on the critical periods of perturbed isochronous centers abstract consider a family of planar systems x x x e having a center at the origin and assume that for e 0 they have an isochronous center firstly we give an explicit formula for the first order term in e of the derivative of the period function we apply this formula to prove that up to first order in e at most one critical period bifurcates from the periodic orbits of isochronous quadratic systems when we perturb them inside the class of quadratic reversible centers moreover necessary and sufficient conditions for the existence of this critical period are explicitly given from the tools developed in this paper we also provide a new characterization of planar isochronous centers

quadratic systems with center and their perturbations abstract we study the quadratic systems on a plane z i z az2 b z 2 cz2 z x iy we give a simple algebraic proof of the center conditions 0 and b 0 or a 1 2 b 1 or a b 1 c c or a 2 b 1 c 1 and of the theorem of bautin that the number of small amplitude limit cycles bifurcating from a center or a focus is not greater than 3 we present the bifurcational diagrams and phase portraits of the systems with center and describe the cyclicity precisely in each case here one mistake in bautin s work is revealed and some questions concerning focus numbers are answered we study also global not small limit cycles for a small perturbation of the center case with two invariant lines the lotka volterra system using abelian integrals we show that the number of zeroes of the corresponding abelian integral is 0 1 or 2 some attention is devoted to the problem of limit cycles for a small perturbation of a system with a two fold center when two center conditions hold the problem turns out to be equivalent to the problem of zeroes of some integral with polynomial coefficients

the monotonicity of the period function for planar hamiltonian vector fields if the hamiltonian system with hamiltonian h x y 12y2 v x has a center at the origin it is shown that the period function for the family of periodic trajectories surrounding the center is monotone when the function v v 2 is convex this theorem is applied to determine existence and uniqueness of solutions for the neumann boundary value problem x a x 2 bx c x 0 x 1 0

the bfgs algorithm for a nonlinear least squares problem arising from blood flow in arteries using the arbitrary lagrangian eulerian coordinates and the least squares method a two dimensional steady fluid structure interaction problem is transformed in an optimal control problem sensitivity analysis is presented the bfgs algorithm gives satisfactory numerical results even when we use a reduced number of discrete controls

a stable time advancing scheme for solving fluid structure interaction problem at small structural displacements a semi implicit time advancing scheme for transient fluid structure interaction problem is presented at every time step a least squares problem is solved by partitioned procedures such that the continuity of the velocity as well as the continuity of the stress hold at the interface during the iterative method for solving the optimization problem the fluid mesh does not move which reduces the computational effort the stability of the algorithm is derived the numerical results presented in this paper show that the computed solution is similar to the one obtained by the implicit algorithm but the computational time is reduced

a class of hamiltonian systems with increasing periods on considere un systeme hamiltonien de la forme x g y y f x ou h f et h g satisfont certaines hypotheses on montre qu il y a un intervalle maximal 0 a a 0 tel que chaque solution x t y t avec x 0 a 0 a y 0 0 est periodique avec son orbite enfermant 0 0 soit p a la plus petite periode de cette solution alors p 0 a r est differentiable avec p a 0

bifurcation of critical periods from the reversible rigidly isochronous centers abstract in this paper we study bifurcation of critical periods by perturbing a nonlinear vector field containing m th degree homogeneous terms with a rigidly isochronous center at the origin first we give expressions of period bifurcation functions in the form of integrals and then study the number of critical periods for cases of m 1 2 3 respectively

on a multicommodity stochastic flow network with unreliable nodes subject to budget constraint from the quality management and decision making view point reliability and unreliability are important indices to measure the quality level for a stochastic flow network in a multicommodity stochastic flow network with unreliable nodes the branches and nodes all have several possible capacities and may fail different types of the commodity which are transmitted through the same network simultaneously compete the capacities of branches and nodes in this paper we first define the system capacity as a vector for a multicommodity stochastic flow network with unreliable nodes then we design a performance index which is the probability that the upper bound of the system capacity is a given pattern subject to the budget constraint it can be applied to evaluate the quality level for such a network a simple approach based on minimal cuts is thus presented to evaluate the performance index

