Travelling-wave solutions bifurcating from relative periodic orbits in plane Poiseuille flow
Rawat, Subhendu; Rincon, François
2016-01-01
Travelling-wave solutions are shown to bifurcate from relative periodic orbits in plane Poiseuille flow at Re = 2000 in a saddle-node infinite period bifurcation. These solutions consist in self-sustaining sinuous quasi-streamwise streaks and quasi- streamwise vortices located in the bulk of the flow. The lower branch travelling-wave solutions evolve into spanwise localized states when the spanwise size Lz of the domain in which they are computed is increased. On the contrary, upper branch of travelling-wave solutions develop multiple streaks when Lz is increased. Upper branch travelling-wave solutions can be continued into coherent solutions of the filtered equations used in large-eddy simulations where they represent turbulent coherent large-scale motions.
Uniformly Asymptotic Stability and Existence of Periodic Solutions and Almost Periodic Solutions
林发兴
1994-01-01
We introduce the concepts of uniformly stable solutions and uniformly-asymptotically stable solutions, and then give the relation between Lyapunov function and those concepts. Furthermore, we establish the theorem that an almost periodic system or periodic system has uniformly-asymptotically stable solutions and Lipschitz’ condition has an almost periodic solution or periodic solution.
Periodicity of chaotic solutions
Berezowski, Marek
2016-01-01
The scope of the paper is the analysis of the impact of flow reversal on the dynamics of cascades of reactors. Periodic and chaotic oscillations occur in the analyzed system. There is a dependence between the oscillation period of the state variable of the system without flow reversal and the recurrence period of windows of chaos in the steady-state diagram of the system with flow reversal.
Periodic solutions and slow manifolds
Verhulst, F.
2006-01-01
After reviewing a number of results from geometric singular perturbation theory, we give an example of a theorem for periodic solutions in a slow manifold. This is illustrated by examples involving the van der Pol-equation and a modified logistic equation. Regarding nonhyperbolic transitions we disc
Eliana Henriques de Brito
1990-01-01
Full Text Available In continuing from previous papers, where we studied the existence and uniqueness of the global solution and its asymptotic behavior as time t goes to infinity, we now search for a time-periodic weak solution u(t for the equation whose weak formulation in a Hilbert space H isddt(u′,v+δ(u′,v+αb(u,v+βa(u,v+(G(u,v=(h,vwhere: ′=d/dt; (′ is the inner product in H; b(u,v, a(u,v are given forms on subspaces U⊂W, respectively, of H; δ>0, α≥0, β≥0 are constants and α+β>0; G is the Gateaux derivative of a convex functional J:V⊂H→[0,∞ for V=U, when α>0 and V=W when α=0, hence β>0; v is a test function in V; h is a given function of t with values in H.
Photolysis of Periodate and Periodic Acid in Aqueous Solution
Sehested, Knud; Kläning, U. K.
1978-01-01
The photochemistry of periodate and periodic acid in aqueous solution was studied (i) by quantum yield measurements at low light intensity (ii) by flash photolysis, and (iii) by photolysis of glassy samples at 77 K. The photochemical studies were supplemented with pulse radiolysis studies...... of aqueous periodate solutions and with kinetic studies using stopped-flow technique. In strongly alkaline solution the photodecomposition of periodate proceeds via formation of O– and IVI. At pH
Positive periodic solutions of delayed periodic Lotka-Volterra systems
Lin Wei [Laboratory of Nonlinear Mathematics Science, Institute of Mathematics, Fudan University, Shanghai 200433 (China)]. E-mail: weilin@fudan.edu.cn; Chen Tianping [Laboratory of Nonlinear Mathematics Science, Institute of Mathematics, Fudan University, Shanghai 200433 (China)]. E-mail: tchen@fudan.edu.cn
2005-01-17
In this Letter, for a general class of delayed periodic Lotka-Volterra systems, we prove some new results on the existence of positive periodic solutions by Schauder's fixed point theorem. The global asymptotical stability of positive periodic solutions is discussed further, and conditions for exponential convergence are given. The conditions we obtained are weaker than the previously known ones and can be easily reduced to several special cases.
Periodic Solution of the Hematopoiesis Equation
Ji-Huan He
2013-01-01
Full Text Available Wu and Liu (2012 presented some results for the existence and uniqueness of the periodic solutions for the hematopoiesis model. This paper gives a simple approach to find an approximate period of the model.
Asymptotically periodic solutions of Volterra integral equations
Muhammad N. Islam
2016-03-01
Full Text Available We study the existence of asymptotically periodic solutions of a nonlinear Volterra integral equation. In the process, we obtain the existence of periodic solutions of an associated nonlinear integral equation with infinite delay. Schauder's fixed point theorem is used in the analysis.
Periodic solutions of nonlinear vibrating beams
J. Berkovits
2003-01-01
Full Text Available The aim of this paper is to prove new existence and multiplicity results for periodic semilinear beam equation with a nonlinear time-independent perturbation in case the period is not prescribed. Since the spectrum of the linear part varies with the period, the solvability of the equation depends crucially on the period which can be chosen as a free parameter. Since the period of the external forcing is generally unknown a priori, we consider the following natural problem. For a given time-independent nonlinearity, find periods T for which the equation is solvable for any T-periodic forcing. We will also deal with the existence of multiple solutions when the nonlinearity interacts with the spectrum of the linear part. We show that under certain conditions multiple solutions do exist for any small forcing term with suitable period T. The results are obtained via generalized Leray-Schauder degree and reductions to invariant subspaces.
PERIODIC-SOLUTIONS IN SPONTANEOUSLY BROKEN THEORIES
BRIHAYE, Y; KUNZ, J
1992-01-01
A class of spontaneously broken field theories is proposed, and the occurrence of their periodic, classical solutions is investigated in detail. The emergence of multiple solutions is observed, their normal modes of oscillation are studied, and the bifurcations of the classical energy functional are
Quasi-periodic solutions of the Boomeron equation
Martini, R.; Wesselius, W.
1985-01-01
The quasi-periodic solutions for the Boomeron equation are determined by means of function-theoretical methods related to Riemann surfaces and theta functions. Also determined are the so-called Boomerons as degenerations of the quasi-periodic solutions. Moreover it is indicated that there are no hig
Periodic solutions of dissipative systems revisited
Górniewicz Lech
2006-01-01
Full Text Available We reprove in an extremely simple way the classical theorem that time periodic dissipative systems imply the existence of harmonic periodic solutions, in the case of uniqueness. We will also show that, in the lack of uniqueness, the existence of harmonics is implied by uniform dissipativity. The localization of starting points and multiplicity of periodic solutions will be established, under suitable additional assumptions, as well. The arguments are based on the application of various asymptotic fixed point theorems of the Lefschetz and Nielsen type.
Periodic solutions of dissipative systems revisited
Lech Górniewicz
2006-05-01
Full Text Available We reprove in an extremely simple way the classical theorem that time periodic dissipative systems imply the existence of harmonic periodic solutions, in the case of uniqueness. We will also show that, in the lack of uniqueness, the existence of harmonics is implied by uniform dissipativity. The localization of starting points and multiplicity of periodic solutions will be established, under suitable additional assumptions, as well. The arguments are based on the application of various asymptotic fixed point theorems of the Lefschetz and Nielsen type.
Periodic solutions of Volterra integral equations
M. N. Islam
1988-01-01
Full Text Available Consider the system of equationsx(t=f(t+∫−∞tk(t,sx(sds, (1andx(t=f(t+∫−∞tk(t,sg(s,x(sds. (2Existence of continuous periodic solutions of (1 is shown using the resolvent function of the kernel k. Some important properties of the resolvent function including its uniqueness are obtained in the process. In obtaining periodic solutions of (1 it is necessary that the resolvent of k is integrable in some sense. For a scalar convolution kernel k some explicit conditions are derived to determine whether or not the resolvent of k is integrable. Finally, the existence and uniqueness of continuous periodic solutions of (1 and (2 are btained using the contraction mapping principle as the basic tool.
Periodic Solutions for Circular Restricted -Body Problems
Xiaoxiao Zhao
2013-01-01
Full Text Available For circular restricted -body problems, we study the motion of a sufficiently small mass point (called the zero mass point in the plane of equal masses located at the vertices of a regular polygon. By using variational minimizing methods, for some , we prove the existence of the noncollision periodic solution for the zero mass point with some fixed wingding number.
PERIODIC SOLUTIONS OF ASYMPTOTICALLY LINEAR HAMILTONIAN SYSTEMS
FEIGUIHUA; QIUQINGJIU
1997-01-01
The authors establish the existence of nontrival periodic solutions of the asymptotically linear Hamiltomian systems in the general case that the asymptotic matrix may be degenerate and time-dependent.This is done by using the critical point theory,Galerkin approximation procedure and the Maslov-type index theory introduced and generalized by Conley,Zehnder and Long.
Numerical bifurcation of Hamiltonian relative periodic orbits
Wulff, Claudia; Schilder, Frank
2009-01-01
that the family of choreographies rotating around the $e^2$-axis bifurcates to the family of rotating choreographies that connects to the Lagrange relative equilibrium. Moreover, we compute several relative period-doubling bifurcations and a turning point of the family of planar rotating choreographies, which...... to symmetry-breaking/symmetry-increasing pitchfork bifurcations or to period-doubling/period-halving bifurcations. We apply our methods to the family of rotating choreographies which bifurcate from the famous figure eight solution of the three-body problem as angular momentum is varied. We find...
YaoZhijian
2005-01-01
In this paper, a two-species nonautonomous competitive model with stage structure and harvesting is considered. Sufficient conditions for the existence, uniqueness, global attractivity of positive periodic solution and the existence, uniform asvmntotic stability of almost neriodic solution are obtained.
Exact Periodic Solitary Solutions to the Shallow Water Wave Equation
LI Dong-Long; ZHAO Jun-Xiao
2009-01-01
Exact solutions to the shallow wave equation are studied based on the idea of the extended homoclinic test and bilinear method. Some explicit solutions, such as the one soliton solution, the doubly-periodic wave solution and the periodic solitary wave solutions, are obtained. In addition, the properties of the solutions are investigated.
Garcia Velarde, M.
1977-07-01
Thermo convective instabilities in horizontal fluid layers are discussed with emphasis on the Rayleigh-Bernard model problem. Steady solutions and time-dependent phenomena (relaxation oscillations and transition to turbulence) are studied within the nonlinear Boussinesq-Oberbeck approximation. Homogeneous steady solutions, limit cycles, and inhomogeneous (ordered) spatial structures are also studied in simple reaction-diffusion systems. Lastly, the non-periodic attractor that appears at large Rayleigh numbers in the truncated Boussinesq-Oberbeck model of Lorenz, is constructed, and a discussion of turbulent behavior is given. (Author) 105 refs.
Unbounded Periodic Solutions to Serrin's Overdetermined Boundary Value Problem
Fall, Mouhamed Moustapha; Minlend, Ignace Aristide; Weth, Tobias
2017-02-01
We study the existence of nontrivial unbounded domains {Ω} in RN such that the overdetermined problem {-Δ u = 1 quad in Ω}, quad u = 0, quad partial_{ν} u = const quad on partial Ω admits a solution u. By this, we complement Serrin's classification result from 1971, which yields that every bounded domain admitting a solution of the above problem is a ball in RN. The domains we construct are periodic in some variables and radial in the other variables, and they bifurcate from a straight (generalized) cylinder or slab. We also show that these domains are uniquely self Cheeger relative to a period cell for the problem.
Exact periodic wave solutions for some nonlinear partial differential equations
El-Wakil, S.A. [Theoretical Physics Research Group, Department of Physics, Faculty of Science, Mansoura University, Mansoura 35516 (Egypt); Elgarayhi, A. [Theoretical Physics Research Group, Department of Physics, Faculty of Science, Mansoura University, Mansoura 35516 (Egypt)]. E-mail: elgarayhi@yahoo.com; Elhanbaly, A. [Theoretical Physics Research Group, Department of Physics, Faculty of Science, Mansoura University, Mansoura 35516 (Egypt)
2006-08-15
The periodic wave solutions for some nonlinear partial differential equations, including generalized Klein-Gordon equation, Kadomtsev-Petviashvili (KP) equation and Boussinesq equations, are obtained by using the solutions of Jacobi elliptic equation. Under limit conditions, exact solitary wave solutions, shock wave solutions and triangular periodic wave solutions have been recovered.
ALMOST PERIODIC SOLUTIONS TO SOME NONLINEAR DELAY DIFFERENTIAL EQUATION
无
2009-01-01
The existence of an almost periodic solutions to a nonlinear delay diffierential equation is considered in this paper. A set of sufficient conditions for the existence and uniqueness of almost periodic solutions to some delay diffierential equations is obtained.
