the stochastic system without impulses the existence and uniqueness of the positive solution is proven and sufficient conditions that guarantee the extinction and persistence of the population in the mean are achieved we show the existence of a nontrivial positive periodic solution by constructing appropriate lyapunov functions and using khasminskii s theory moreover the global attractiveness and stochastic persistence in probability of the stochastic model are discussed results show that the stronger noises and nonlinear harvesting component can significantly influence the dynamics of the system and lead to the extinction of the predator population additionally for the stochastic predator prey system with impulsive effect we prove that there exists a positive periodic solution numerical simulations are conducted to show the effectiveness and feasibility of the obtained results

mixed types of waves in a discrete diffusive epidemic model with nonlinear incidence and time delay abstract in this paper we investigate the traveling wave solutions of a discrete diffusive epidemic model with nonlinear incidence and time delay employing the method of upper and lower solutions schauder s fixed point theorem and a limiting approach we prove the existence of bounded super critical and critical traveling wave solutions moreover we obtain the positiveness and asymptotic boundary of the traveling wave solutions which guarantee that the traveling wave solutions are non trivial the existence results show that the traveling waves are mixed of front type and pulse type by way of contradiction and two sided laplace transform we derive the non existence of non trivial positive and bounded traveling wave solutions it is the first time to apply the method of upper and lower solutions together with schauder s fixed point theorem and two sided laplace transform to investigate the existence and non existence of traveling wave solutions for discrete diffusive epidemic models respectively

optimal harvesting of a stochastic delay competitive lotka volterra model with levy jumps abstract this paper systematically investigates the optimal harvesting of a stochastic delay competitive lotka volterra model with levy jumps under some simple assumptions the sufficient conditions for extinction and stable in the time average of each species are established the stability in distribution of this model is proved under our assumptions finally the sufficient and necessary criteria for the existence of optimal harvesting policy are established and the explicit expression of the optimal harvesting effort and the maximum of sustainable yield are also obtained and some numerical simulations are introduced to demonstrate the theoretical results

spreading speed and traveling waves for a multi type sis epidemic model abstract the theory of asymptotic speeds of spread and monotone traveling waves for monotone semiflows is applied to a multi type sis epidemic model to obtain the spreading speed c and the nonexistence of traveling waves with wave speed c c then the method of upper and lower solutions is used to establish the existence of monotone traveling waves connecting the disease free and endemic equilibria for c c this shows that the spreading speed coincides with the minimum wave speed for monotone traveling waves we also give an affirmative answer to an open problem presented by rass and radcliffe l rass j radcliffe spatial deterministic epidemics math surveys monogr 102 amer math soc providence ri 2003

bifurcations of a ratio dependent predator prey system with constant rate harvesting the ratio dependent predator prey model exhibits rich interesting dynamics due to the singularity of the origin the objective of this paper is to study the dynamical properties of the ratio depend

optimal harvesting policy for stochastic logistic population model abstract in this paper we consider some optimal harvesting policies for single population models in which the harvest effort and the intrinsic growth rate are disturbed by environment noises we choose the maximum sustainable yield and the maximum retained profits as two management objectives and obtain the optimal harvesting policies respectively for the two objectives we give the optimal harvest effort that maximizes the sustainable yield or retained profits the maximum of expectation of sustainable yield or retained profits and the corresponding variance their explicit expressions are determined by the coefficients of equation and the disturbance intensity

adaptive linear step up procedures that control the false discovery rate we provide a new two stage procedure in which the linear step up procedure is used in stage one to estimate mo providing a new level q which is used in the linear step up procedure in the second stage we prove that a general form of the two stage procedure controls the false discovery rate at the desired level q this framework enables us to study analytically the properties of other procedures that exist in the literature a simulation study is presented that shows that two stage adaptive procedures improve in power over the original procedure mainly because they provide tighter control of the false discovery rate we further study the performance of the current suggestions some variations of the procedures and previous suggestions in the case where the test statistics are positively dependent a case for which the original procedure controls the false discovery rate in the setting studied here the newly proposed two stage procedure is the only one that controls the false discovery rate the procedures are illustrated with two examples of biological importance

