dynamics of differential equations on invariant manifolds abstract the simplification resulting from reduction of dimension involved in the study of invariant manifolds of differential equations is often difficult to achieve in practice appropriate coordinate systems are difficult to find or are essentially local in nature thus complicating analysis of global dynamics this paper develops an approach which avoids the selection of coordinate systems on the manifold conditions are given in terms compound linear differential equations for the stability of equilibria and periodic orbits global results include criteria for the nonexistence of periodic orbits and a discussion of the nature of limit sets as an application a global stability criterion is established for the endemic equilibrium in an epidemiological model

matrices of 3 iet preserving morphisms we study matrices of morphisms preserving the family of words coding 3 interval exchange transformations it is well known that matrices of morphisms preserving sturmian words i e words coding 2 interval exchange transformations with the maximal possible factor complexity form the monoid m n 2 x 2 detm 1 m n 2 x 2 mem t e where e 01 10 we prove that in the case of exchange of three intervals the matrices preserving words coding these transformations and having the maximal possible subword complexity belong to the monoid m n 3 x 3 mem t e detm 1 where e 011 101 1 10

every ergodic transformation is disjoint from almost every interval exchange transformation we show that every transformation is disjoint from almost every interval exchange transformation iet answering a question of bufetov in particular we prove that almost every pair of iets is disjoint it follows that the product of almost every pair is uniquely ergodic a key step in the proof is showing that any sequence of density 1 contains a rigidity sequence for almost every iet strengthening a result of veech

on bendixson s criterion abstract for autonomous differential equations in r n criteria are developed which preclude the existence of invariant closed curves such as periodic or homoclinic trajectories the technique is based on the study of functionals on 2 surfaces results generalize to higher dimensions a criterion of bendixson for the nonexistence of nonconstant periodic solutions in the case n 2 as an example an application to the lorenz system in r 3 is given

complex dynamics of an seir epidemic model with saturated incidence rate and treatment abstract in this paper we describe the dynamics of an seir epidemic model with saturated incidence treatment function and optimal control rigorous mathematical results have been established for the model the stability analysis of the model is investigated and found that the model is locally asymptotically stable when r 0 1 the model is locally as well as globally asymptotically stable at endemic equilibrium when r 0 1 the proposed model may possess a backward bifurcation the optimal control problem is designed and obtained their necessary results numerical results have been presented for justification of theoretical results

geometric approach for global asymptotic stability of three dimensional lotka volterra systems abstract in this paper by applying the geometric criterion and time average property to lotka volterra systems some results for the global asymptotic stability of the systems are obtained furthermore we consider li wang conjecture for a three dimensional system which is transformed from a lotka volterra system

inheritance of oscillation in chemical reaction networks abstract some results are presented on how oscillation is inherited by chemical reaction networks crns when they are built in natural ways from smaller oscillatory networks the main results describe four important ways in which a crn can be enlarged while preserving its capacity for oscillation the results are for general crns not necessarily fully open but lead to an important corollary for fully open networks if a fully open crn r with mass action kinetics admits a nondegenerate resp linearly stable periodic orbit then so do all such crns which include r as an induced subnetwork this claim holds for other classes of kinetics but fails in general for crns which are not fully open where analogous results for multistationarity can be proved using the implicit function theorem alone the results here call on regular and singular perturbation theory equipped with these results and with the help of some analysis and numerical simulation lower bounds are put on the proportion of small fully open crns capable of stable oscillation under various assumptions on the kinetics this exploration suggests that small oscillatory motifs are an important source of oscillation in crns

synchronized hopf bifurcation analysis in a neural network model with delays we consider the synchronized periodic oscillation in a ring neural network model with two different delays in self connection and nearest neighbor coupling employing the center manifold theorem and normal form method introduced by hassard et al we give an algorithm for determining the hopf bifurcation properties using the global hopf bifurcation theorem for fde due to wu and bendixson s criterion for high dimensional ode due to li and muldowney we obtain several groups of conditions that guarantee the model have multiple synchronized periodic solutions when the transfer coefficient or time delay is sufficiently large