Numbers of Subnormal Solutions for Higher Order Periodic Differential Equations
Zong Xuan CHEN; Kwang Ho SHON
2011-01-01
In this paper,we estimate the number of subnormal solutions for higher order linear periodic differential equations,and estimate the growth of subnormal solutions and all other solutions.We also give a representation of subnormal solutions of a class of higher order linear periodic differential equations.
PERTURBED PERIODIC SOLUTION FOR BOUSSINESQ EQUATION
Jiang Xinhua; Wang Zhen
2009-01-01
We consider the solution of the good Boussinesq equation Utt- Uxx + Uxxxx> = (U2)xx - ∞ 0, the difference between the true solution u(x, t; ε) and the N-th partial sum of the asymptotic series is bounded by εN+1 multiplied by a constant depending on T and N, for all -∞ < x < ∞ 0 ≤｜ε｜t ≤ T and 0 ≤ ｜ε｜≤ε0.
MULTIPLICITY OF PERIODIC SOLUTIONS OF DUFFING'S EQUATIONS WITH LIPSCHITZIAN CONDITION
无
2000-01-01
This paper deals with the existence and multiplicity of periodic solutions of Duffing equations x + g(x) ＝ p(t). The author proves an infinity of periodic solutions to the periodically forced nonlinear Duffing equations provided that g(x) satisfies the globally lipschitzian condition and the time-mapping satisfies the weaker oscillating property.
Yuan, Rong
2007-06-01
In this paper, we study almost periodic logistic delay differential equations. The existence and module of almost periodic solutions are investigated. In particular, we extend some results of Seifert in [G. Seifert, Almost periodic solutions of certain differential equations with piecewise constant delays and almost periodic time dependence, J. Differential Equations 164 (2000) 451-458].
Periodic solutions of quasi-differential equations
Abdelkader Boucherif
1996-01-01
Full Text Available Existence principles and theorems are established for the nonlinear problem Lu=f(t,u where Lu=−(pu′′+hu is a quasi-differential operator and f is a Carathéodory function. We prove a maximum principle for the operator L and then we show the validity of the upper and lower solution method as well as the monotone iterative technique.
Periodic Solutions for Highly Nonlinear Oscillation Systems
Ghadimi, M; Barari, Amin; Kaliji, H.D
2012-01-01
In this paper, Frequency-Amplitude Formulation is used to analyze the periodic behavior of tapered beam as well as two complex nonlinear systems. Many engineering structures, such as offshore foundations, oil platform supports, tower structures and moving arms, are modeled as tapered beams...
Periodic solutions of nonautonomous differential systems modeling obesity population
Arenas, Abraham J. [Departamento de Matematicas y Estadistica, Universidad de Cordoba Monteria (Colombia)], E-mail: aarenas@sinu.unicordoba.edu.co; Gonzalez-Parra, Gilberto [Departamento de Calculo, Universidad de los Andes, Merida (Venezuela, Bolivarian Republic of)], E-mail: gcarlos@ula.ve; Jodar, Lucas [Instituto de Matematica Multidisciplinar, Universidad Politecnica de Valencia Edificio 8G, 2o, 46022 Valencia (Spain)], E-mail: ljodar@imm.upv.es
2009-10-30
In this paper we study the periodic behaviour of the solutions of a nonautonomous model for obesity population. The mathematical model represented by a nonautonomous system of nonlinear ordinary differential equations is used to model the dynamics of obese populations. Numerical simulations suggest periodic behaviour of subpopulations solutions. Sufficient conditions which guarantee the existence of a periodic positive solution are obtained using a continuation theorem based on coincidence degree theory.
PERIODIC SOLUTIONS IN ONE-DIMENSIONAL COUPLED MAP LATTICES
郑永爱; 刘曾荣
2003-01-01
It is proven that the existence of nonlinear solutions with time period in one-dimensional coupled map lattice with nearest neighbor coupling. This is a class of systemswhose behavior can be regarded as infinite array of coupled oscillators. A method forestimating the critical coupling strength below which these solutions with time period persistis given. For some particular nonlinear solutions with time period, exponential decay inspace is proved.
Periodic Solutions of a Model of Mitosis in Frog Eggs
Bei-ye Feng; Zuo-huan Zheng
2002-01-01
In this paper,we discuss a simplified model of mitosis in frog eggs proposed by M.T. Borisuk and J.J.Tyson in [1]. By using rigorous qualitative analysis, we prove the existence of the periodic solutions on a large scale and present the space region of the periodic solutions and the parameter region coresponding to the periodic solution. We also present the space region and the parameter region where there are no periodic solutions. The results are in accordance with the numerical results in [1] up to the qualitative property.
Time-periodic solutions of the Einstein’s field equations Ⅰ:general framework
无
2010-01-01
In this paper,we develop a new algorithm to find the exact solutions of the Einstein’s field equations.Time-periodic solutions are constructed by using the new algorithm.The singularities of the time-periodic solutions are investigated and some new physical phenomena,such as degenerate event horizon and time-periodic event horizon,are found.The applications of these solutions in modern cosmology and general relativity are expected.
Pseudo almost periodic solutions to parabolic boundary value inverse problems
2008-01-01
We first define the pseudo almost periodic functions in a more general setting.Then we show the existence,uniqueness and stability of pseudo almost periodic solutions of parabolic inverse problems for a type of boundary value problems.
POSITIVE PERIODIC SOLUTIONS OFIMPULSIVE LATKA-VOLTERRA EQUATIONS
LiJianli; ShenJianhua
2005-01-01
By using the continuation of coincidence degree theory, we study the periodic Lotka-Volterra equations with impulses, and some sufficient onditions for the existence of positive periodic solutions are obtained.
NONLINEAR WAVES AND PERIODIC SOLUTION IN FINITE DEFORMATION ELASTIC ROD
Liu Zhifang; Zhang Shanyuan
2006-01-01
A nonlinear wave equation of elastic rod taking account of finite deformation, transverse inertia and shearing strain is derived by means of the Hamilton principle in this paper. Nonlinear wave equation and truncated nonlinear wave equation are solved by the Jacobi elliptic sine function expansion and the third kind of Jacobi elliptic function expansion method. The exact periodic solutions of these nonlinear equations are obtained, including the shock wave solution and the solitary wave solution. The necessary condition of exact periodic solutions, shock solution and solitary solution existence is discussed.
ROBUST CONTROL OF PERIODIC BIFURCATION SOLUTIONS
梁建术; 陈予恕; 梁以德
2004-01-01
The topological bifurcation diagrams and the coefficients of bifurcation equation were obtained by C-L method.According to obtained bifurcation diagrams and combining control theory,the method of robust control of periodic bifurcation was presented,which differs from generic methods of bifurcation control.It can make the existing motion pattern into the goal motion pattern.Because the method does not make strict requirement about parametric values of the controller,it is convenient to design and make it.Numerical simulations verify validity of the method.
Quasi-periodic and periodic solutions of the Toda lattice via the hyperelliptic sigma function
Kodama, Yuji; Previato, Emma
2010-01-01
M. Toda in 1967 (\\textit{J. Phys. Soc. Japan}, \\textbf{22} and \\textbf{23}) considered a lattice model with exponential interaction and proved it, as observed by the Fermi-Pasta-Ulam experiments, to have exact periodic and soliton solutions. The Toda lattice, as it came to be known, was then extensively studied as one of the completely integrable (differential-difference) non-linear equations which admit exact solutions in terms of theta functions of hyperelliptic curves. In this paper, we extend Toda's original approach to give hyperelliptic solutions of the Toda lattice in terms of hyperelliptic Kleinian (sigma) functions for arbitrary genus. The key identities are given by generalized addition formulae for the hyperelliptic sigma functions (J.C. Eilbeck \\textit{et al.}, {\\it J. reine angew. Math.} {\\bf 619}, 2008). We then show that periodic solutions of the Toda lattice correspond to the zeros of Kiepert-Brioschi's division polynomials, and note these are related to solutions of Poncelet's closure problem...
Positive periodic solutions for third-order nonlinear differential equations
Jingli Ren
2011-05-01
Full Text Available For several classes of third-order constant coefficient linear differential equations we obtain existence and uniqueness of periodic solutions utilizing explicit Green's functions. We discuss an iteration method for constant coefficient nonlinear differential equations and provide new conditions for the existence of periodic positive solutions for third-order time-varying nonlinear and neutral differential equations.
Peaked Periodic Wave Solutions to the Broer–Kaup Equation
Jiang, Bo; Bi, Qin-Sheng
2017-01-01
By qualitative analysis method, a sufficient condition for the existence of peaked periodic wave solutions to the Broer–Kaup equation is given. Some exact explicit expressions of peaked periodic wave solutions are also presented. Supported by National Nature Science Foundation of China under Grant No. 11102076 and Natural Science Fund for Colleges and Universities in Jiangsu Province under Grant No. 15KJB110005
ON THE PERIODIC SOLUTIONS OF DIFFERENTIAL INCLUSIONS AND APPLICATIONS
李国成; 薛小平; 宋士吉
2004-01-01
The periodic problem of evolution inclusion is studied and its results are used to establish existence theorems of periodic solutions of a class of semi-linear differential inclusion.Also existence theorem of the extreme solutions and the strong relaxation theorem are given for this class of semi-linear differential inclusion. An application to some feedback control systems is discussed.
Periodic solutions for a coupled pair of delay difference equations
Kang Shugui
2005-01-01
Full Text Available Based on the fixed-point index theory for a Banach space, positive periodic solutions are found for a system of delay difference equations. By using such results, the existence of nontrivial periodic solutions for delay difference equations with positive and negative terms is also considered.
PSEUDO-ALMOST PERIODIC SOLUTIONS TO SOME FUNCTIONAL DIFFERENTIAL EQUATIONS
无
2010-01-01
This paper is concerned with the pseudo-almost periodic solutions to some functional differential equations. By the exponential dichotomy theory and Schauder’s fixed-point theorem, some results on the existence and uniqueness of pseudo-almost periodic solutions to the system are obtained.
Yongkun Li
2011-01-01
Full Text Available Firstly, we propose a concept of uniformly almost periodic functions on almost periodic time scales and investigate some basic properties of them. When time scale T=ℝ or ℤ, our definition of the uniformly almost periodic functions is equivalent to the classical definitions of uniformly almost periodic functions and the uniformly almost periodic sequences, respectively. Then, based on these, we study the existence and uniqueness of almost periodic solutions and derive some fundamental conditions of admitting an exponential dichotomy to linear dynamic equations. Finally, as an application of our results, we study the existence of almost periodic solutions for an almost periodic nonlinear dynamic equations on time scales.
Global Bifurcation of Periodic Solutions with Symmetry,
1987-07-01
homotopy method for concrete applications. The simplest example is the monitoring of signs of determinants of the linearization, i.e. of Brouwer ...mechanics, cf. [Poi, ch.XXX[, 1899. The general planar case was discussed extensively by Andronov and coworkers since 1929, see e.g. [And&Chai, And& Leo ...approximation, which is common place e.g. in Brouwer degree theory [Dei, Chow&Hal and which relates to the question of homotopy invariance of the index k, is
Existence of extremal periodic solutions for quasilinear parabolic equations
Siegfried Carl
1997-01-01
bounded domain under periodic Dirichlet boundary conditions. Our main goal is to prove the existence of extremal solutions among all solutions lying in a sector formed by appropriately defined upper and lower solutions. The main tools used in the proof of our result are recently obtained abstract results on nonlinear evolution equations, comparison and truncation techniques and suitably constructed special testfunction.
Periodic and almost periodic solutions for multi-valued differential equations in Banach spaces
E. Hanebaly
2000-03-01
Full Text Available It is known that for $omega$-periodic differential equations of monotonous type, in uniformly convex Banach spaces, the existence of a bounded solution on ${Bbb R}^+$ is equivalent to the existence of an omega-periodic solution (see Haraux [5] and Hanebaly [7, 10]. It is also known that if the Banach space is strictly convex and the equation is almost periodic and of monotonous type, then the existence of a continuous solution with a precompact range is equivalent to the existence of an almost periodic solution (see Hanebaly [8]. In this note we want to generalize the results above for multi-valued differential equations.
Almost Periodic Solution of a Discrete Commensalism System
Yalong Xue
2015-01-01
Full Text Available A nonautonomous discrete two-species Lotka-Volterra commensalism system with delays is considered in this paper. Based on the discrete comparison theorem, the permanence of the system is obtained. Then, by constructing a new discrete Lyapunov functional, a set of sufficient conditions which guarantee the system global attractivity are obtained. If the coefficients are almost periodic, there exists an almost periodic solution and the almost periodic solution is globally attractive.