detection of focal changes in human cortical thickness spherical wavelets versus gaussian smoothing subtle but progressive variations in human cortical thickness have been associated with the initial phases of prevalent neurological and psychiatric conditions but slight changes in cortical thickness at preclinical stages are typically masked by effects of the gaussian kernel smoothing on the cortical surface shape descriptors here we present the first study aimed at detecting changes in human cortical thickness maps by applying soft thresholding to multiresolution spherical wavelet coefficients in order to make gaussian and wavelet smoothing methods comparable the trade off between sensitivity and specificity was optimized to detect simulated thickness changes in various cortical areas of healthy elderly subjects results revealed a better sensitivity specificity trade off when using wavelet based methods as compared to gaussian smoothing in both the whole neocortex p 10 7 and cortical region based statistical analyses p 10 9 which was mainly due to the higher specificity obtained with the wavelet approach the lower smoothing introduced by wavelets and their adaptive properties may account for the enhanced specificity and sensitivity when compared with gaussian spatial filters these results strongly support the use of spherical wavelet methods to detect subtle variations in cortical thickness maps which may be crucial in better understanding the course of neuronal loss in normal aging and in finding early markers of cortical degeneration

false discovery rates for spatial signals the problem of multiple testing for the presence of signal in spatial data can involve numerous locations traditionally each location is tested separately for signal presence but then the findings are reported in terms of clusters of nearby locations this is an indication that the units of interest for testing are clusters rather than individual locations the investigator may know a priori these more natural units or an approximation to them we suggest testing these cluster units rather than individual locations thus increasing the signal to noise ratio within the unit tested as well as reducing the number of hypothesis tests conducted because the signal may be absent from part of each cluster we define a cluster as containing a signal if the signal is present somewhere within the cluster we suggest controlling the false discovery rate fdr on clusters i e the expected proportion of clusters rejected erroneously out of all clusters rejected or its extension to general weights wfdr we int

epidemic waves of a spatial sir model in combination with random dispersal and non local dispersal abstract in this paper a spatial sir model in combination with random dispersal and non local dispersal is proposed we establish the existence and non existence of the traveling wave solutions connecting the disease free equilibrium and the endemic equilibrium for the model the main difficulties lie in the fact that the semiflow generated here does not admit the order preserving property and the solutions lack of regularity we use a proper iteration scheme to construct a pair of upper and lower solutions and then apply the schauder s fixed point theorem polar coordinates transform to study the threshold dynamics of the model that is we show that if the basic reproduction number of the model r 0 1 there is a positive constant critical number c such that for each c c the model admits a non trivial and positive traveling wave with wave speed c and if r 0 1 and 0

propagation dynamics of a nonlocal dispersal fisher kpp equation in a time periodic shifting habitat abstract this paper is devoted to the study of the propagation dynamics of a nonlocal dispersal fisher kpp equation in a time periodic shifting habitat we first show that this equation admits a periodic forced wave with the speed at which the habitat is shifting by using the monotone iteration method combined with a pair of generalized super and sub solutions then we establish the nonexistence uniqueness and global exponential stability of periodic forced waves by applying the sliding technique and the comparison argument finally we obtain the spreading properties for a large class of solutions

homoclinic bifurcation of prey predator model with impulsive state feedback control abstract in this paper homoclinic bifurcations of a prey predator system with state impulse are investigated firstly the existence of order 1 homoclinic cycle of system 1 2 with 0 is investigated secondly choosing q as a control parameter the sufficient conditions of existence and stability of order 1 periodic solution of system 1 2 with 0 are obtained by means of the geometry theory of semi continuous dynamic systems thirdly on the basis of the theory of rotated vector fields homoclinic bifurcation of system 1 2 about parameter are also studied finally some simulations are provided to prove the main results the methods used in this paper are intuitive to prove the existence of order 1 homoclinic cycle and homoclinic bifurcations

dynamic behaviour of a delayed predator prey model with harvesting abstract in this paper we analyze the dynamics of a delayed predator prey system in the presence of harvesting this is a modified version of the leslie gower and holling type ii scheme the main result is given in terms of local stability global stability influence of harvesting and bifurcation direction of hopf bifurcation and the stability of bifurcating periodic solutions are also studied by using the normal form method and center manifold theorem

optimal harvesting policy of a stochastic food chain population model this note studies the optimal harvesting policy of a stochastic three species food chain model the almost sufficient and necessary conditions for the existence of optimal harvesting policy are established meanwhile the optimal harvesting effort and the maximum of expectation of sustainable yield are obtained

existence of traveling wavefronts in a cooperative systems with discrete delays in this paper we consider an important lotka volterra model describing a two species cooperative system with diffusive and discrete delays and investigate the existence of traveling wavefronts by some mathematics tools including the monotone iteration technique as well as the upper and lower solution method the results obtained can be seen as a generalization of previous results