global stability of a stage structured epidemic model with a nonlinear incidence in this paper a stage structured epidemic model with a nonlinear incidence with a factor s p is investigated by using limit theory of differential equations and theorem of busenberg and van den driessche global dynamics of the model is rigorously established we prove that if the basic reproduction number r 0 is less than one the disease free equilibrium is globally asymptotically stable and the disease dies out if r 0 is greater than one then the disease persists and the unique endemic equilibrium is globally asymptotically stable numerical simulations support our analytical results and illustrate the effect of p on the dynamic behavior of the model

bifurcation analysis in a neutral differential equation the dynamics of a neural network model in neutral form is investigated we prove that a sequence of hopf bifurcations occurs at the origin as the delay increases the direction of the hopf bifurcations and the stability of the bifurcating periodic solutions are determined by using normal form method and center manifold theory global existence of periodic solutions is established using a global hopf bifurcation result of krawcewicz et al and a bendixson s criterion for higher dimensional ordinary differential equations due to li and muldowney

cocycles over interval exchange transformations and multivalued hamiltonian flows we consider interval exchange transformations of periodic type and construct different classes of recurrent ergodic cocycles of dimension geq 1 over this special class of iets then using poincare sections we apply this construction to obtain recurrence and ergodicity for some smooth flows on non compact manifolds which are extensions of multivalued hamiltonian flows on compact surfaces

global dynamics of nicholsonʼs blowflies equation revisited onset and termination of nonlinear oscillations abstract we revisit nicholson s blowflies model with natural death rate incorporated into the delay feedback we consider the delay as a bifurcation parameter and examine the onset and termination of hopf bifurcations of periodic solutions from a positive equilibrium we show that the model has only a finite number of hopf bifurcation values and we describe how branches of hopf bifurcations are paired so the existence of periodic solutions with specific oscillation frequencies occurs only in bounded delay intervals the bifurcation analysis and the matlab package dde biftool developed by engelborghs et al guide some numerical simulations to identify ranges of parameters for coexisting multiple attractive periodic solutions

topological mixing for some residual sets of interval exchange transformations we show that a residual set of non degenerate iets on more than 3 letters is topologically mixing this shows that there exists a uniquely ergodic topologically mixing iet this is then applied to show that some billiard flows in a fixed direction in an l shaped polygon are topologically mixing

global existence of periodic solutions in a tri neuron network model with delays we consider a delayed differential system that models a network of three neurons with memory using a global hopf bifurcation theorem for fde due to j wu and a bendixson s criterion for high dimensional ode due to li and muldowney we obtain a group of sufficient conditions for the system to have multiple periodic solutions when the sum of delays is sufficiently large

some examples describing the need of modifying the bendixson criterion for piecewise c1 systems abstract some numerical examples to clarify the use of distributions in ordinary differential equations with discontinuous right hand sides

a negative bendixson like criterion for a class of hybrid systems a condition which ensures the absence of periodic orbits for nonsmooth dynamical systems is presented the condition is a higher dimensional generalization of bendixson s criterion applicable to differential inclusions that are useful in the description of hybrid systems the main argument is based on contraction analysis of the d measured volume along the system trajectories a connection to methods for estimating the hausdorff dimension is emphasized for a class of hybrid systems described by a linear system with relay feedback the conditions are presented in the form of linear matrix inequalities a simple but illustrative example is analyzed

global dynamics of an seir epidemic model with vertical transmission we study a population model for an infectious disease that spreads in the host population through both horizontal and vertical transmission the total host population is assumed to have constant density and the incidence term is of the bilinear mass action form we prove that the global dynamics are completely determined by the basic reproduction number r0 p q where p and q are fractions of infected newborns from the exposed and infectious classes respectively if r 0 p q le 1 the disease free equilibrium is globally stable and the disease always dies out if r0 p q 1 a unique endemic equilibrium exists and is globally stable in the interior of the feasible region and the disease persists at an endemic equilibrium state if it initially exists the contribution of the vertical transmission to the basic reproduction number is also analyzed