Periodic Solutions of Multispecies Mutualism System with Infinite Delays
Wenbo Zhao
2014-01-01
Full Text Available We studied the delayed periodic mutualism system with Gilpin-Ayala effect. Some new and interesting sufficient conditions are obtained to guarantee the existence of periodic solution for the multispecies mutualism system with infinite delays. Our method is based on Mawhin's coincidence degree. To the best knowledge of the authors, there is no paper considering the existence of periodic solutions for n-species mutualism system with infinite delays.
Cepheids : the period-luminosity relation
Beaulieu, JP
1997-01-01
The Cepheids are relatively young, bright, periodic supergiant variable stars showing a correlation between their periods and luminosities. Since the beginning of the century, the Cepheid Period-Luminosity relation has been the corner stone of distance determination, and of the measure of the correl
Periodic Solutions of Periodic Delay Predator-Prey System with Nonmonotonic Functional Response
宋永利; 韩茂安
2003-01-01
By using the continuation theorem of coincidence degree theory, sufficient conditions are obtained for theexistence of positive periodic solutions of a delayed predator-prey system with nonmonotonic functional response ina periodic environment.
EXISTENCE AND UNIQUENESS OF PERIODIC SOLUTIONS TO A HIGHER DIMENSIONAL PERIODIC SYSTEM WITH DELAY
无
2008-01-01
In this paper, using fixed point theorem, we discuss a higher dimensional nonautonomous periodic system with delay and give some suffcient criteria for the existence and uniqueness of periodic solution. Our results extend and improve some results in previous researches.
Symmetric Periodic Solutions of the Anisotropic Manev Problem
Santoprete, Manuele
2002-01-01
We consider the Manev Potential in an anisotropic space, i.e., such that the force acts differently in each direction. Using a generalization of the Poincare' continuation method we study the existence of periodic solutions for weak anisotropy. In particular we find that the symmetric periodic orbits of the Manev system are perturbed to periodic orbits in the anisotropic problem.
Time-periodic solutions of the Benjamin-Ono equation
Ambrose , D.M.; Wilkening, Jon
2008-04-01
We present a spectrally accurate numerical method for finding non-trivial time-periodic solutions of non-linear partial differential equations. The method is based on minimizing a functional (of the initial condition and the period) that is positive unless the solution is periodic, in which case it is zero. We solve an adjoint PDE to compute the gradient of this functional with respect to the initial condition. We include additional terms in the functional to specify the free parameters, which, in the case of the Benjamin-Ono equation, are the mean, a spatial phase, a temporal phase and the real part of one of the Fourier modes at t = 0. We use our method to study global paths of non-trivial time-periodic solutions connecting stationary and traveling waves of the Benjamin-Ono equation. As a starting guess for each path, we compute periodic solutions of the linearized problem by solving an infinite dimensional eigenvalue problem in closed form. We then use our numerical method to continue these solutions beyond the realm of linear theory until another traveling wave is reached (or until the solution blows up). By experimentation with data fitting, we identify the analytical form of the solutions on the path connecting the one-hump stationary solution to the two-hump traveling wave. We then derive exact formulas for these solutions by explicitly solving the system of ODE's governing the evolution of solitons using the ansatz suggested by the numerical simulations.
Three positive doubly periodic solutions of a nonlinear telegraph system
Fang-lei WANG; Yu-kun AN
2009-01-01
This paper studies existence of at least three positive doubly periodic solutions of a coupled nonlinear telegraph system with doubly periodic boundary conditions. First, by using the Green function and maximum principle, existence of solutions of a nonlinear telegraph system is equivalent to existence of fixed points of an operator. By imposing growth conditions on the nonlinearities, existence of at least three fixed points in cone is obtained by using the Leggett-Williams fixed point theorem to cones in ordered Banach spaces. In other words, there exist at least three positive doubly periodic solutions of nonlinear telegraph system.
Periodic solutions and flip bifurcation in a linear impulsive system
Jiang Gui-Rong; Yang Qi-Gui
2008-01-01
In this paper,the dynamical behaviour of a linear impulsive system is discussed both theoretically and numerically.The existence and the stability of period-one solution are discussed by using a discrete map.The conditions of existence for flip bifurcation are derived by using the centre manifold theorem and bifurcation theorem.The bifurcation analysis shows that chaotic solutions appear via a cascade of period-doubling in some interval of parameters.Moreover,the periodic solutions,the bifurcation diagram,and the chaotic attractor,which show their consistence with the theoretical analyses,are given in an example.中图分类:O547
Cantor families of periodic solutions for completely resonant wave equations
2008-01-01
We present recent existence results of Cantor families of small amplitude periodic solutions for completely resonant nonlinear wave equations. The proofs rely on the Nash-Moser implicit function theory and variational methods.
Feng, Lian-Li; Tian, Shou-Fu; Yan, Hui; Wang, Li; Zhang, Tian-Tian
2016-07-01
In this paper, a lucid and systematic approach is proposed to systematically study the periodic-wave solutions and asymptotic behaviors of a (2 + 1) -dimensional generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt (gKDKK) equation, which can be used to describe certain situations from the fluid mechanics, ocean dynamics and plasma physics. Based on Bell's polynomials, the bilinear formalism and N -soliton solution of the gKDKK equation are derived, respectively. Furthermore, based on multidimensional Riemann theta functions, the periodic-wave solutions of the equation are also constructed. Finally, an asymptotic relation between the periodic-wave solutions and soliton solutions are strictly established under a limited procedure.
Periodic Solutions of Schr(o)dinger Flow from S3 to S2
Hao YIN
2006-01-01
This paper deals with the periodic solutions of Schr(o)dinger flow from S3 to S2. It is shown that the periodic solution is related to the variation of some functional and there exist S1-invariant critical points to this functional. The proof makes use of the Principle of Symmetric Criticality of Palais.
ALMOST PERIODIC SOLUTIONS TO STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS
无
2012-01-01
By applying the properties of almost periodic function and exponential dichotomy of linear system as well as Banach fixed point theorem,we establish the conditions for the existence and uniqueness of square-mean almost periodic solution to some stochastic functional differential equations.
Oscillatory Periodic Solutions of Nonlinear Second Order Ordinary Differential Equations
Yong Xiang LI
2005-01-01
In this paper the existence results of oscillatory periodic solutions are obtained for a second order ordinary differential equation -u"(t) = f(t, u(t)), where f: R2 → R is a continuous odd function and is 2π-periodic in t. The discussion is based on the fixed point index theory in cones.
Quasi-periodic solutions for an asymmetric oscillation
Huang, Peng; Li, Xiong; Liu, Bin
2016-10-01
In this paper we study the dynamical behaviour of the differential equation x‧‧+ax+-bx-=f(t), where {{x}+}=\\max ≤ft\\{x,0\\right\\} , {{x}-}=\\max ≤ft\\{-x,0\\right\\} , a and b are two different positive constants, and f (t) is a smooth quasi-periodic function. For this purpose, firstly, we have to establish some variants of the invariant curve theorem of planar smooth quasi-periodic mappings, which was proved recently by the authors (see Huang et al preprint). Then we will discuss the boundedness of all solutions and the existence of quasi-periodic solutions for the above asymmetric oscillation.
Solution space analysis of Double Lunar-Swingby periodic trajectory
无
2010-01-01
The Double Lunar-Swingby(DLS)periodic trajectory is a type of large-scale trajectory in Restricted Three-Body Problem framework.First,the principium of the DLS periodic trajectory is studied,and a preliminary design of the DLS trajectory is developed by the Patched Conic method.Second,the solution space of the DLS periodic trajectory is discussed in detail and in combination with numerical simulation,a distribution about orbital parameter relationship in the solution space is given.Finally,the variations of the orbital elements with different rotation angular velocities of geocentric apsidal line are found,and two typical orbits are given according to three reference frames.It is shown that Patched Conic method is feasible for the DLS periodic trajectory solution space analysis,and the conclusions will be valuable to the deep-space exploration orbit design in future.
On some classes of mKdV periodic solutions
Kevrekidis, P G [Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003-4515 (United States); Khare, Avinash [Institute of Physics, Bhubaneswar, Orissa 751005 (India); Saxena, A [Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545 (United States); Herring, G [Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003-4515 (United States)
2004-11-12
We obtain exact periodic solutions of the positive and negative modified Kortweg-de Vries (mKdV) equations. We examine the dynamical stability of these solitary wave lattices through direct numerical simulations. While the positive mKdV breather lattice solutions are found to be unstable, the two-soliton lattice solution of the same equation is found to be stable. Similarly, a negative mKdV lattice solution is found to be stable. We also touch upon the implications of these results for the KdV equation.
Eventually Periodic Solutions of a Max-Type Difference Equation
Taixiang Sun
2014-01-01
Full Text Available We study the following max-type difference equation xn=max{An/xn-r,xn-k}, n=1,2,…, where {An}n=1+∞ is a periodic sequence with period p and k,r∈{1,2,…} with gcd(k,r=1 and k≠r, and the initial conditions x1-d,x2-d,…,x0 are real numbers with d=max{r,k}. We show that if p=1 (or p≥2 and k is odd, then every well-defined solution of this equation is eventually periodic with period k, which generalizes the results of (Elsayed and Stevic´ (2009, Iričanin and Elsayed (2010, Qin et al. (2012, and Xiao and Shi (2013 to the general case. Besides, we construct an example with p≥2 and k being even which has a well-defined solution that is not eventually periodic.
Periodic Wave Solutions and Their Limits for the Generalized KP-BBM Equation
Ming Song; Zhengrong Liu
2012-01-01
We use the bifurcation method of dynamical systems to study the periodic wave solutions and their limits for the generalized KP-BBM equation. A number of explicit periodic wave solutions are obtained. These solutions contain smooth periodic wave solutions and periodic blow-up solutions. Their limits contain periodic wave solutions, kink wave solutions, unbounded wave solutions, blow-up wave solutions, and solitary wave solutions.
Sun Wen [School of Mathematics and Statistics, Wuhan University, Wuhan 430072 (China); Chen Shihua [School of Mathematics and Statistics, Wuhan University, Wuhan 430072 (China)]. E-mail: shcheng@whu.edu.cn; Hong Zhiming [School of Mathematics and Statistics, Wuhan University, Wuhan 430072 (China); Wang Changping [Department of Mathematics and Statistics, Dalhousie University, Halifax, NS, B3H 3J5 (Canada)
2007-08-15
A two-species periodic competition Lotka-Volterra system with time delay and diffusion is investigated. Some sufficient conditions of the existence of positive periodic solution are established for the system by using the continuation theorem of coincidence degree theory.
Pseudo almost periodic solutions for a Lasota-Wazewska model
Samira Rihani
2016-03-01
Full Text Available In this work, we consider a new model describing the survival of red blood cells in animals. Specifically, we study a class of Lasota-Wazewska equation with pseudo almost periodic varying environment and mixed delays. By using the Banach fixed point theorem and some inequality analysis, we find sufficient conditions for the existence, uniqueness and stability of solutions. We generalize some results known for one type of delay and for the Lasota-Wazewska model with almost periodic and periodic coefficients. An example illustrates the proposed model.
Periodic Solutions for Functional Differential Inclusions With Infinite Delay
李勇; 周钦德; 吕显瑞
1994-01-01
By means of asymptotic fixed point theory,it is established that every dissipative functional differential inclusion (probably with infinite delay) has a periodic solution.This provides a theoretical basis for the applications of Liapunov’s second method to multivalued systems.As a result,a positive answer to Hutson’s open problem is given for more general multivalued systems.
Almost periodic solutions to systems of parabolic equations
Janpou Nee
1994-01-01
Full Text Available In this paper we show that the second-order differential solution is 2-almost periodic, provided it is 2-bounded, and the growth of the components of a non-linear function of a system of parabolic equation is bounded by any pair of con-secutive eigenvalues of the associated Dirichlet boundary value problems.
Almost Periodic Viscosity Solutions of Nonlinear Parabolic Equations
Zhang Shilin
2009-01-01
Full Text Available We generalize the comparison result 2007 on Hamilton-Jacobi equations to nonlinear parabolic equations, then by using Perron's method to study the existence and uniqueness of time almost periodic viscosity solutions of nonlinear parabolic equations under usual hypotheses.
Periodic Solutions of a Discrete Time Predator-Prey System
Yong-li Song; Mao-an Han
2006-01-01
In this paper, we discuss a discrete predator-prey system with a non-monotonic functional response,which models the dynamics of the prey and the predator having non-overlapping generations. By using the coincidence degree theory, sufficient conditions are obtained for the existence of positive periodic solutions.