complex dynamics of a diffusive predator prey model with strong allee effect and threshold harvesting abstract in this paper complex dynamics of a diffusive predator prey model is investigated where the prey is subject to strong allee effect and threshold harvesting the existence and stability of nonnegative constant steady state solutions are discussed the existence and nonexistence of nonconstant positive steady state solutions are analyzed to identify the ranges of parameters of pattern formation spatially homogeneous and nonhomogeneous hopf bifurcation and discontinuous hopf bifurcation are proved these results show that the introduction of strong allee effect and threshold harvesting increases the system spatiotemporal complexity finally numerical simulations are presented to validate the theoretical results

diffusion has no influence on the global asymptotical stability of the lotka volterra prey predator model incorporating a constant number of prey refuges by constructing a suitable lyapunov function we obtain the global asymptotical stability of the lotka volterra prey predator model incorporating a constant number of prey refuges and diffusion it is shown that diffusion has no influence on the global asymptotical stability of the system with homogeneous neumann boundary condition

spreading speeds and traveling wavefronts for second order integrodifference equations this paper is concerned with the spreading speeds and traveling wavefronts for second order integrodifference equations by introducing an auxiliary integrodifference system the spreading speed is established for the integrodifference equation it is shown that the spreading speed coincides with the minimal wave speed for monotonic traveling wavefronts furthermore we prove that the traveling wavefronts are stable by applying the squeezing technique finally we analyze the different effects of the delay term appearing in the integrodifference equation from the viewpoint of ecology

exact quantification of the complexity of spacewise pattern growth in cellular automata we analyze the two possible ways of simulating complex systems with cellular automata by using the familiar timewise updating or by using the complementary spacewise updating both updating algorithms operate on identical sets of initial conditions defining the state of the automaton while timewise growth generally probes just vanishingly small sets of initial conditions producing statistical samples of the asymptotic attractors spacewise growth operates with much restricted sets which allow one to simulate them all exhaustively our main result is the derivation of an exact analytical formula to quantify precisely one of the two sources of algorithmic complexity of spacewise detection of the complete set of attractors for elementary 1d cellular automata with generic non periodic architectures of any arbitrary size the formula gives the total number of initial conditions that need to be investigated to locate rigorously all possible patterns for any given rule as simple applications we illustrate how this knowledge may be used i to uncover missing patterns in previous classifications in the literature and ii to obtain surprisingly novel patterns that are totally unreachable with the time honored technique of artificially imposing spatially periodic boundary conditions

positive periodic solutions in a non selective harvesting predator prey model with multiple delays abstract this paper is concerned with a predator prey model with hassell varley type functional response non selective harvesting and multiple delays some new sufficient conditions are obtained for the existence of positive periodic solutions by applying the coincidence degree theorem in addition the results are delay dependent which is different from the previous work finally simulations illustrate the effectiveness of our results

dynamics of generalist predator in a stochastic environment modified ratio dependent holling tanner model with prey refuge is considered delays are taken in logistic growth of prey as feedback mechanism and gestation period of predator model system exhibits hopf bifurcation when the delay parameters cross their critical values stochastic analysis of the model system is carried out by incorporating gaussian white noise using fourier transform technique fluctuation and stability of the stochastic model is studied in this paper an attempt has been made to understand the dynamics of a prey predator system with multiple time delays where the predator population is regarded as a generalist type in this regard we consider a modified holling tanner prey predator system where a constant time delay is incorporated in the logistic growth of the prey to represent a delayed density dependent feedback mechanism and the second time delay is considered to account for the length of the gestation period of the predator predator s interference in prey predator relationship provides better descriptions of predator s feeding over a range of prey predator abundances so the predator s functional response is considered to be type ii ratio dependent and foraging efficiency of predator largely varies with the refuge strategy of prey population in accordance with previous studies it is observed that delay destabilizes the system in general and stability loss occurs via hopf bifurcation in particular we show that there exists critical values of the delay parameters below which the coexistence equilibrium is stable and above which it is unstable hopf bifurcation occurs when the delay parameters cross their critical values also environmental stochasticity in the form of gaussian white noise plays a significant role to describe the system and its values numerical computation is also performed to validate and visualize different theoretical results presented the analysis and results in this work are interesting both in mathematical and biological point of views

traveling wavefronts in diffusive and cooperative lotka volterra system with delays existence of traveling wave front solutions is established for diffusive and cooperative lotka volterra system with delays the result is an extension of an existing result for delayed logistic scaler equation to systems and is somewhat parallel to the existing result for diffusive and competitive lotka volterra systems without delay the approach used in this paper is the upper lower solution technique and the monotone iteration recently developed by wu and zou j dynam differential equations 13 2001 651 687 for delayed reaction diffusion systems without the so called quasimonotonicity 2002 elsevier science usa all rights reserved