fully automated detection of cerebral water content changes study of age and gender related h2o patterns with quantitative mri we present a simple and robust method for the automated image analysis of quantitative cerebral water content maps acquired with mri the method is based on a new approach for the absolute and quantitative mapping of water content in vivo water content maps were automatically segmented into grey and white matter by employing the quantitative t1 information acquired as part of the water content mapping procedure based on the segmented maps twenty two parameters sensitive to both absolute water content and its spatial organisation are automatically extracted without user interaction the parameters include amongst others absolute water content in grey and white matter and spatial asymmetries of the cerebral water content distribution significant age and gender related changes in the parameters determined were observed in a study of forty four healthy subjects most notably the grey matter water content decreases at a rate of 0 034 year for females between the 3rd and 8th decade of life whilst a much stronger decrease is observed in males which sets in after the 5th decade of life in addition female grey matter water content is on average 1 2 higher than the respective male grey matter water content in contrast to the heterogeneity observed in grey matter no significant physiological variation was observed for white matter water content in addition to absolute grey matter water content characteristic age and gender specific variations were also observed in most of the other variables to check the potential loss of information associated with the large reduction of the dimensionality of the dataset to 22 parameters only the age and gender of each individual subject were predicted by employing robust linear discriminant analysis based on only the determined twenty two variables the median deviation between predicted and real age was 6 3 years resulting in a high correlation coefficient between both values r 0 69 gender is correctly predicted in 68 2 of all cases which improves to 87 5 when age dependent effects are first corrected demonstrating the high information content present in the variables even though the dimension of the dataset was significantly reduced these results form the baseline for future studies of cerebral pathology the method presented is fully automated robust and flexible making it an ideal tool for routine application in both neuroscientific studies and clinical diagnosis based on the quantitative measurement of cerebral water content

flows without wandering points on compact connected surfaces given a compact 2 dimensional manifold m we classify all continuous flows without wandering points on m this classification is performed by finding finitely many pairwise disjoint open invariant subsets u 1 u 2 u n of m such that n i 1 u i m and each u i is either a suspension of an interval exchange transformation or a maximal open cylinder made up of closed trajectories of

from rational billiards to dynamics on moduli spaces this short expository note gives an elementary introduction to the study of dynamics on certain moduli spaces and in particular the recent breakthrough result of eskin mirzakhani and mohammadi we also discuss the context and applications of this result and connections to other areas of mathematics such as algebraic geometry teichmuller theory and ergodic theory on

on conditions for regularity of solutions for a piecewise linear system abstract we study a piecewise linear system approximating the behaviour of a switched dc dc converter we give conditions for a unique limit cycle in our different cases and give examples of complicated phenomena that might occur the stability of a state space trajectory controlled converter is addressed

obtaining certificates for complete synchronisation of coupled oscillators abstract in this paper we provide a novel reformulation of sufficient conditions that guarantee global complete synchronisation of coupled identical oscillators to make them computationally implementable to this end we use semidefinite programming techniques for the first time we can efficiently search for and obtain certificates for synchronisability and additionally also optimise associated cost functions in this paper a lyapunov like function certificate is used to certify that all trajectories of a networked system consisting of coupled dynamical systems will eventually converge towards a common one which implies synchronisation moreover we establish new conditions for complete synchronisation which are based on the so called bendixson s criterion for higher dimensional systems this leads to major improvements on the lower bound of the coupling constant that guarantees global complete synchronisation importantly the certificates are obtained by analysing the connection network and the model representing an individual system only in order to illustrate the strength of our method we apply it to a system of coupled identical lorenz oscillators and to coupled van der pol oscillators

weak mixing directions in non arithmetic veech surfaces we show that the billiard in a regular polygon is weak mixing in almost every invariant surface except in the trivial cases which give rise to lattices in the plane triangle square and hexagon more generally we study the problem of prevalence of weak mixing for the directional flow in an arbitrary non arithmetic veech surface and show that the hausdorff dimension of the set of non weak mixing directions is not full we also provide a necessary condition verified for instance by the veech surface corresponding to the billiard in the pentagon for the set of non weak mixing directions to have positive hausdorff dimension

mathematical modeling of tumor immune competitive system considering the role of time delay abstract in this paper we consider a three dimensional nonlinear delay differential system tumor cells cytotoxic t lymphocytes t helper cells with single interaction delay we perform linear stability of the equilibria and the existence of hopf bifurcation in which the discrete time delay is used as a bifurcation parameter we estimate the length of delay to preserve the stability of period 1 limit cycle we also investigate the direction period and the stability of bifurcated periodic solutions by applying normal form method and center manifold theory we observe that the discrete time delay plays an important role in stability switching numerical simulations are presented to illustrate the rich dynamical behavior of the model with different values for the time delay including the existence of periodic oscillations which demonstrate the phenomena of long term tumor relapse