Periodic and Subharmonic Solutions for Second Order -Laplacian Difference Equations
Xia Liu; Yuanbiao Zhang; Bo Zheng; Haiping Shi
2011-11-01
In this paper, some sufficient conditions for the existence and multiplicity of periodic and subharmonic solutions to second order -Laplacian difference equations are obtained by using the critical point theory. The proof is based on the Linking theorem in combination with variational technique.
ZHANG DuanZhi
2014-01-01
We study some monotonicity and iteration inequality of the Maslov-type index i-1of linear Hamiltonian systems.As an application we prove the existence of symmetric periodic solutions with prescribed minimal period for first order nonlinear autonomous Hamiltonian systems which are semipositive,even,and superquadratic at zero and infinity.This result gives a positive answer to Rabinowitz’s minimal period conjecture in this case without strictly convex assumption.We also give a different proof of the existence of symmetric periodic solutions with prescribed minimal period for classical Hamiltonian systems which are semipositive,even,and superquadratic at zero and infinity which was proved by Fei,Kim and Wang in 2001.
Quasi-periodic solutions of nonlinear beam equations with quintic quasi-periodic nonlinearities
Qiuju Tuo
2015-01-01
Full Text Available In this article, we consider the one-dimensional nonlinear beam equations with quasi-periodic quintic nonlinearities $$ u_{tt}+u_{xxxx}+(B+ \\varepsilon\\phi(tu^5=0 $$ under periodic boundary conditions, where B is a positive constant, $\\varepsilon$ is a small positive parameter, $\\phi(t$ is a real analytic quasi-periodic function in t with frequency vector $\\omega=(\\omega_1,\\omega_2,\\dots,\\omega_m$. It is proved that the above equation admits many quasi-periodic solutions by KAM theory and partial Birkhoff normal form.
RR Lyrae period luminosity relations with Spitzer
Neeley, Jillian R.; Marengo, Massimo; CRRP Team
2017-01-01
RR Lyrae variable stars have long been known to be valuable distance indicators, but only recently has a well defined period luminosity relationship been utilized at infrared wavelengths. In my thesis, I am combining Spitzer Space Telescope data of RR Lyrae stars obtained as part of the Carnegie RR Lyrae Program with ground based NIR data to characterize the period-luminosity-metallicity (PLZ) relation and provide an independent Population II calibration of the cosmic distance scale. I will discuss the ongoing efforts to calibrate this relation using objects such as M4 and NGC 6441 and how the first data release from the Gaia mission impacts our findings. I will also compare my preliminary empirical relations to theoretical PLZ relations derived from stellar pulsation models.
On the integrability and quasi-periodic wave solutions of the Boussinesq equation in shallow water
Ma, Pan-Li; Tian, Shou-Fu; Tu, Jian-Min; Xu, Mei-Juan
2015-05-01
In this paper, the complete integrability of the Boussinesq equation in shallow water is systematically investigated. By using generalized Bell's polynomials, its bilinear formalism, bilinear Bäcklund transformations, Lax pairs of the Boussinesq equation are constructed, respectively. By virtue of its Lax equations, we find its infinite conservation laws. All conserved densities and fluxes are obtained by lucid recursion formulas. Furthermore, based on multidimensional Riemann theta functions, we construct periodic wave solutions of the Boussinesq equation. Finally, the relations between the periodic wave solutions and soliton solutions are strictly constructed. The asymptotic behaviors of the periodic waves are also analyzed by a limiting procedure.
Vargas, Edgar Villagran; Hustert, Reinhold; Gumrich, Peter; Jackson, Andrew D; Heimburg, Thomas
2010-01-01
Close to melting transitions it is possible to propagate solitary electromechanical pulses which reflect many of the experimental features of the nerve pulse including mechanical dislocations and reversible heat production. Here we show that one also obtains the possibility of periodic pulse generation when the boundary condition for the nerve is the conservation of the overall length of the nerve. This condition generates an undershoot beneath the baseline (`hyperpolarization') and a `refractory period', i.e., a minimum distance between pulses. In this paper, we outline the theory for periodic solutions to the wave equation and compare these results to action potentials from the femoral nerve of the locust (locusta migratoria). In particular, we describe the frequently occurring minimum-distance doublet pulses seen in these neurons and compare them to the periodic pulse solutions.
Zhou Yubin; Wang Mingliang; Miao Tiande
2004-03-15
The periodic wave solutions for a class of nonlinear partial differential equations, including the Davey-Stewartson equations and the generalized Zakharov equations, are obtained by using the F-expansion method, which can be regarded as an overall generalization of the Jacobi elliptic function expansion method recently proposed. In the limit cases the solitary wave solutions of the equations are also obtained.
PERIODIC OSCILLATORY SOLUTION TO DELAYED BAM NEURAL NETWORKS WITH PERIODIC COEFFICIENTS
无
2008-01-01
In this paper,using the continuation theorem of coincidence degree theory,Lyapu- nov functionals and some new inequality techniques,some new sufficient criteria are obtained to ensure the existence and global exponential stability of periodic solution. Our results are less restrictive than previous works and more effective than those in [12],which plays a significant role in designing globally exponentially stable and peri- odic oscillatory BAM neural networks with periodic coefficients.One example is al...
Light curve solutions of the ultrashort-period $Kepler$ binaries
Kjurkchieva, Diana
2015-01-01
We carried out light curve solutions of the ultrashort-period binaries with MS components observed by $Kepler$. All six targets turned out almost in thermal contact with contact or slightly overcontact configurations. Two of them, KID 4921906 and KID 6309193, are not eclipsing but reveal ellipsoidal and spot variability. One of the components of KID 8108785 exhibits inherent, quasi-sinusoidal, small-amplitude variability. KID 12055255 turned out a very rare case of ultrashort-period overcontact binary consisting of two M dwarfs. Our modeling indicated that the variability of KID 9532219 is due to eclipses but not to $\\delta$ Sct pulsations as it was previously supposed.
Almost Periodic Solutions for Impulsive Fractional Stochastic Evolution Equations
Toufik Guendouzi
2014-08-01
Full Text Available In this paper, we consider the existence of square-mean piecewise almost periodic solutions for impulsive fractional stochastic evolution equations involving Caputo fractional derivative. The main results are obtained by means of the theory of operators semi-group, fractional calculus, fixed point technique and stochastic analysis theory and methods adopted directly from deterministic fractional equations. Some known results are improved and generalized.
Periodic Solutions of Nonautonomous Second Order Hamiltonian Systems
Shi Xia LUAN; An Min MAO
2005-01-01
In this paper, we develop the local linking theorem given by Li and Willem by replacing the Palais-Smale condition with a Cerami one, and apply it to the study of the existence of periodic solutions of the nonautonomous second order Hamiltonian systems (H) ü + A (t)U+▽V(t,u)=0,u∈RN,t∈R. We handle the case of superquadratic nonlinearities which differ from those used previously. Our results extend the theorems given by Li and Willem.
PERIODIC SOLUTIONS OF LINEAR NEUTRAL INTEGRO-DIFFERENTIAL EQUATIONS
马世旺; 王志成; 许强
2004-01-01
Consider the linear neutral FDEd/dt[x(t)+ Ax(t -7)] =∫R[dL(8)]x(t+s)+f(t)where x and f are n-dimensional vectors;A is an n×n constant matrix and L(s) is an n×n matrix function with bounded total variation. Some necessary and sufficient conditions are given which guarantee the existence and uniqueness of periodic solutions to the above equation.
Abouelmagd, Elbaz I; Elzayat, E M A; Abbas, Ibrahim A
2013-01-01
The aim of the present work is to reduce the secular solution around the triangular equilibrium points to periodic solution in the frame work of the generalized restricted thee-body problem. This model is generalized in sense that both the primaries are oblate and radiating as well as the gravitational potential from a belt. We show that the linearized equation of motion of the infinitesimal body around the triangular equilibrium points has a secular solution when the value of mass ratio equals the critical mass value. Moreover, we reduce this solution to periodic solution, as well as some numerical and graphical investigations for the effects of the perturbed forces are introduced. This model can be used to examine the existence of a dust particle near the triangular points of an oblate and radiating binary stars system surrounded by a belt.
Pseudo analytical solution to time periodic stiffness systems
Wang Yan-Zhong; Zhou Yuan-Zi
2011-01-01
An analytical form of state transition matrix for a system of equations with time periodic stiffness is derived in order to solve the free response and also allow for the determination of system stability and bifurcation. A pseudoclosed form complete solution for parametrically excited systems subjected to inhomogeneous generalized forcing is developed, based on the Fourier expansion of periodic matrices and the substitution of matrix exponential terms via Lagrange-Sylvester theorem. A Mathieu type of equation with large amplitude is presented to demonstrate the method of formulating state transition matrix and Floquet multipliers. A two-degree-of-freedom system with irregular time periodic stiffness characterized by spiral bevel gear mesh vibration is presented to find forced response in stability and instability. The obtained results are presented and discussed.
Multiwavelength Characteristics of Period-Luminosity Relations
Madore, Barry F
2011-01-01
We present a physically motivated explanation for the observed, monotonic increase in slope, and the simultaneous (and also monotonic) decrease in the width/scatter of the Leavitt Law (the Cepheid Period-Luminosity (PL) relation) as one systematically moves from the blue and visual into the near and mid-infared. We calibrate the wavelength-dependent, surface-brightness sensitivities to temperature using the observed slopes of PL relations from the optical through the mid-infrared, and test the calibration by comparing the theoretical predictions with direct observations of the wavelength dependence of the scatter in the Large Magellanic Cloud Cepheid PL relation. In doing so we find the slope of the Period-Radius (PR) relation is c = 0.724 +/- 0.006. Investigating the effect of differential reddening suggests that this value may be overestimated by as much as 10%; however the same slope of the PR relation fits the (very much unreddened) Cepheids in IC1613, albeit with lower precision. The discussion given is ...
Quasi-doubly periodic solutions to a generalized Lame equation
Pawellek, Michael
2007-01-01
We consider the algebraic form of a generalized Lame equation with five free parameters. By introducing a generalization of Jacobi's elliptic functions we transform this equation to a 1-dim time-independent Schroedinger equation with (quasi-doubly) periodic potential. We show that only for a finite set of integral values for the five parameters quasi-doubly periodic eigenfunctions expressible in terms of generalized Jacobi functions exist. For this purpose we also establish a relation to the generalized Ince equation.
CHEN Yong; YAN Zhen-Ya; LI Biao; ZHANG Hong-Qing
2002-01-01
In this paper, we study the generalized coupled Hirota Satsuma KdV system by using the new generalizedtransformation in homogeneous balance method. As a result, many explicit exact solutions, which contain new solitarywave solutions, periodic wave solutions, and the combined formal solitary wave solutions, and periodic wave solutions,are obtained.
CHENYong; YANZhen－Ya; 等
2002-01-01
In this paper,we study the generalized coupled Hirota-Satsuma KdV system by using the new generalized transformation in homogeneous balance method.As a result,many explicit exact solutions,which contain new solitary wave solutions,periodic wave solutions,and the combined formal solitary wave solutions,and periodic wave solutions ,are obtained.
Quasi-periodic Solutions to the K(-2, -2) Hierarchy
Wu, Lihua; Geng, Xianguo
2016-07-01
With the help of the characteristic polynomial of Lax matrix for the K(-2, -2) hierarchy, we define a hyperelliptic curve 𝒦n+1 of arithmetic genus n+1. By introducing the Baker-Akhiezer function and meromorphic function, the K(-2, -2) hierarchy is decomposed into Dubrovin-type differential equations. Based on the theory of hyperelliptic curve, the explicit Riemann theta function representation of meromorphic function is given, and from which the quasi-periodic solutions to the K(-2, -2) hierarchy are obtained.
Periodic Solutions of the Forced Pendulum: Exchange of Stability and Bifurcations
Katriel, Guy
2002-06-01
We study the T-periodic solutions of the forced pendulum equation u″+cu‧+a sin(u)=λf(t), where f satisfies f(t+{T}/{2})=-f(t). We prove that this equation always has at least two geometrically distinct T-periodic solutions u0 and u1. We then investigate the dependence of the set of T-periodic solutions on the forcing strength λ. We prove that under some restriction on the parameters a,c, the periodic solutions found before can be smoothly parameterized by λ, and that there are some λ-intervals for which u0(λ), u1(λ) are the only T-periodic solutions up to geometrical equivalence, but there are other λ-intervals in which additional T-periodic solutions bifurcate off the branches u0(λ), u1(λ). We characterize the global structure of the bifurcating branches. Related to this bifurcation phenomenon is the phenomenon of 'exchange of stability' - in some λ-intervals u0(λ) is dynamically stable and u1(λ) is unstable, while in other λ-intervals the reverse is true, a phenomenon which has important consequences for the dynamics of the forced pendulum, as we show by both theoretical analysis and numerical simulation.