weighted fourier series representation and its application to quantifying the amount of gray matter we present a novel weighted fourier series wfs representation for cortical surfaces the wfs representation is a data smoothing technique that provides the explicit smooth functional estimation of unknown cortical boundary as a linear combination of basis functions the basic properties of the representation are investigated in connection with a self adjoint partial differential equation and the traditional spherical harmonic spharm representation to reduce steep computational requirements a new iterative residual fitting irf algorithm is developed its computational and numerical implementation issues are discussed in detail the computer codes are also available at http www stat wisc edu mchung softwares weighted spharm weighted spharm html as an illustration the wfs is applied in quantifying the amount of gray matter in a group of high functioning autistic subjects within the wfs framework cortical thickness and gray matter density are computed and compared

coexistence region and global dynamics of a harvested predator prey system the study of populational dynamics with harvesting is related to the optimal man agement of renewable resources in this paper we consider a predator prey model in which two ecologically interacting species are harvested independently with constant rates the main purpose of the present work is to offer a complete mathematical analysis for the model and to describe some of the significant qualitative results that may be expected to arise from the interplay of biological forces our study shows that the maximum safe harvest may be far less than what would be assumed from a local analysis for the equilibria it is also proved that the harvested predator prey system may exhibit very complicated dynamics such as a spontaneous appearance of a homoclinic orbit and multiple limit cycles

test retest repeatability of human speech biomarkers from static and real time dynamic magnetic resonance imaging static anatomical and real time dynamic magnetic resonance imaging rt mri of the upper airway is a valuable method for studying speech production in research and clinical settings the test retest repeatability of quantitative imaging biomarkers is an important parameter since it limits the effect sizes and intragroup differences that can be studied therefore this study aims to present a framework for determining the test retest repeatability of quantitative speech biomarkers from static mri and rt mri and apply the framework to healthy volunteers subjects n 8 4 females 4 males are imaged in two scans on the same day including static images and dynamic rt mri of speech tasks the inter study agreement is quantified using intraclass correlation coefficient icc and mean within subject standard deviation e inter study agreement is strong to very strong for static measures icc min median max 0 71 0 89 0 98 e 0 90 2 20 6 72 mm poor to strong for dynamic rt mri measures of articulator

existence and stability of traveling wave fronts in reaction advection diffusion equations with nonlocal delay this paper is concerned with the existence uniqueness and globally asymptotic stability of traveling wave fronts in the quasi monotone reaction advection diffusion equations with nonlocal delay under bistable assumption we construct various pairs of super and subsolutions and employ the comparison principle and the squeezing technique to prove that the equation has a unique nondecreasing traveling wave front up to translation which is monotonically increasing and globally asymptotically stable with phase shift the influence of advection on the propagation speed is also considered comparing with the previous results our results recovers and or improves a number of existing ones in particular these results can be applied to a reaction advection diffusion equation with nonlocal delayed effect and a diffusion population model with distributed maturation delay some new results are obtained

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

enhanced signal detection in neuroimaging by means of regional control of the global false discovery rate in the context of neuroimaging experiments it is essential to account for the multiple comparisons problem when thresholding statistical mappings various methods are in use to deal with this issue but they differ in their signal detection power for small and large scale effects in this paper we comprehensively describe a new method that is based on control of the false discovery rate fdr our method increases sensitivity by exploiting the spatially clustered nature of neuroimaging effects this is achieved by using a sliding window technique in which fdr control is first applied at a regional level thus a new statistical map that is related to the regionally achieved fdr is derived from the available voxelwise p values on the basis of receiver operating characteristic roc curves thresholding based on this map is demonstrated to have better discriminatory power than conventional thresholding based on p values secondly it is shown that the resulting maps can be thresholded at a level that results in control of the global fdr by means of statistical arguments and numerical simulations under widely varying conditions our method is validated characterized and compared to some other common voxel based methods uncorrected thresholding bonferroni correction and conventional fdr control it is found that our method shows considerably higher sensitivity as compared to conventional fdr control while still controlling the achieved fdr at the same level or better finally our method is applied to two diverse neuroimaging experiments to assess its practical merits resulting in substantial improvements as compared to the other methods