stability and bifurcation in plant pathogens interactions we consider a plant pathogen interaction model and perform a bifurcation analysis at the threshold where the pathogen free equilibrium loses its hyperbolicity we show that a stimulatory inhibitory host response to infection load may be responsible for the occurrence of multiple steady states via backward bifurcations we also find sufficient conditions for the global stability of the pathogen present equilibrium in case of null or linear inhibitory host response the results are discussed in the framework of the recent literature on the subject

equivalent embeddings of the dynamics on an invariant manifold a dynamical system admitting an invariant manifold can be interpreted as a single element of an infinite class of dynamical systems that all exhibit the same behaviour on the invariant manifold this observation is used in the context of autonomous ordinary differential equations to generalize a global stability result of li and muldowney the new result is demonstrated on an epidemiological model

on the use of the geometric approach to global stability for three dimensional ode systems a bilinear case abstract in this paper we consider a general bilinear three dimensional ode system whose structure generalizes many mathematical models of biological interest including many from epidemics our main goal is to find sufficient conditions expressed in terms of the parameters of the system ensuring that the geometric approach to global stability analysis due to m y li j s muldowney a geometric approach to global stability problems siam j math anal 27 4 1996 1070 1083 may be successfully applied we completely determine the dynamics of the general system including thresholds and global stability of the nontrivial equilibrium the obtained result is applied to several epidemic models we further show how the role of new parameters on stability of well established models may be emphasized

dynamical behavior of a vector host epidemic model with demographic structure in the paper we propose a model that tracks the dynamics of many diseases spread by vectors such as malaria dengue or west nile virus all spread by mosquitoes our model incorporates demographic structure with variable population size which is described by nonlinear birth rate and linear death rate the stability of the system is analyzed for the existence of the disease free and endemic equilibria points we find the basic reproduction number r 0 in terms of measurable epidemiological and demographic parameters is the threshold condition that determines the dynamics of disease infection if r 0 1 the disease remains endemic the threshold condition provides important guidelines for accessing control of the vector diseases and implies that it is an efficient way to halt the spread of vector epidemic by reducing the carrying capacity of the environment for the vector and the host moreover sufficient conditions are also obtained for the global stability of the unique endemic equilibrium e

dynamic model of worms with vertical transmission in computer network an e epidemic seirs model for the transmission of worms in computer network through vertical transmission is formulated it has been observed that if the basic reproduction number is less than or equal to one the infected part of the nodes disappear and the worm dies out but if the basic reproduction number is greater than one the infected nodes exists and the worms persist at an endemic equilibrium state numerical methods are employed to solve and simulate the system of equations developed we have analyzed the behavior of the susceptible exposed infected and recovered nodes in the computer network with real parametric values

an algorithm to identify automorphisms which arise from self induced interval exchange transformations we give an algorithm to determine if the dynamical system generated by a positive automorphism of the free group can also be generated by a self induced interval exchange transformation the algorithm effectively yields the interval exchange transformation in case of success

quantisations of piecewise parabolic maps on the torus and their quantum limits for general quantum systems the semiclassical behaviour of eigenfunctions in relation to the ergodic properties of the underlying classical system is quite difficult to understand the wignerfunctions of eigenstates converge weakly to invariant measures of the classical system the so called quantum limits and one would like to understand which invariant measures can occur that way thereby classifying the semiclassical behaviour of eigenfunctions

three dimensional competitive lotka volterra systems with no periodic orbits the following conjecture of m l zeeman is proved if three interacting species modeled by a competitive lotka volterra system can each resist invasion at carrying capacity then there can be no coexistence of the species indeed two of the species are driven to extinction it is also proved that in the other extreme if none of the species can resist invasion from either of the others then there is stable coexistence of at least two of the species in this case if the system has a fixed point in the interior of the positive cone in r3 then that fixed point is globally asymptotically stable representing stable coexistence of all three species otherwise there is a globally asymptotically stable fixed point in one of the coordinate planes of r3 representing stable coexistence of two of the species

bifurcation analysis of a population model and the resulting sis epidemic model with delay this paper deals with the model for matured population growth proposed in cooke et al interaction of matiration delay and nonlinear birth in population and epidemic models j math biol 39 1999 332 352 and the resulting sis epidemic model the dynamics of these two models are still largely undetermined and in this paper we perform some bifurcation analysis to the models by applying the global bifurcation theory for functional differential equations we are able to show that the population model allows multiple periodic solutions for the sis model we obtain some local bifurcation results and derive formulas for determining the bifurcation direction and the stability of the bifurcated periodic solution