New Doubly Periodic Solutions for the Coupled Nonlinear Klein-Gordon Equations
LIU Chun-Ping
2005-01-01
By using the general solutions of a new coupled Riccati equations, a direct algebraic method is described to construct doubly periodic solutions (Jacobi elliptic function solution) for the coupled nonlinear Klein-Gordon equations.It is shown that more doubly periodic solutions and the corresponding solitary wave solutions and trigonometric function solutions can be obtained in a unified way by this method.
Periodic segregation of solute atoms in fully coherent twin boundaries.
Nie, J F; Zhu, Y M; Liu, J Z; Fang, X Y
2013-05-24
The formability and mechanical properties of many engineering alloys are intimately related to the formation and growth of twins. Understanding the structure and chemistry of twin boundaries at the atomic scale is crucial if we are to properly tailor twins to achieve a new range of desired properties. We report an unusual phenomenon in magnesium alloys that until now was thought unlikely: the equilibrium segregation of solute atoms into patterns within fully coherent terraces of deformation twin boundaries. This ordered segregation provides a pinning effect for twin boundaries, leading to a concomitant but unusual situation in which annealing strengthens rather than weakens these alloys. The findings point to a platform for engineering nano-twinned structures through solute atoms. This may lead to new alloy compositions and thermomechanical processes.
Quasi-periodic Solutions of the General Nonlinear Beam Equations
GAO YI-XIAN
2012-01-01
In this paper,one-dimensional (1D) nonlinear beam equations of the form utt - uxx + uxxxx + mu = f(u)with Dirichlet boundary conditions are considered,where the nonlinearity f is an analytic,odd function and f(u) = O(u3).It is proved that for all m ∈ (0,M*] (∈) R(M* is a fixed large number),but a set of small Lebesgue measure,the above equations admit small-amplitude quasi-periodic solutions corresponding to finite dimensional invariant tori for an associated infinite dimensional dynamical system.The proof is based on an infinite dimensional KAM theory and a partial Birkhoff normal form technique.
Tang, Xianhua; Cao, Daomin; Zou, Xingfu
We consider a periodic Lotka-Volterra competition system without instantaneous negative feedbacks (i.e., pure-delay systems) x(t)=x(t)[r(t)-∑j=1na(t)x(t-τ(t))], i=1,2,…,n. We establish some 3/2-type criteria for global attractivity of a positive periodic solution of the system, which generalize the well-known Wright's 3/2 criteria for the autonomous delay logistic equation, and thereby, address the open problem proposed by both Kuang [Y. Kuang, Global stability in delayed nonautonomous Lotka-Volterra type systems without saturated equilibria, Differential Integral Equations 9 (1996) 557-567] and Teng [Z. Teng, Nonautonomous Lotka-Volterra systems with delays, J. Differential Equations 179 (2002) 538-561].
Positive Periodic Solutions for Three Species Lotka.Volterra Mixed Ecosystems with Periodic Stocking
LiBi-werl; ZhengLu-zhou
2003-01-01
By using a new method, a set of easily verifiable sufficient conditions are derived for the existence of positive periodic solutions for three-species Lotka-Volterra mixed systems with periodic stocking{x′1(t)=x1(t)(b1(t)-a11(t)x1(t)-a12(t)x2(t)-a13(t)x3(t))+S1(t)；x′2(t)=x2(t)(-b2(t)+a21(t)x1(t)-a22(t)x2(t)-a23(t)x3(t))+S2(t)；x′3=x3(t)(-b3(t)+a31(t)-a32(t)x2(t)-a33(t)x3(t))+S3(t) ；where bi(t) ,aij (t)(i,j = 1,2,3) are positive continuous T-periodic functions, Si (t)(i = 1,2,3) are nonnegative continuous T-periodic functions.
Positive Periodic Solutions for Three Species Lotka-Volterra Mixed Ecosystems with Periodic Stocking
Li Bi-wen; Zheng Lu-zhou
2003-01-01
By using a new method, a set of easily verifiable sufficient conditions are derived for the existence of positive periodic solutions for three-species Lotka-Volterra mixed systems with periodic stocking:x′1(t) =x1 (t) (b1 (t) - a11 (t)x1 (t) - a12 (t)x2 (t) - a13 (t)x3 (t)) + S1 (t)x′2(t) = x2 (t) (- b2 (t) + a21 (t)x1 (t) - a22 (t)x2 (t) - a23 (t)x3 (t)) + S2 (t)x′3(t) = x3 (t)(- b3 (t) + a31 (t)x1 (t) - a32 (t)x2 (t) - a33 (t)x3 (t)) + S3 (t)where bi ( t ), aij (t) ( i,j= 1,2,3 ) are positive continuous T- periodic functions, Si (t) (i = 1,2,3) are nonnegative continuous T-periodic functions.
A Two-Component Generalization of Burgers' Equation with Quasi-Periodic Solution
Pan, Hongfei; Xia, Tiecheng; Chen, Dengyuan
2014-10-01
In this paper, we aim for the theta function representation of quasi-periodic solution and related crucial quantities for a two-component generalization of Burgers' equation. Our tools include the theory of algebraic curves, meromorphic functions, Baker-Akhiezer functions and the Dubrovin-type equations for auxiliary divisor. Eith these tools, the explicit representations for above quantities are obtained.
Periodic Solutions of Evolution Variational Inequalities-a Method of Guiding Functions
Samir ADLY; Daniel GOELEVEN; Michel TH(E)RA
2009-01-01
This paper focuses on a part of the presentation given by the third author at the Shanghai Forum on Industrial and Applied Mathematics (Shanghai 2006). It is related to the existence of a periodic solution of evolution variational inequalities. The approach is based on the method of guiding functions.
A new class of symmetric periodic solutions of the spatial elliptic restricted three-body problem
XU XingBo; FU YanNing
2009-01-01
We show that there exists a new class of symmetric periodic solutions of the spatial elliptic restricted three-body problem.In such a solution,the infinitesimal body is confined to the vicinity of a primary and moves on a nearly circular orbit.This orbit is almost perpendicular to the orbital plane of the pri-maries,where the line of symmetry of the orbit lies.The existence is shown by applying a corollary of Arenstorf's fixed point theorem to s periodicity equation system of the problem.And this existence doesn't require any restriction on the mass ratio of the primaries,nor on the eccentricity of their rela-tive elliptic orbit.Potential relevance of this new class of periodic solutions to real celestial body sys-tems and the follow-up studies in this respect are also discussed.
A new class of symmetric periodic solutions of the spatial elliptic restricted three-body problem
无
2009-01-01
We show that there exists a new class of symmetric periodic solutions of the spatial elliptic restricted three-body problem. In such a solution, the infinitesimal body is confined to the vicinity of a primary and moves on a nearly circular orbit. This orbit is almost perpendicular to the orbital plane of the primaries, where the line of symmetry of the orbit lies. The existence is shown by applying a corollary of Arenstorf’s fixed point theorem to a periodicity equation system of the problem. And this existence doesn’t require any restriction on the mass ratio of the primaries, nor on the eccentricity of their relative elliptic orbit. Potential relevance of this new class of periodic solutions to real celestial body systems and the follow-up studies in this respect are also discussed.
Basic relations for the period variation models of variable stars
Mikulášek, Zdeněk; Gráf, Tomáš; Zejda, Miloslav; Zhu, Liying; Qian, Shen-Bang
2012-01-01
Models of period variations are basic tools for period analyzes of variable stars. We introduce phase function and instant period and formulate basic relations and equations among them. Some simple period models are also presented.
Periodic blow-up solutions and their limit forms for the generalized Camassa-Holm equation
Zhengrong Liu; Boling Guo
2008-01-01
In this paper, we consider the generalized Camassa-Holm equation ut + 2kux -uxxt + au2ux = 2uxuxx-uuxxxUnder substitution ζ = x - ct, some new explicit periodic wave solutions and their limit forms are presented through some special phase orbits. These periodic wave solutions tend to infinity on ζ - u plane periodically. Thus we call them periodic blow-up solutions. To our knowledge, such periodic blow-up solutions have not been found in any other equations.
WANG Qi; CHEN Yong; ZHANG Hong-Qing
2005-01-01
In this work we devise an algebraic method to uniformly construct rational form solitary wave solutions and Jacobi and Weierstrass doubly periodic wave solutions of physical interest for nonlinear evolution equations. With the aid of symbolic computation, we apply the proposed method to solving the (1+1)-dimensional dispersive long wave equation and explicitly construct a series of exact solutions which include the rational form solitary wave solutions and elliptic doubly periodic wave solutions as special cases.
Positive periodic solutions of periodic neutral Lotka-Volterra system with distributed delays
Li Yongkun [Department of Mathematics, Yunnan University Kunming, Yunnan 650091 (China)], E-mail: yklie@ynu.edu.cn
2008-07-15
By using a fixed point theorem of strict-set-contraction, some criteria are established for the existence of positive periodic solutions of the following periodic neutral Lotka-Volterra system with distributed delays (dx{sub i}(t))/(dt) =x{sub i}(t)[a{sub i}(t)-{sigma}{sub j=1}{sup n}b{sub ij}(t){integral}{sub -T{sub ij}}{sup 0}K{sub ij}({theta})x{sub j}( t+{theta})d{theta}-{sigma}{sub j=1}{sup n}c{sub ij}(t){integral}{sub -T{sub ij}}{sup 0}K{sub ij}({theta}) x{sub j}{sup '}(t+{theta})d{theta}],i=1,2,...,n, where a{sub i},b{sub ij},c{sub ij} element of C(R,R{sup +}) (i, j = 1, 2, ..., n) are {omega}-periodic functions, T{sub ij},T{sub ij} element of (0,{infinity}) (i, j = 1, 2, ..., n) and K{sub ij},K{sub ij} element of (R,R{sup +}) satisfying {integral}{sub -T{sub ij}}{sup 0}K{sub ij}({theta})d{theta}=1,{integral}{sub -T{sub ij}}{sup 0}K{sub ij}({theta})d{theta}=1, i, j = 1, 2, ..., n.
Time-periodic Solution to a Nonlinear Parabolic Type Equation of Higher Order
Yan-ping Wang; You-lin Zhang
2008-01-01
In this paper, the existence and uniqueness of time-periodic generalized solutions and time-periodic classical solutions to a class of parabolic type equation of higher order are proved by Gaierkin method.
Time-Periodic Solution of a 2D Fourth-Order Nonlinear Parabolic Equation
Xiaopeng Zhao; Changchun Liu
2014-08-01
By using the Galerkin method, we study the existence and uniqueness of time-periodic generalized solutions and time-periodic classical solutions to a fourth-order nonlinear parabolic equation in 2D case.
PERIODIC SOLUTIONS TO p-LAPLACIAN GENERALIZED LINARD EQUATION WITH DEVIATING ARGUMENTS
无
2008-01-01
Using the theory of coincidence degree,we study a kind of periodic solutions to p-Laplacian generalized Liénard equation with deviating arguments. A result on the existence of periodic solutions is obtained.
Ji, Shanming; Yin, Jingxue; Cao, Yang
2016-11-01
In this paper, we consider the periodic problem for semilinear heat equation and pseudo-parabolic equation with logarithmic source. After establishing the existence of positive periodic solutions, we discuss the instability of such solutions.
Staggered and short period solutions of the Saturable Discrete Nonlinear Schr\\"odinger Equation
Khare, Avinash; Samuelsen, Mogens R; Saxena, Avadh; 10.1088/1751-8113/42/8/085002
2010-01-01
We point out that the nonlinear Schr{\\"o}dinger lattice with a saturable nonlinearity also admits staggered periodic as well as localized pulse-like solutions. Further, the same model also admits solutions with a short period. We examine the stability of these solutions and find that the staggered as well as the short period solutions are stable in most cases. We also show that the effective Peierls-Nabarro barrier for the pulse-like soliton solutions is zero.
EXISTENCE OF TIME PERIODIC SOLUTIONS FOR A DAMPED GENERALIZED COUPLED NONLINEAR WAVE EQUATIONS
房少梅; 郭柏灵
2003-01-01
The time periodic solution problem of damped generalized coupled nonlinear wave equations with periodic boundary condition was studied. By using the Galerkin method to construct the approximating sequence of time periodic solutions, a priori estimate and Laray-Schauder fixed point theorem to prove the convergence of the approximate solutions, the existence of time periodic solutions for a damped generalized coupled nonlinear wave equations can be obtained.
Relating Functional Groups to the Periodic Table
Struyf, Jef
2009-01-01
An introduction to organic chemistry functional groups and their ionic variants is presented. Functional groups are ordered by the position of their specific (hetero) atom in the periodic table. Lewis structures are compared with their corresponding condensed formulas. (Contains 5 tables.)