period function for a class of hamiltonian systems abstract this paper studies the period function of the class of hamiltonian systems x h y y h x where h x y has the special form h x y f x g y and the origin is a non degenerate center more concretely if t h denotes the period of the periodic orbit contained in h x y h we solve the inverse problem of characterizing all systems with a given function t h we also characterize the limiting behaviour of t at infinity when the origin is a global center and apply this result to prove among other results that there are no nonlinear polynomial isochronous centers in this family

delay dependent stability for uncertain stochastic neural networks with time varying delay abstract this paper is concerned with the robust stability analysis problem for uncertain stochastic neural networks with time varying delay the parameter uncertainties are assumed to be norm bounded by defining a new lyapunov krasovskii functional the restrictions such as the time varying delay was required to be differentiable and its derivative was strictly smaller than one are removed based on the linear matrix inequality approach delay dependent stability criteria are obtained such that for all admissible uncertainties the stochastic neural network is globally asymptotically stable in the mean square two slack variables are introduced into the obtained stability criteria to reduce the conservatism finally a numerical example is given to illustrate the effectiveness of the developed method

a rotated multiplier applied to the controllability of waves elasticity and tangential stokes control a new family of multipliers with rotated direction is introduced this technique is applied to obtain new results concerning controllability of waves elasticity and stokes equations the boundary exact controllability for the wave equation and the dynamic elasticity system is reviewed generalizing the classical exit condition in the case of explicit observability constants approximate controllability for the stokes system is also studied using a boundary control acting only on the tangential component of the velocity a geometric sufficient condition of exit generalized type is deduced

limit cycles appearing from the perturbation of a system with a multiple line of critical points abstract consider planar ordinary differential equations of the form x y c x y y x c x y where c x y is an algebraic curve we are interested in knowing whether the existence of multiple factors for c is important or not when we study the maximum number of zeros of the abelian integral m that controls the limit cycles that bifurcate from the period annulus of the origin when we perturb it with an arbitrary polynomial vector field with this aim we study in detail the case c x y 1 y m where m is a positive integer number and prove that m has essentially no impact on the number of zeros of m this result improves the known studies on m one of the key points of our approach is that we obtain a simple expression of m based on some successive reductions of the integrals appearing during the procedure

a reduced basis model with parametric coupling for fluid structure interaction problems we present a new model reduction technique for steady fluid structure interaction problems when the fluid domain deformation is suitably parametrized the coupling conditions between the fluid and the structure can be formulated in the low dimensional space of geometric parameters moreover we apply the reduced basis method to reduce the cost of repeated fluid solutions necessary to achieve convergence of fluid structure iterations in this way a reduced order model with reliable a posteriori error bounds is obtained the proposed method is validated with an example of steady stokes flow in an axisymmetric channel where the structure is described by a simple one dimensional generalized string model we demonstrate rapid convergence of the reduced solution of the parametrically coupled problem as the number of geometric parameters is increased

geometric methods for two point nonlinear boundary value problems on considere une classe d equations differentielles de la forme x f x g x avec des conditions aux limites soit de dirichlet soit de neumann on etudie l existence de la solution triviale

the monotonicity of period function for codimension four quadratic system q4 abstract in this paper we study the codimension four quadratic system q 4 z iz 4 z 2 2 z 2 b ic z 2 where b and c are real constants i 2 1 z x iy b ic 2 it is proved that the period function of periodic trajectories for q 4 is monotone the content of this paper can be viewed as a contribution to the proof of chicone s conjecture cf mr 94h 58072