deviation of ergodic averages for substitution dynamical systems with eigenvalues of modulus 1 deviation of ergodic sums is studied for substitution dynamical systems with a matrix that admits eigenvalues of mod ulus 1 the functions we consider are the corresponding eigen functions in theorem 1 1 we prove that the limit inferior of the ergodic sums n x 0 x n 1 n n is bounded for every point x in the phase space in theorem 1 2 we prove existence of limit distributions along certain exponential subsequences of times for substitutions of constant length under additional assumptions we prove that ergodic integrals satisfy the central limit theorem theorem 1 3 theorem 1 9

global stability for a class of mass action systems allowing for latency in tuberculosis a very general compartmental model of the spread of an infectious disease with mass action incidence is given the global stability of this system is completely determined using lyapunov functions the general system exhibits the traditional threshold behaviour the dimension of the system is arbitrary allowing in particular for detailed modelling of the distribution of latency times for tuberculosis

hodge teichmuller planes and finiteness results for teichmuller curves we prove that there are only finitely many algebraically primitive teichmuller curves in the minimal stratum in each prime genus at least 3 the proof is based on the study of certain special planes in the first cohomology of a translation surface which we call hodge teichmuller planes we also show that algebraically primitive teichmuller curves are not dense in any connected component of any stratum in genus at least 3 the closure of the union of all such curves in a fixed stratum is equal to a finite union of affine invariant submanifolds with unlikely properties results of this type hold even without the assumption of algebraic primitivity combined with work of nguyen and the second author a corollary of our results is that there are at most finitely many nonarithmetic teichmuller curves in h 4

global stability for an hiv 1 infection model including an eclipse stage of infected cells abstract we consider the mathematical model for the viral dynamics of hiv 1 introduced in rong et al 2007 37 one main feature of this model is that an eclipse stage for the infected cells is included and cells in this stage may revert to the uninfected class the viral dynamics is described by four nonlinear ordinary differential equations in rong et al 2007 37 the stability of the infected equilibrium has been analyzed locally here we perform the global stability analysis using two techniques the lyapunov direct method and the geometric approach to stability based on the higher order generalization of bendixson s criterion we obtain sufficient conditions written in terms of the system parameters numerical simulations are also provided to give a more complete representation of the system dynamics

dulac criteria for autonomous systems having an invariant affine manifold abstract for a class of higher dimensional autonomous systems that have an invariant affine manifold conditions are derived to preclude the existence of periodic solutions on the invariant manifold it is established that these conditions are robust under certain types of local perturbations of the vector field as a consequence each bounded semitrajectory on the invariant manifold is shown to converge to a single equilibrium using a c 1 closing lemma for this class applications to autonomous systems that are homogeneous of degree 1 are also considered

new proof and generalizations of the demidowitsch schneider criterion a new proof of the demidowitsch schneider criterion on the absence of closed trajectories of r3 is given the new proof is generalized and applied in several directions rn vector fields n 3

energy functions on moduli spaces of flat surfaces with erasing forest this paper follows on from nguyen geom funct anal 20 1 192 228 2010 in which we study flat surfaces with erasing forest these surfaces are obtained by deforming the metric structure of translation surfaces and their moduli space can be viewed as a deformation of the moduli space of translation surfaces we showed that the moduli spaces of such surfaces are complex orbifolds and admit a natural volume form tr the aim of this paper is to show that the volume of those moduli spaces with respect to tr normalized by some energy function involving the area and the total length of the erasing forest is finite note that translation surfaces and flat surfaces of genus zero can be viewed as special cases of flat surfaces with erasing forest and on their moduli space the volume form tr equals the usual ones up to a multiplicative constant using this result we obtain new proofs for some classical results due to masur veech and thurston concerning the finiteness of the volume of the moduli space of translation sufaces and of the moduli space of polyhedral flat surfaces