Relating Functional Groups to the Periodic Table
Struyf, Jef
2009-01-01
An introduction to organic chemistry functional groups and their ionic variants is presented. Functional groups are ordered by the position of their specific (hetero) atom in the periodic table. Lewis structures are compared with their corresponding condensed formulas. (Contains 5 tables.)
谢惠琴; 王全义
2004-01-01
In this paper, we study the existence, uniqueness, and the global exponential stability of the periodic solution and equilibrium of hybrid bidirectional associative memory neural networks with discrete delays. By ingeniously importing real parameters di > 0 (i = 1, 2,..., n) which can be adjusted, making use of the Lyapunov functional method and some analysis techniques, some new sufficient conditions are established. Our results generalize and improve the related results in [9]. These conditions can be used both to design globally exponentially stable and periodical oscillatory hybrid bidirectional associative neural networks with discrete delays, and to enlarge the area of designing neural networks. Our work has important significance in related theory and its application.
王金良; 周笠
2003-01-01
In this paper,our main aim is to study the existence and uniqueness of the periodic solution of delayed Logistic equation and its asymptotic behavior.In case the coefficients are periodic,we give some sufficient conditions for the existence and uniqueness of periodic solution.Furthermore,we also study the effect of time-delay on the solution.
A global solution curve for a class of periodic problems, including the pendulum equation
Korman, Philip
2007-09-01
Using continuation methods and bifurcation theory, we study the exact multiplicity of periodic solutions, and the global solution structure, for a class of periodically forced pendulum-like equations. Our results apply also to the first order equations. We also show that by choosing a forcing term, one can produce periodic solutions with any number of Fourier coefficients arbitrarily prescribed.
Periodic solutions of first-order functional differential equations in population dynamics
Padhi, Seshadev; Srinivasu, P D N
2014-01-01
This book provides cutting-edge results on the existence of multiple positive periodic solutions of first-order functional differential equations. It demonstrates how the Leggett-Williams fixed-point theorem can be applied to study the existence of two or three positive periodic solutions of functional differential equations with real-world applications, particularly with regard to the Lasota-Wazewska model, the Hematopoiesis model, the Nicholsons Blowflies model, and some models with Allee effects. Many interesting sufficient conditions are given for the dynamics that include nonlinear characteristics exhibited by population models. The last chapter provides results related to the global appeal of solutions to the models considered in the earlier chapters. The techniques used in this book can be easily understood by anyone with a basic knowledge of analysis. This book offers a valuable reference guide for students and researchers in the field of differential equations with applications to biology, ecology, a...
Rousselet, Bernard
2013-01-01
We consider {\\it small solutions} of a vibrating mechanical system with smooth non-linearities for which we provide an approximate solution by using a triple scale analysis; a rigorous proof of convergence of the triple scale method is included; for the forced response, a stability result is needed in order to prove convergence in a neighbourhood of a primary resonance. The amplitude of the response with respect to the frequency forcing is described and it is related to the frequency of a free periodic vibration.
Probabilistic solution of relative entropy weighted control
Bierkens, Joris
2012-01-01
We show that stochastic control problems with a particular cost structure involving a relative entropy term admit a purely probabilistic solution, without the necessity of applying the dynamic programming principle. The argument is as follows. Minimization of the expectation of a random variable with respect to the underlying probability measure, penalized by relative entropy, may be solved exactly. In the case where the randomness is generated by a standard Brownian motion, this exact solution can be written as a Girsanov density. The stochastic process appearing in the Girsanov exponent has the role of control process, and the relative entropy of the change of probability measure is equal to the integral of the square of this process. An explicit expression for the control process may be obtained in terms of the Malliavin derivative of the density process. The theory is applied to the problem of minimizing the maximum of a Brownian motion (penalized by the relative entropy), leading to an explicit expressio...
An infinite branching hierarchy of time-periodic solutions of the Benjamin-Ono equation
Wilkening, Jon
2008-07-01
We present a new representation of solutions of the Benjamin-Ono equation that are periodic in space and time. Up to an additive constant and a Galilean transformation, each of these solutions is a previously known, multi-periodic solution; however, the new representation unifies the subset of such solutions with a fixed spatial period and a continuously varying temporal period into a single network of smooth manifolds connected together by an infinite hierarchy of bifurcations. Our representation explicitly describes the evolution of the Fourier modes of the solution as well as the particle trajectories in a meromorphic representation of these solutions; therefore, we have also solved the problem of finding periodic solutions of the ordinary differential equation governing these particles, including a description of a bifurcation mechanism for adding or removing particles without destroying periodicity. We illustrate the types of bifurcation that occur with several examples, including degenerate bifurcations not predicted by linearization about traveling waves.
New periodic solutions to a generalized Hirota-Satsuma coupled KdV system
闫庆友; 张玉峰; 魏小鹏
2003-01-01
Using expansions in terms of the Jacobi elliptic cosine function and third Jacobi elliptic function, some new periodic solutions to the generalized Hirota-Satsuma coupled KdV system are obtained with the help of the algorithm Mathematica. These periodic solutions are also reduced to the bell-shaped solitary wave solutions and kink-shape solitary solutions. As special cases, we obtain new periodic solution, bell-shaped and kink-shaped solitary solutions to the well-known Hirota-Satsuma equations.
Periodic solutions for second-order Hamiltonian systems with the p-Laplacian
Weigao Ge
2006-10-01
Full Text Available In this paper, we investigate the periodic solutions of Hamiltonian system with the p-Laplacian. By using Mountain Pass Theorem the existence of at least one periodic solution is obtained, Furthermore, under suitable assumptions, we obtain the existence of infinitely many solutions via $Z_2$-symmetric version of the Mountain Pass Theorem.
Staggered and short-period solutions of the saturable discrete nonlinear Schrodinger equation
Khare, A.; Rasmussen, K.O.; Samuelsen, Mogens Rugholm
2009-01-01
We point out that the nonlinear Schrodinger lattice with a saturable nonlinearity also admits staggered periodic aswell as localized pulse-like solutions. Further, the same model also admits solutions with a short period. We examine the stability of these solutions and find that the staggered...
无
2009-01-01
In this paper, by fixed point theorem of Krasnoselskii, we study the positive pe- riodic solution to a class of nonautonomous differential equation with impulses and delay. Firstly, definition of periodic solution and some lemmas are stated. Then some results on the existence of positive periodic solution to the equation are obtained.
Modulation equations for spatially periodic systems: derivation and solutions
Schielen, R.; Doelman, A.
2001-01-01
We study a class of partial dierential equations in one spatial dimension, which can be seen as model equations for the analysis of pattern formation in physical systems dened on unbounded, weakly oscillating domains. We perform a linear and weakly nonlinear stability analysis for solutions that bif
Exact periodic solution in coupled nonlinear Schrodinger equations
Li Qi-Liang; Chen Jun-Lang; Sun Li-Li; Yu Shu-Yi; Qian Sheng
2007-01-01
The coupled nonlinear Schrodinger equations (CNLSEs) of two symmetrical optical fibres are nonintegrable, however the transformed CNLSEs have integrability. Integrability of the transformed CNLSEs is proved by the Hamilton dynamics theory and Galilei transform. Making use of a transform for CNLSEs and using the ansatz with Jacobi elliptic function form, this paper obtains the exact optical pulse solutions.
Modulation equations for spatially periodic systems: derivation and solutions
Schielen, R.; Doelman, A.
1996-01-01
We study a class of partial dierential equations in one spatial dimension, which can be seen as model equations for the analysis of pattern formation in physical systems dened on unbounded, weakly oscillating domains. We perform a linear and weakly nonlinear stability analysis for solutions that bif
Periodic Relativity: Deflection of Light, Acceleration, Rotation Curves
Zaveri V. H.
2015-01-01
Full Text Available Vectorial analysis relating to derivation of deflection of light is presented. Curvilinear acceleration is distinguished from the Newtonian polar conic acceleration. The dif- ference between the two is due to the curvature term. Lorentz invariant expression for acceleration is derived. A physical theory of rotation curves of galaxies based on second solution to Einstein’s field equation is presented. Theory is applied to Milky Way, M31, NGC3198 and Solar system. Modified Kepler’s third law yields correct orbital periods of stars in a galaxy. Deviation factor in the line element of t he theory happens to be the ratio of the Newtonian gravitational acceleration to th e measured acceleration of the star in the galaxy. Therefore this deviation factor can replace the MOND function.
Zijian Liu
2015-01-01
Full Text Available We study a two-patch impulsive migration periodic N-species Lotka-Volterra competitive system. Based on analysis method, inequality estimation, and Lyapunov function method, sufficient conditions for the permanence and existence of a unique globally stable positive periodic solution of the system are established. Some numerical examples are shown to verify our results and discuss the model further.
Zuo, Wenjie; Jiang, Daqing
2016-07-01
In this paper, we investigate the dynamics of the stochastic autonomous and non-autonomous predator-prey systems with nonlinear predator harvesting respectively. For the autonomous system, we first give the existence of the global positive solution. Then, in the case of persistence, we prove that there exists a unique stationary distribution and it has ergodicity by constructing a suitable Lyapunov function. The result shows that, the relatively weaker white noise will strengthen the stability of the system, but the stronger white noise will result in the extinction of one or two species. Particularly, for the non-autonomous periodic system, we show that there exists at least one nontrivial positive periodic solution according to the theory of Khasminskii. Finally, numerical simulations illustrate our theoretical results.
EXISTENCE OF PERIODIC SOLUTIONS FOR A DISCRETE-TIME MODEL OF TWO-CELL CNNS
无
2006-01-01
We investigate a class of discrete-time model of two-cell cellular neural networks with symmetric template. By using the Lyapunov direct method, La-Salle's invariance principle, we discuss the existence and the stability of periodic solutions. The model considered has attractive 2-periodic and unstable 2-periodic solutions.
Jing HUI; Lan Sun CHEN
2004-01-01
The general system of differential equations describing predator-prey dynamics with impulsive effects is modified by the assumption that the coefficients are periodic functions of time. By use of standard techniques of bifurcation theory, it is known that this system has a positive periodic solution provided the time average of the predator's net uninhibited death rate is in a suitable range.The bifurcation is from the periodic solution of the time-dependent logistic equation for the prey (which results in the absence of predator).
PSEUDO-ALMOST PERIODIC SOLUTIONS TO SOME NON-AUTONOMOUS DIFFERENCE EQUATIONS WITH DELAY
无
2009-01-01
This paper is concerned with the pseudo-almost periodic solutions to the nonautonomous difference equations with delay. Under some suitable assumptions, some results for the existence and uniqueness of pseudo-almost solutions are obtained.
The Periodic Solutions of the Compound Singular Fractional Differential System with Delay
XuTing Wei
2010-01-01
Full Text Available The paper gives sufficient conditions on the existence of periodic solution for a class of compound singular fractional differential systems with delay, involving Nishimoto fractional derivative. Furthermore, for the particular functions, the necessary conditions on the existence of periodic solution are also derived. Especially, for two-dimensional compound singular fractional differential equation with delay, the criteria of existence of periodic solution are obtained. Finally, two examples are presented to verify the validity of criteria.
Li, Wan-Tong; Wang, Jia-Bing; Zhang, Li
2016-08-01
This paper is concerned with the new types of entire solutions other than traveling wave solutions of nonlocal dispersal equations with monostable nonlinearity in space periodic habitats. We first establish the existence and properties of spatially periodic solutions connecting two steady states. Then new types of entire solutions are constructed by combining the rightward and leftward pulsating traveling fronts with different speeds and a spatially periodic solution. Finally, for a class of special heterogeneous reaction, we further establish the uniqueness of entire solutions and the continuous dependence of such an entire solution on parameters, such as wave speeds and the shifted variables. In other words, we build a five-dimensional manifold of solutions and the traveling wave solutions are on the boundary of the manifold.
The Single Period Inventory Model: Origins, Solutions, Variations, and Applications.
1977-09-01
34News boy problem ", [1] "Newspaper boy problem ", [2] "Newspaper vendor problem ", [3] " Newsvendor problem ", [4] "Christmas tree problem ", [5] and so...miXr) % ^The classic newspaper boy or single period inventory problem is reviewed, and its origins and development during the past 30 years are...traced. The review reveals several variations for the classic problem , both in cost structure and in the decision principles involved. The critical
Ground state solutions for asymptotically periodic Schrodinger equations with critical growth
Hui Zhang
2013-10-01
Full Text Available Using the Nehari manifold and the concentration compactness principle, we study the existence of ground state solutions for asymptotically periodic Schrodinger equations with critical growth.