the influence of connectivity on the firing rate in a neuronal network with electrical and chemical synapses a b s t r a c t we study the firing rate properties of a cellular automaton model for a neuronal network with chemical synapses we propose a simple mechanism in which the nonlocal connections are included through electrical and chemical synapses in the latter case we introduce a time delay which produces self sustained activity nonlocal connections or shortcuts are randomly introduced according to a specified connection probability there is a range of connection probabilities for which neuron firing occurs as well as a critical probability for which the firing ceases in the absence of time delay the critical probability for nonlocal shortcuts depends on the network size according to a power law we also compute the firing rate amplification factor by varying both the connection probability and the time delay for different network sizes

analysis of predator prey models with continuous threshold harvesting abstract we formulate an alternative form of threshold harvesting and investigate its properties within the framework of a predator prey model our formulation accounts for economic constraints and is defined as a continuous harvesting function of the predator species theoretical and numerical analysis indicate that our formulation which we call continuous threshold policy ctp can help improve undesirable behavior of the predator prey ecosystem our study includes uniform boundedness of solutions stability of equilibria and periodic orbits bifurcations and heteroclinic orbits

controlling the false discovery rate a practical and powerful approach to multiple testing summary the common approach to the multiplicity problem calls for controlling the familywise error rate fwer this approach though has faults and we point out a few a different approach to problems of multiple significance testing is presented it calls for controlling the expected proportion of falsely rejected hypotheses the false discovery rate this error rate is equivalent to the fwer when all hypotheses are true but is smaller otherwise therefore in problems where the control of the false discovery rate rather than that of the fwer is desired there is potential for a gain in power a simple sequential bonferronitype procedure is proved to control the false discovery rate for independent test statistics and a simulation study shows that the gain in power is substantial the use of the new procedure and the appropriateness of the criterion are illustrated with examples

bifurcation branch of stationary solutions in a general predator prey system with prey taxis abstract in this paper a general reaction diffusive predator prey system with prey taxis subject to the homogeneous neumann boundary condition is considered firstly we investigate the local stability of the unique positive equilibrium by analyzing the characteristic equation and study a priori estimates of positive solutions by the iterative technique and then choosing the prey tactic sensitivity coefficient as bifurcation parameter we proved that a branch of nonconstant solutions can bifurcate from the unique positive equilibrium when the prey tactic sensitivity is repulsive moreover we find the stable bifurcating solutions near the bifurcation point by the spectrum theory under some suitable conditions our results show that prey taxis can destabilize the uniform equilibrium and yields the occurrence of spatial patterns

optimal denoising in redundant representations image denoising methods are often designed to minimize mean squared error mse within the subbands of a multiscale decomposition however most high quality denoising results have been obtained with overcomplete representations for which minimization of mse in the subband domain does not guarantee optimal mse performance in the image domain we prove that despite this suboptimality the expected image domain mse resulting from applying estimators to subbands that are made redundant through spatial replication of basis functions e g cycle spinning is always less than or equal to that resulting from applying the same estimators to the original nonredundant representation in addition we show that it is possible to further exploit overcompleteness by jointly optimizing the subband estimators for image domain mse we develop an extended version of stein s unbiased risk estimate sure that allows us to perform this optimization adaptively for each observed noisy image we demonstrate this methodology using a new class of estimator formed from linear combinations of localized ldquobumprdquo functions that are applied either pointwise or on local neighborhoods of subband coefficients we show through simulations that the performance of these estimators applied to overcomplete subbands and optimized for image domain mse is substantially better than that obtained when they are optimized within each subband this performance is in turn substantially better than that obtained when they are optimized for use on a nonredundant representation

critical traveling waves in a diffusive disease model abstract in this paper the existence of a non trivial positive and bounded critical traveling wave solution of a diffusive disease model whose reaction system has infinitely many equilibria is obtained for the first time this gives an affirmative answer to an open problem left in wang et al 2012 19 our result shows that the critical traveling wave in this model is a mix of front s component and pulse i component type

traveling waves for the diffusive nicholson s blowflies equation we consider traveling wave front solutions for the diffusive nicholson s blowflies equation on the real line the existence of such solutions is proved using the technique developed by j wu and x zou j dyn differ equations 13 3 2001 some numerical simulation using the iteration formula of wu and zou 7 is also provided

dynamics of prey threshold harvesting and refuge the dynamics of a predator prey model with continuous threshold prey harvesting and prey refuge is studied one central question is how harvesting and refuge could directly affect the dynamics of the ecosystem such as the stability properties of some coexistence equilibria and periodic solutions theoretical and numerical methods are used to investigate boundedness of solutions existence of bionomic equilibria as well as the existence and stability properties of equilibrium points and periodic solutions several bifurcations are also studied