complex dynamics in a delay differential equation with two delays in tick growth with diapause abstract we consider a delay differential equation for tick population with diapause derived from an age structured population model with two time lags due to normal and diapause mediated development we derive threshold conditions for the global asymptotic stability of biologically important equilibria and give a general geometric criterion for the appearance of hopf bifurcations in the delay differential system with delay dependent parameters by choosing the normal development time delay as a bifurcation parameter we analyze the stability switches of the positive equilibrium and examine the onset and termination of hopf bifurcations of periodic solutions from the positive equilibrium under some technical conditions we show that global hopf branches are bounded and connected by a pair of hopf bifurcation values this allows us to show that diapause can lead to the occurrence of multiple stability switches coexistence of two stable limit cycles among other rich dynamical behaviours

quantitative water content mapping at clinically relevant field strengths a comparative study at 1 5 t and 3 t abstract purpose quantitative water content mapping in vivo using mri is a very valuable technique to detect monitor and understand diseases of the brain at 1 5 t this technology has already been successfully used but it has only recently been applied at 3 t because of significantly increased rf field inhomogeneity at the higher field strength to validate the technology at 3 t we estimate and compare in vivo quantitative water content maps at 1 5 t and 3 t obtained with a protocol proposed recently for 3 t mri methods the proposed mri protocol was applied on twenty healthy subjects at 1 5 t and 3 t the same post processing algorithms were used to estimate the water content maps the 1 5 t and 3 t maps were subsequently aligned and compared on a voxel by voxel basis statistical analysis was performed to detect possible differences between the estimated 1 5 t and 3 t water maps results our analysis indicates that the water content values obtained at 1 5 t and 3 t did not show significant systematic differences on average the difference did not exceed the standard deviation of the water content at 1 5 t furthermore the contrast to noise ratio cnr of the estimated water content map was increased at 3 t by a factor of at least 1 5 conclusions vulnerability to rf inhomogeneity increases dramatically with the increasing static magnetic field strength however using advanced corrections for the sensitivity profile of the mr coils it is possible to preserve quantitative accuracy while benefiting from the increased cnr at the higher field strength indeed there was no significant difference in the water content values obtained in the brain at 1 5 t and 3 t

geometric approach for global asymptotic stability for three species competitive gompertz models abstract this paper deals with the three dimensional competitive models with gompertz growth in population dynamics by using the geometric criterion and time average property to gompertz models a new criterion on the global asymptotical stability of the models is established furthermore based on this criterion a partial affirmative answer to jiang niu zhu s open problems is given

global stability and periodicity on sis epidemic models with backward bifurcation in this paper we study sis epidemic models with the vaccine efficacy and waning first continuous vaccination to both newborns and susceptible individuals is considered in this case a backward bifurcation leading to bistability possibly occurs and global dynamics are shown by compound matrices and geometric approaches second we consider the impulsive vaccination to susceptible individuals which is more realistic the global stability of positive periodic infection free solution is proved further by bifurcation theory we obtain a supercritical bifurcation at the threshold for the period of pulsing lastly we change constant incidence rate to a general periodic contact rate due to seasonal variation besides the global stability of disease free equilibrium we also show the existence of positive periodic solution with the help of the continuation theorem based on coincidence degree

on codings and dynamics of planar piecewise rotations abstract in this paper we investigate codings and dynamics of the piecewise rotations belonging to a sub class of piecewise isometries we show that the irrational set is empty for some piecewise rational rotations under some assumptions while a piecewise irrational rotation has at least one irrational coding by extending the definition of the coding map onto the entire phase space we further prove that the cell corresponding to irrational coding is a single point set for a piecewise irrational rotation

weak mixing for interval exchange transformations and translation flows we prove that a typical interval exchange transformation is either weakly mixing or it is an irrational rotation we also conclude that a typical translation flow on a typical translation surface of genus g 2 with prescribed singularity types is weakly mixing

generic continuous spectrum for ergodic schrodinger operators we consider families of discrete schrodinger operators on the line with potentials generated by a homeomorphism on a compact metric space and a continuous sampling function we introduce the concepts of topological and metric repetition property assuming that the underlying dynamical system satisfies one of these repetition properties we show using gordon s lemma that for a generic continuous sampling function the set of elements in the associated family of schrodinger operators that have no eigenvalues is large in a topological or metric sense respectively we present a number of applications particularly to shifts and skew shifts on the torus