EXISTENCE AND GLOBAL ATTRACTIVITY OF ALMOST PERIODIC SOLUTION TO A DELAYED DIFFERENTIAL EQUATION
无
2011-01-01
A new fixed point theorem is presented and sufficient conditions are obtained for the existence, uniqueness and global attractivity of a positive almost periodic solution to a delayed differential equation with almost periodic factors.
Positive Periodic Solution of a Discrete Predator-prey Patch-system
Shu-yuan Shen; Pei-xuan Weng
2008-01-01
A periodic difference predator-prey model with Holling-(m+1)(m>2) type functional response and impulses is established. Sufficient conditions are derived for the existence of periodic solutions by using a continuation theorem in coincidence degree.
无
2008-01-01
In this paper, we consider almost periodic discrete two-species competitive sys-tems. By using Lyapunov functional, the existence conditions and uniqueness of almost periodic solutions for the this type of systems are obtained.
BIFURCATION OF PERIODIC SOLUTION IN A THREE-UNIT NEURAL NETWORK WITH DELAY
林怡平; ROLAND LEMMERT; PETER VOLKMANN
2001-01-01
A system of three-unit networks with no self-connection is investigated, the general formula for bifurcation direction of Hopf bifurcation is calculated, and the estimation formula of the period for periodic solution is given.
Positive Periodic Solutions of an Epidemic Model with Seasonality
Gui-Quan Sun
2013-01-01
Full Text Available An SEI autonomous model with logistic growth rate and its corresponding nonautonomous model are investigated. For the autonomous case, we give the attractive regions of equilibria and perform some numerical simulations. Basic demographic reproduction number Rd is obtained. Moreover, only the basic reproduction number R0 cannot ensure the existence of the positive equilibrium, which needs additional condition Rd>R1. For the nonautonomous case, by introducing the basic reproduction number defined by the spectral radius, we study the uniform persistence and extinction of the disease. The results show that for the periodic system the basic reproduction number is more accurate than the average reproduction number.
Almost Periodic Solution for Memristive Neural Networks with Time-Varying Delays
Huaiqin Wu
2013-01-01
Full Text Available This paper is concerned with the dynamical stability analysis for almost periodic solution of memristive neural networks with time-varying delays. Under the framework of Filippov solutions, by applying the inequality analysis techniques, the existence and asymptotically almost periodic behavior of solutions are discussed. Based on the differential inclusions theory and Lyapunov functional approach, the stability issues of almost periodic solution are investigated, and a sufficient condition for the existence, uniqueness, and global exponential stability of the almost periodic solution is established. Moreover, as a special case, the condition which ensures the global exponential stability of a unique periodic solution is also presented for the considered memristive neural networks. Two examples are given to illustrate the validity of the theoretical results.
Lee Yong-Hoon
1998-01-01
Full Text Available We prove a multiplicity result of Ambrosetti–Prodi type problems of higher order. Proofs are based on upper and lower solutions method for higher order periodic boundary value problems and coincidence degree arguments.
EXISTENCE OF PERIODIC SOLUTIONS TO A PERTURBED FOUR-DIMENSIONAL SYSTEM
无
2009-01-01
Consider a k multiple closed orbit on an invariant surface of a four dimensional system, after a suitable perturbation, the closed orbit can generate periodic orbits and double-period orbits. Using bifurcation methods and techniques, sufficient conditions for the existence of periodic solutions to the perturbed four dimensional system are obtained, and the period-doubling bifurcations is discussed.
Periodic current oscillations of zinc in nitric acid solutions
ERVIN SALLÓ
2008-02-01
Full Text Available The charge percolation mechanism (CPM of olefin polymerization in the presence of transition metal compounds has been applied to explain the polymerization of ethylene by silica supported chromium oxide. In the previous work of this series, the fundamental issues and mechanism of this polymerization were presented. In this work the compatibility of the CPM with the empirical findings is confirmed. The CPM has been applied to explain: the appearance of an induction period; the deactivation of active centers and the formation of oligomers; the effects of chromium concentration on the silica surface, the silica surface discontinuity and the pore size of silica on polymerization and the formation of the structure of polyethylene. A mathematical model has been derived to explain the effects of the CrOx/SiO2 ratio on the productivity of Phillips catalysts in the polymerization of ethylene. The empirical findings have also been confirmed by computer simulations.
Quasi-periodic non-stationary solutions of 3D Euler equations for incompressible flow
Ershkov, Sergey V
2015-01-01
A novel derivation of non-stationary solutions of 3D Euler equations for incompressible inviscid flow is considered here. Such a solution is the product of 2 separated parts: - one consisting of the spatial component and the other being related to the time dependent part. Spatial part of a solution could be determined if we substitute such a solution to the equations of motion (equation of momentum) with the requirement of scale-similarity in regard to the proper component of spatial velocity. So, the time-dependent part of equations of momentum should depend on the time-parameter only. The main result, which should be outlined, is that the governing (time-dependent) ODE-system consist of 2 Riccati-type equations in regard to each other, which has no solution in general case. But we obtain conditions when each component of time-dependent part is proved to be determined by the proper elliptical integral in regard to the time-parameter t, which is a generalization of the class of inverse periodic functions.
Xing, Qiuxia; Wang, Lihong; Mihalache, Dumitru; Porsezian, Kuppuswamy; He, Jingsong
2017-05-01
In this paper, we consider the real modified Korteweg-de Vries (mKdV) equation and construct a special kind of breather solution, which can be obtained by taking the limit λj → λ1 of the Lax pair eigenvalues used in the n-fold Darboux transformation that generates the order-n periodic solution from a constant seed solution. Further, this special kind of breather solution of order n can be used to generate the order-n rational solution by taking the limit λ1 → λ0, where λ0 is a special eigenvalue associated with the eigenfunction ϕ of the Lax pair of the mKdV equation. This eigenvalue λ0, for which ϕ(λ0)=0, corresponds to the limit of infinite period of the periodic solution. Our analytical and numerical results show the effective mechanism of generation of higher-order rational solutions of the mKdV equation from the double eigenvalue degeneration process of multi-periodic solutions.
Refined Rotational Period, Pole Solution & Shape Model for (3200) Phaethon
Ansdell, Megan; Hainaut, Olivier; Buie, Marc W; Kaluna, Heather; Bauer, James; Dundon, Luke
2014-01-01
(3200) Phaethon exhibits both comet- and asteroid-like properties, suggesting it could be a rare transitional object such as a dormant comet or previously volatile-rich asteroid. This justifies detailed study of (3200) Phaethon's physical properties, as a better understanding of asteroid-comet transition objects can provide insight into minor body evolution. We therefore acquired time-series photometry of (3200) Phaethon over 15 nights from 1994 to 2013, primarily using the Tektronix 2048x2048 pixel CCD on the University of Hawaii 2.2-m telescope. We utilized light curve inversion to: (1) refine (3200) Phaethon's rotational period to P=3.6032+/-0.0008 h; (2) estimate a rotational pole orientation of lambda=+85+/-13 degrees and beta=-20+/-10 degrees; and (3) derive a shape model. We also used our extensive light curve dataset to estimate the slope parameter of (3200) Phaethon's phase curve as G~0.06, consistent with C-type asteroids. We discuss how this highly oblique pole orientation with a negative ecliptic ...
Asymptotic stability and periodic solutions of vector Li\\'enard equations
Briata, F.; Sabatini, M.
2010-01-01
We prove the asymptotic stability of the equilibrium solution of a class of vector Li\\'enard equations by means of LaSalle invariance principle. The key hypothesis consists in assuming that the intersections of the manifolds in $\\{\\dot V = 0\\}$ be isolated. We deduce an existence theorem for periodic solutions of periodically perturbed vector Li\\'enard equations.
Bound and periodic solutions of the Riccati equation in Banach space
A. Ya. Dorogovtsev
1995-01-01
Full Text Available An abstract, nonlinear, differential equation in Banach space is considered. Conditions are presented for the existence of bounded solutions of this equation with a bounded right side, and also for the existence of stationary (periodic solutions of this equation with a stationary (periodic process in the right side.
ON THE EXISTENCE OF PERIODIC SOLUTIONS FOR NONLINEAR SYSTEM WITH MULTIPLE DELAYS
曹显兵
2003-01-01
The existence of T-periodic solutions of the nonlinear system with multiple delaysis studied. By using the topological degree method, sufficient conditions are obtained forthe existence of T-periodic solutions. As an application, the existence of positive periodicsolution for a logarithmic population model is established under some conditions.
EXISTENCE OF POSITIVE PERIODIC SOLUTIONS FOR INFINITE DELAY FUNCTIONAL DIFFERENTIAL EQUATIONS
无
2006-01-01
In this paper, the existence of positive periodic solutions for infinite delay functional differential equations(FDEs for short) is discussed by utilizing a fixed point theorem on a cone in Banach space. Some results on the existence of positive periodic solutions are derived.
EXISTENCE OF MULTIPLE POSITIVE PERIODIC SOLUTIONS TO A CLASS OF INTEGRO-DIFFERENTIAL EQUATION
无
2011-01-01
In this paper,by the Avery-Henderson fixed point theorem,we investigate the existence of multiple positive periodic solutions to a class of integro-differential equation. Some suficient conditions are obtained for the existence of multiple positive periodic solutions.
EXISTENCE OF PERIODIC SOLUTION TO HIGHER ORDER DIFFERENTIAL EQUATIONS WITH DEVIATING ARGUMENT
无
2009-01-01
In this paper,using the coincidence degree theory of Mawhin,we investigate the existence of periodic solutions to higher order differential equations with deviating argument. Some new results on the existence of periodic solutions to the equations are obtained. In addition,we give an example to illustrate the main results.
Time-periodic solutions of the Einstein’s field equations II:geometric singularities
无
2010-01-01
In this paper,we construct several kinds of new time-periodic solutions of the vacuum Einstein’s field equations whose Riemann curvature tensors vanish,keep finite or take the infinity at some points in these space-times,respectively.The singularities of these new time-periodic solutions are investigated and some new physical phenomena are discovered.
THE EXISTENCE, UNIQUENESS AND STABILITY OF ALMOST PERIODIC SOLUTION FOR A CLASS OF NONLINEAR SYSTEM
方聪娜; 王全义
2004-01-01
In this paper, we study the problems on the existence, uniqueness and stability of almost periodic solution for a class of nonlinear system. Using fixed point theorem and Lyapunov functional, the sufficient conditions are given which guarantee the existence, uniqueness and stability of almost periodic solution for the system.
PERIODIC SOLUTIONS TO A HIGH-ORDER NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATION
无
2012-01-01
In this paper,using the principle of a priori boundedness,we study the existence and uniqueness of periodic solutions to a high-order neutral functional differential equation.Some new results for the existence and uniqueness of the periodic solution are obtained.
A PRIORI BOUNDS FOR PERIODIC SOLUTIONS TO A FUNCTIONAL DIFFERENTIAL EQUATION WITH DELAY
无
2012-01-01
A priori bounds are established for periodic solutions to a functional differential equation with delay.By means of these bounds,an existence theorem for periodic solutions is obtained using Mawhin's continuation theorem.Our work generalizes the known result.
PERIODIC SOLUTIONS TO A KIND OF NEUTRAL DIFFERENTIAL SYSTEM:VIA (h,k)-DICHOTOMY
无
2012-01-01
In this paper, based on the theory of (h, k)-Dichotomy of linear system and Kras-noselskii's fixed point theorem, we study the existence of periodic solutions to a neutral differential equation. Some new sufficient conditions are obtained to guarantee the existence and uniqueness of T-periodic solution to the equation.
Existence of almost periodic solution of a model of phytoplankton allelopathy with delay
Abbas, Syed; Mahto, Lakshman
2012-09-01
In this paper we discuss a non-autonomous two species competitive allelopathic phytoplankton model in which both species are producing chemical which stimulate the growth of each other. We have studied the existence and uniqueness of an almost periodic solution for the concerned model system. Sufficient conditions are derived for the existence of a unique almost periodic solution.
Quasi-periodic solutions to the hierarchy of four-component Toda lattices
Wei, Jiao; Geng, Xianguo; Zeng, Xin
2016-08-01
Starting from a discrete 3×3 matrix spectral problem, the hierarchy of four-component Toda lattices is derived by using the stationary discrete zero-curvature equation. Resorting to the characteristic polynomial of the Lax matrix for the hierarchy, we introduce a trigonal curve Km-2 of genus m - 2 and present the related Baker-Akhiezer function and meromorphic function on it. Asymptotic expansions for the Baker-Akhiezer function and meromorphic function are given near three infinite points on the trigonal curve, from which explicit quasi-periodic solutions for the hierarchy of four-component Toda lattices are obtained in terms of the Riemann theta function.