fluid structure interaction with large structural displacements the calculation of viscous flows inside deformable structures faces major difficulties when enforcing the kinematic compatibility at the fluid structure interface and updating the geometry of the domain this paper proposes to overcome these problems by considering the fluid and the structure as a unique continuous medium to be studied in a fixed reference configuration the resulting problem is then split into a fluid and a structural part through an additive decomposition of the space of kinematically admissible test functions this approach treats the structure in a fully lagrangian way and uses an associated arbitrary lagrangian eulerian ale formulation for the fluid such a strategy has three advantages which are detailed in the present paper it can be discretised in time by implicit stable energy conserving time integration schemes and solved by simple iterative uncoupled algorithms the fluid and the structural problems can be approximated by independent finite element spaces the most recent geometrically exact nonlinear shell models can be used for the structures the full strategy has been implemented into an industrial cfd code results obtained in the simulation of industrial hydraulic shock absorbers are presented at the end of the paper

internet packet routing application of a k quickest path algorithm this paper describes a study on the application of an algorithm to rank the k quickest paths to the routing of data packets in internet networks for this purpose an experimental framework was developed by considering two types of random generated networks to simulate values of the ip packet sizes a truncated pareto distribution was defined having in mind to reflect a key feature of internet traffic namely its self similar stochastic nature results concerning the average cpu times of the algorithm for the different sets of experiments will be presented and discussed

global bifurcation of steady state solutions in this paper we study the bifurcation of steady state solutions of a reaction diffusion equation in one space variable the steady state solutions satisfy the equation a f u 0 on the interval l 0 or 0 for some nonzero function c c a for the neumann problem we use entirely different techniques to prove that s is never critical for any cubic polynomial j this implies at once that the neumann problem can have at most one nonconstant solution having a given number of maxima or minima this solution is necessarily strongly nondegenerate in the sense that zero is not contained in the spectrum of the linearized operator see 2 for the dirichlet problem the situation is far more complicated and the bifurcation diagrams undergo qualitative changes depending on the positions of the roots off for example fig 1 shows the bifurcation diagram for the positive solutions for two different cubic functions of the form f u a u u b u c it is interesting to note however that in every case we study there are at most three solutions to the dirichlet problem for each

critical periods of perturbations of reversible rigidly isochronous centers abstract in this paper we discuss bifurcation of critical periods in an m th degree time reversible system which is a perturbation of an n th degree homogeneous vector field with a rigidly isochronous center at the origin we present period bifurcation functions as integrals of analytic functions which depend on perturbation coefficients and reduce the problem of critical periods to finding zeros of a judging function this procedure gives not only the number of critical periods bifurcating from the period annulus but also the location of these critical periods applying our procedure to the case n m 2 we determine the maximum number of critical periods and their location to the case n m 3 we investigate the bifurcation of critical periods up to the first order in e and obtain the expression of the second period bifurcation function when the first one vanishes

on the number of critical periods for planar polynomial systems abstract in this paper we get some lower bounds for the number of critical periods of families of centers which are perturbations of the linear one we give a method which lets us prove that there are planar polynomial centers of degree l with at least 2 l 2 2 critical periods as well as study concrete families of potential reversible and lienard centers this last case is studied in more detail and we prove that the number of critical periods obtained with our approach does not increases with the order of the perturbation

on the number of critical points of the period in the study of subharmonic bifurcations from a planar hamiltonian system it is often assumed that the period of a one parameter family of periodic orbits of the unperturbed system is a monotone function of the parameter see e g hale and taboas s chow and hale es however this hypothesis is in many instances difficult to verify for example it is well known that every orbit in the first quadrant of the vollterra lotka equation is periodic it is only in recent years that the monotonicity of the periods of these periodic orbits has been shown hsu 9 and waldvogel 151 such problems also occur in the study of bifurcation of steady state solutions of a reaction diffusion equation in one space variable the steady state solutions satisfy the equation u f u o uer 1 1 on some interval in 14 smoller and wasserman showed that if f u u u u u cc