painleve formulas of the limiting distributions for nonnull complex sample covariance matrices in a recent study of large non null sample covariance matrices a new sequence of functions gener alizing the gue tracy widom distribution of random matrix theory was obtained this paper derives painleve formulas of these functions and use them to prove that they are indeed distribution functions applications of these new distribution functions to last passage percolation queues in tandem and to tally asymmetric simple exclusion process are also discussed as a part of the proof a representation of orthogonal polynomials on the unit circle in terms of an operator on a discrete set is presented

global results for an epidemic model with vaccination that exhibits backward bifurcation vaccination of both newborns and susceptibles is included in a transmission model for a disease that confers immunity the interplay of the vaccination strategy together with the vaccine efficacy and waning is studied in particular it is shown that a backward bifurcation leading to bistability can occur under mild parameter constraints compound matrices are used to show that each orbit limits to an equilibrium in the case of bistability this global result requires a novel approach since there is no compact absorbing set

hausdorff dimension bounds for smoothness of holonomies for codimension 1 hyperbolic dynamics we prove that the stable holonomies of a proper codimension 1 attractor lambda for a c r diffeomorphism f of a surface are not c1 theta for theta greater than the hausdorff dimension of the stable leaves of f intersected with lambda to prove this result we show that there are no diffeomorphisms of surfaces with a proper codimension 1 attractor that are affine on a neighbourhood of the attractor and have affine stable holonomies on the attractor

ergodic properties of infinite extensions of area preserving flows we consider volume preserving flows phi f t t in mathbb r on s times mathbb r where s is a compact connected surface of genus g 2 and phi f t t in mathbb r has the form phi f t x y phi t x y int 0 t f phi s x ds where phi t t in mathbb r is a locally hamiltonian flow of hyperbolic periodic type on s and f is a smooth real valued function on s we investigate ergodic properties of these infinite measure preserving flows and prove that if f belongs to a space of finite codimension in fancyscript c 2 epsilon s then the following dynamical dichotomy holds if there is a fixed point of phi t t in mathbb r on which f does not vanish then phi f t t in mathbb r is ergodic otherwise if f vanishes on all fixed points it is reducible i e isomorphic to the trivial extension phi 0 t t in mathbb r the proof of this result exploits the reduction of phi f t t in mathbb r to a skew product automorphism over an interval exchange transformation of periodic type if there is a fixed point of phi t t in mathbb r on which f does not vanish the reduction yields cocycles with symmetric logarithmic singularities for which we prove ergodicity

the cohomological equation for roth type interval exchange maps 0 introduction 0 1 interval exchange maps 0 2 the cohomological equation 0 3 summary of the contents 1 the continued fraction algorithm for interval exchange maps 1 1 interval exchange maps 1 2 the continued fraction algorithm 1 3 roth type interval exchange maps 2 the cohomological equation 2 1 the theorem of gottschalk and hedlund 2 2 special birkhoff sums 2 3 estimates for functions of bounded variation 2 4 primitives of functions of bounded variation 3 suspensions of interval exchange maps 3 1 suspension data 3 2 construction of a riemann surface 3 3 compactification of m 3 4 the cohomological equation for higher smoothness 4 proof of full measure for roth type 4 1 the basic operation of the algorithm for suspensions 4 2 the teichmuller flow 4 3 the absolutely continuous invariant measure 4 4 integrability of log z 1 4 5 conditions b and c have full measure 4 6 the main step 4 7 condition a has full measure 4 8 proof of the proposition appendix a roth type conditions in a concrete family of interval exchange maps appendix b a nonuniquely ergodic interval exchange map satisfying condition a

investigation of the spatial correlation in human white matter and the influence of age using 3 dimensional variography applied to mp rage data abstract a novel method for the quantification of heterogeneity and spatial correlation in 3d mp rage images of white matter is presented the technique is based on the variogram a tool commonly used in geosciences for the analysis of spatial data and was tailored to the special requirements of mr image analysis influences from intensity non uniformities noise and arbitrary greyscale were quantified and considered in the calculations the obtained variograms were fitted with spherical model functions to infer parameters that quantify heterogeneity and size of the correlation structures of the tissue numerically generated samples with well defined correlation properties were employed to validate the estimation process and to provide an interpretation of the parameters obtained it is shown that the method gives reliable results in an interval of correlation structures sized between 2 mm and 20 mm the method was applied to 24 mp rage datasets of healthy female volunteers ranging in age from 19 to 73 years white matter was found to have two prominent correlation structures with sizes of approximately 3 mm and 23 mm the heterogeneity of the smaller structure increases significantly with age r 0 83 p 6

stability bifurcation and global existence of a hopf bifurcating periodic solution for a class of three neuron delayed network models in this paper a system of three delay differential equations representing a hopfield type general model for three neurons with two way bidirectional time delayed connections between the neurons and time delayed self connection from each neuron to itself is studied delay independent and delay dependent sufficient conditions for linear stability instability and the occurrence of a hopf bifurcation about the trivial equilibrium are addressed the partition of the resulting parametric space into regions of stability instability and hopf bifurcation in the absence of self connection is realized to extend the local hopf branches for large delay values a particular bidirectional delayed tri neuron model without self connection is investigated sufficient conditions for global existence of multiple non constant periodic solutions are obtained for such a model using the global hopf bifurcation theorem for functional differential equations due to j wu and the bendixson criterion for higher dimensional ordinary differential equations due to li and muldowney and following the approach developed by wei and li

limit theorems for translation flows the aim of this paper is to obtain an asymptotic expansion for ergodic integrals of translation flows on flat surfaces of higher genus theorem 1 and to give a limit theorem for these flows theorem 2

a differential lyapunov framework for contraction analysis lyapunov s second theorem is an essential tool for stability analysis of differential equations the paper provides an analog theorem for incremental stability analysis by lifting the lyapunov function to the tangent bundle the lyapunov function endows the state space with a finsler structure incremental stability is inferred from infinitesimal contraction of the finsler metrics through integration along solutions curves

existence of periodic orbits for high dimensional autonomous systems abstract we give a result on existence of periodic orbits for autonomous differential systems with arbitrary finite dimension it is based on a poincare bendixson property enjoyed by a new class of monotone systems introduced in l a sanchez cones of rank 2 and the poincare bendixson property for a new class of monotone systems j differential equations 216 2009 1170 1190 a concrete application is done to a scalar differential equation of order 4

holder regularity of the solutions of the cohomological equation for roth type interval exchange maps we prove that the solutions of the cohomological equation for roth type interval exchange maps are holder continuous provided that the datum is of class c r with r 1 and belongs to a finite codimension linear subspace

on spectral disjointness of powers for rank one transformations and mobius orthogonality abstract we study the spectral disjointness of the powers of a rank one transformation for a large class of rank one constructions including those for which the cutting and stacking parameters are bounded and other examples such as rigid generalized chacon s maps and katok s map we prove that different positive powers of the transformation are pairwise spectrally disjoint on the continuous part of the spectrum our proof involves the existence in the weak closure of u t k k z of sufficiently many analytic functions of the operator u t then we apply these disjointness results to prove sarnak s conjecture for the possibly non uniquely ergodic symbolic models associated to these rank one constructions all sequences realized in these models are orthogonal to the mobius function

criteria on the nonexistence of invariant lipschitz submanifolds for dynamical systems abstract conditions are given for smooth finite dimensional mappings which are precluding the existence of invariant lipschitz compact submanifolds for those mappings flows their discretizations and their averagings are studied as well mappings and flows with constraints are also investigated

linearization of generalized interval exchange maps a standard interval exchange map is a one to one map of the interval that is locally a translation except at nitely many singularities we dene for such maps in terms of the rauzy veech continuous fraction algorithm a diophantine arithmetical condition called restricted roth type which is almost surely satised in parameter space let t0 be a standard interval exchange map of restricted roth type and let r be an integer 2 we prove that amongst c r 3 deformations of t0 that are c r 3 tangent to t0 at the singularities those that are conjugated to t0 by a c r dieomorphism close to the identity form a c 1 submanifold of codimension g 1 2r 1 s here g is the genus and s is the number of marked points of the translation surface obtained by suspension of t0 both g and s can be computed from the combinatorics of t0

hopf bifurcation analysis in a delayed nicholson blowflies equation abstract the dynamics of a nicholson s blowflies equation with a finite delay are investigated we prove that a sequence of hopf bifurcations occur at the positive equilibrium as the delay increases explicit algorithm for determining the direction of the hopf bifurcations and the stability of the bifurcating periodic solutions are derived using the theory of normal form and center manifold global existence of periodic solutions are established using a global hopf bifurcation result of wu trans amer math soc 350 1998 4799 and a bendixson criterion for higher dimensional ordinary differential equations due to li and muldowney j differential equations 106 1994 27