on the number of critical periods for planar polynomial systems of arbitrary degree we construct a class of planar systems of arbitrary degree n having a reversible center at the origin and such that the number of critical periods on its period annulus grows quadratically with n as far as we know the previous results on this subject gave systems having linear growth

perturbed rigidly isochronous centers and their critical periods abstract this paper investigates the bifurcation of critical periods from a cubic rigidly isochronous center under any small polynomial perturbations of degree n it proves that for n 3 4 and 5 there are at most 2 and 4 critical periods induced by periodic orbits of the unperturbed cubic system respectively and in each case this upper bound is sharp moreover for any n 5 there are at most n 1 2 critical periods induced by periodic orbits of the unperturbed cubic system an example is given to show that the upper bound in the case of n 11 can be reached

the period function for quadratic integrable systems with cubic orbits this paper is concerned with the monotonicity of the period function for families of quadratic systems with centers whose orbits lie on cubic planar curves it is proved that each such system has a period function with at most one critical point

bifurcation of critical periods of polynomial systems abstract we describe a general approach to studying bifurcations of critical periods based on a complexification of the system and algorithms of computational algebra using this approach we obtain upper bounds on the number of critical periods of several families of cubic systems in some cases we overcome the problem of nonradicality of a relevant ideal by moving it to a subalgebra generated by invariants of a group of linear transformations

bifurcation of critical periods for plane vector fields on etudie un probleme de bifurcation dans des familles de champs de vecteurs analytiques plans qui ont un centre non degenere a l origine pour toutes les valeurs d un parametre r n on definit la fonction periode p on determine les points critiques de cette fonction pres du centre avec comme parametre de bifurcation

reliability evaluation of a revised stochastic flow network with uncertain minimum time abstract this paper constructs a revised stochastic flow network to model a realistic computer network in which each arc has a lead time and a stochastic capacity the minimum time to send a specified amount of data through the network is thus uncertain hence this paper mainly proposes an approach for evaluating the system reliability that d units of data can be transmitted through k minimal paths simultaneously within the time threshold t the idea of lower boundary points for d t the minimal system states satisfying the demand d within the time threshold t is proposed firstly all system states meeting the time and demand requirements can be represented as the union of subsets generated from all lower boundary points for d t and thus the system reliability is computed quickly

finiteness for critical periods of planar analytic vector fields limburgs univ centrum dept math b 3610 diepenbeek belgium chicone c univ missouri dept math columbia mo 65211

the period function of classical lienard equations in this paper we study the number of critical points that the period function of a center of a classical lienard equation can have centers of classical lienard equations are related to scalar differential equations x x f x x 0 with f an odd polynomial let us say of degree 2 1 we show that the existence of a finite upperbound on the number of critical periods only depending on the value of can be reduced to the study of slow fast lienard equations close to their limiting layer equations we show that near the central system of degree 2 1 the number of critical periods is at most 2 2 we show the occurrence of slow fast lienard systems exhibiting 2 2 critical periods elucidating a qualitative process behind the occurrence of critical periods it all provides evidence for conjecturing that 2 2 is a sharp upperbound on the number of critical periods we also show that the number of critical periods multiplicity taken into account is always even

centers with equal period functions abstract we give a sufficient condition for systems with symmetries to have periodic solutions with equal periods we show that the main result can be applied both to hamiltonian and to non hamiltonian systems we apply the main results to produce planar centers with equal period functions

the period in the lotka volterra system is monotonic abstract periodic solutions in a class of hamiltonian systems with one degree of freedom containing the lotka volterra system are considered their period is represented as an integral appropriate for numerical evaluation as well as for theoretical investigations the monotonicity of the period in the lotka volterra system follows as a simple consequence

the critical points of the period function of x x2 x α x 1 0 0 α 1 on etudie les points critiques de la fonction periode des solutions periodiques de l equation x x 2 x x 1 0 0 2 1 on montre que le nombre de ces points critiques est borne