The periodic wave solutions for the generalized Nizhnik-Novikov-Veselov equation
张金良; 任东锋; 王明亮; 王跃明; 方宗德
2003-01-01
The periodic wave solutions expressed by Jacobi elliptic functions for the generalized Nizhnik-Novikov-Veselov equation are obtained using the F-expansion method proposed recently. In the limiting cases, the solitary wave solutions and other types of travelling wave solutions for the system are obtained.
Konopelchenko-Dubrovsky方程的周期解%Periodic Wave Solutions for Konopelchenko-Dubrovsky Equation
张金良; 张令元; 王明亮
2005-01-01
By using F-expansion method proposed recently, we derive the periodic wave solution expressed by Jacobi elliptic functions for Konopelchenko-Dubrovsky equation. In the limit case, the solitary wave solution and other type of the traveling wave solutions are derived.
Applications of F-expansion to Periodic Wave Solutions for Variant Boussinesq Equations
无
2005-01-01
We present an F-expansion method for finding periodic wave solutions of nonlinear evolution equations in mathematical physics, which can be thought of as a concentration of extended Jacobi elliptic function expansion method proposed recently. By using the F-expansion, without calculating Jacobi elliptic functions, we obtain simultaneously many periodic wave solutions expressed by various Jacobi elliptic functions for the variant Boussinesq equations. When the modulus m approaches 1 and 0, the hyperbolic function solutions (including the solitary wave solutions) and trigonometric solutions are also given respectively.
Surfaces and Curves Corresponding to the Solutions Generated from Periodic “Seed” of NLS Equation
Ling ZHANG; Jing Song HE; Yi CHENG; Yi Shen LI
2012-01-01
The solutions q[n] generated from a periodic “seed” q =cei(as+bt) of the nonlinear Schr(o)dinger (NLS) by n-fold Darboux transformation is represented by determinant.Furthermore,the s-periodic solution and t-periodic solution are given explicitly by using q[1].The curves and surfaces (F1,F2,F3) associated with q[n] are given by means of Sym formula.Meanwhile,we show periodic and asymptotic properties of these curves.
Stability and periodicity of solutions for delay dynamic systems on time scales
Zhi-Qiang Zhu
2014-04-01
Full Text Available This article concerns the stability and periodicity of solutions to the delay dynamic system $$ x^{\\triangle}(t=A(t x(t + F(t, x(t, x(g(t+C(t $$ on a time scale. By the inequality technique for vectors, we obtain some stability criteria for the above system. Then, by using the Horn fixed point theorem, we present some conditions under which our system is asymptotically periodic and its periodic solution is unique. In particular, the periodic solution is positive under proper assumptions.
Exact periodic wave solutions to the generalized Nizhnik-Novikov-Veselov equation
Yan-Ze Peng
2005-02-01
The extended mapping method with symbolic computation is developed to obtain exact periodic wave solutions to the generalized Nizhnik{Novikov{Veselov equation. Limit cases are studied and new solitary wave solutions and triangular periodic wave solutions are obtained. The method is applicable to a large variety of non-linear partial differential equations, as long as odd- and even-order derivative terms do not coexist in the equation under consideration.
Positive oriented periodic solutions of the first-order complex ode with polynomial nonlinear part
2006-01-01
Full Text Available We study nonlinear ODE problems in the complex Euclidean space, with the right-hand side being polynomial with nonconstant periodic coefficients. As the coefficients functions, we admit only functions with vanishing Fourier coefficients for negative indices. This leads to an existence theorem which relates the number of solutions with the number of zeros of the averaged right-hand side polynomial. A priori estimates of the norms of solutions are based on the Wirtinger-Poincaré-type inequality. The proof of existence theorem is based on the continuation method of Krasnosielski et al., Mawhin et al., and the Leray-Schauder degree. We give a few applications on the complex Riccati equation and some others.
Outburst-related period changes of recurrent nova CI aquilae
Wilson, R. E.; Honeycutt, R. K., E-mail: honey@astro.indiana.edu, E-mail: rewilson@ufl.edu [Astronomy Department, Indiana University, Swain Hall West, Bloomington, IN 47405 (United States)
2014-11-01
Pre-outburst and post-outburst light curves and post-outburst eclipse timings are analyzed to measure any period (P) change related to nova CI Aql's outburst of early 2000 and a mean post-outburst dP/dt, which then lead to estimates of the accreting component's rate of mass (M) change and its overall outburst-related change of mass over roughly a decade of observations. We apply a recently developed procedure for unified analysis of three timing-related data types (light curves, radial velocities, and eclipse timings), although with only light curves and timings in this case. Fits to the data are reasonably good without need for a disk in the light-curve model, although the disk certainly exists and has an important role in our post-outburst mass flow computations. Initial experiments showed that, although there seems to be an accretion hot spot, it has essentially no effect on derived outburst-related ΔP or on post-outburst dP/dt. Use of atomic time (HJED) in place of HJD also has essentially nil effect on ΔP and dP/dt. We find ΔP consistently negative in various types of solutions, although at best only marginally significant statistically in any one experiment. Pre-outburst HJD {sub 0} and P results are given, as are post-outburst HJD {sub 0}, P, and dP/dt, with light curves and eclipse times as joint input, and also with only eclipse time input. Post-outburst dP/dt is negative at about 2.4σ. Explicit formulae for mass transfer rates and epoch-to-epoch mass change are developed and applied. A known offset in the magnitude zero point for 1991-1994 is corrected.
Existence of Almost-Periodic Solutions for Lotka-Volterra Cooperative Systems with Time Delay
Kaihong Zhao
2012-01-01
Full Text Available This paper considers the existence of positive almost-periodic solutions for almost-periodic Lotka-Volterra cooperative system with time delay. By using Mawhin’s continuation theorem of coincidence degree theory, sufficient conditions for the existence of positive almost-periodic solutions are obtained. An example and its simulation figure are given to illustrate the effectiveness of our results.
Global Analysis of Almost Periodic Solution of a Discrete Multispecies Mutualism System
Hui Zhang
2014-01-01
of the system. Assuming that the coefficients in the system are almost periodic sequences, we obtain the sufficient conditions for the existence of a unique almost periodic solution which is globally attractive. In particular, for the discrete two-species Lotka-Volterra mutualism system, the sufficient conditions for the existence of a unique uniformly asymptotically stable almost periodic solution are obtained. An example together with numerical simulation indicates the feasibility of the main result.
Zhao, Yu; Yuan, Sanling; Zhang, Tonghua
2017-03-01
Phytoplankton allelopathy is an ecological phenomenon that concerns the interaction among toxic-producing phytoplankton. Recently, researchers pay great attention to whether the cyclic outbreaks of the harmful algal blooms are related with the allelopathy in a random fluctuating environment. In this paper, we are particularly interested in a non-autonomous toxic-producing phytoplankton allelopathy model with environmental fluctuation. For the model, we first consider the existence of the global positive solution and the boundary periodic solution. Then, by using Khasminskii's method and Lyapunov function, we derive the sufficient conditions for the existence of the nontrivial positive stochastically periodic solution. Our results show that the allelopathic effect plays an important role in the existence of the stochastic periodic solution, for example it can lead to the decrease of the peaks of the cyclic outbreaks of the harmful algal blooms. Numerical simulations are carried out to support our theoretical results.
Periodic wave solutions of coupled integrable dispersionless equations by residue harmonic balance
Leung, A. Y. T.; Yang, H. X.; Guo, Z. J.
2012-11-01
We introduce the residue harmonic balance method to generate periodic solutions for nonlinear evolution equations. A PDE is firstly transformed into an associated ODE by a wave transformation. The higher-order approximations to the angular frequency and periodic solution of the ODE are obtained analytically. To improve the accuracy of approximate solutions, the unbalanced residues appearing in harmonic balance procedure are iteratively considered by introducing an order parameter to keep track of the various orders of approximations and by solving linear equations. Finally, the periodic solutions of PDEs result. The proposed method has the advantage that the periodic solutions are represented by Fourier functions rather than the sophisticated implicit functions as appearing in most methods.
Topologically Distinct Collision-Free Periodic Solutions for the {N}-Center Problem
Castelli, Roberto
2017-02-01
This work concerns the planar {N}-center problem with homogeneous potential of degree {-α} ({αin[1,2)}). The existence of infinitely many, topologically distinct, non-collision periodic solutions with a prescribed energy is proved. A notion of admissibility in the space of loops on the punctured plane is introduced so that in any admissible class and for any positive {h} the existence of a classical periodic solution with energy {h} for the {N}-center problem with {αin (1,2)} is proven. In case {α=1} a slightly different result is shown: it is the case that there is either a non-collision periodic solution or a collision-reflection solution. The results hold for any position of the centres and it is possible to prescribe in advance the shape of the periodic solutions. The proof combines the topological properties of the space of loops in the punctured plane with variational and geometrical arguments.
YAN Zhen-Ya
2004-01-01
A Weierstrass elliptic function expansion method and its algorithm are developed in this paper. The method changes the problem solving nonlinear evolution equations into another one solving the correspondingsystem of nonlinear algebraic equations. With the aid of symbolic computation (e.g. Maple), the method is applied to the combined KdV-mKdV equation and (2+1)-dimensional coupled Davey-Stewartson equation. As a consequence, many new types of doubly periodic solutions are obtained in terms of the Weierstrass elliptic function. Jacobi elliptic function solutions and solitary wave solutions are also given as simple limits of doubly periodic solutions.
YANZhen-Ya
2004-01-01
A Weierstrass elliptic function expansion method and its algorithm are developed in this paper. The method changes the problem solving nonlinear evolution equations into another one solving the corresponding system of nonlinear algebraic equations. With the aid of symbolic computation (e.g. Maple), the method is applied to the combined KdV-mKdV equation and (2+1)-dimensional coupled Davey-Stewartson equation. As a consequence, many new types of doubly periodic solutions are obtained in terms of the Weierstrass elliptic function. Jacobi elliptic function solutions and solitary wave solutions are also given as simple limits of doubly periodic solutions.
Exact solutions for a periodic assembly of bubbles in a Hele-Shaw channel
Vasconcelos, Giovani L
2014-01-01
Exact solutions are reported for a periodic assembly of bubbles steadily co-travelling in a Hele-Shaw channel. The solutions are obtained as conformal mappings from a multiply connected circular domain in an auxiliary complex plane to the flow region in a period cell. The conformal mappings are constructed using the generalized Schwarz-Christoffel formula for multiply connected polygonal domains in terms of products of Schottky-Klein prime functions. It is shown that previous solutions for multiple steady bubbles in a Hele-Shaw cell are all particular cases of the solutions described herein. Examples of specific bubble configurations are discussed.
On periodic solutions of Goodwin's business cycle model with only floor in induced investment
Antonova, A. O.; Reznik, S. N.; Todorov, M. D.
2013-10-01
We present here an analytical solution of Goodwin's business cycle model in the form of delay differential equation with fixed delay θ and piecewise linear accelerator with only the floor (or the ceiling). We conclude that in this model the time behavior of the solution similar to Goodwin's limit cycle is not possible. These solution looks similar to the oscillation with a period θ, the amplitude of the oscillation growing exponentially to infinity as t →∞. The conditions for existence of the periodic solution in Goodwin's model with fixed delay for the nonlinear accelerator are also discussed.
Jing Liu; Pei-Yong Zhu
2008-01-01
In this paper, the existence, uniqueness and global attractivity are discussed on almost periodic solution of SICNNs (shunting inhibitory cellular neural networks) with continuously distributed delays. By using the fixed point theorem, differential inequality technique and Lyapunov functional method, giving the new ranges of parameters, several sufficient conditions are obtained to ensure the existence, uniqueness and global attractivity of almost periodic solution. Compared with the previous studies, our methods are more effective for almost periodic solution analysis of SICNNs with continuously distributed delays. Some existing results have been improved and extended. In order to show the effectiveness of the obtained results, an example is given in this paper.
Xu, Changjin; Li, Peiluan; Pang, Yicheng
2016-12-01
In this letter, we deal with a class of memristor-based neural networks with distributed leakage delays. By applying a new Lyapunov function method, we obtain some sufficient conditions that ensure the existence, uniqueness, and global exponential stability of almost periodic solutions of neural networks. We apply the results of this solution to prove the existence and stability of periodic solutions for this delayed neural network with periodic coefficients. We then provide an example to illustrate the effectiveness of the theoretical results. Our results are completely new and complement the previous studies Chen, Zeng, and Jiang ( 2014 ) and Jiang, Zeng, and Chen ( 2015 ).
Existence and Attractiveness of Order One Periodic Solution of a Holling I Predator-Prey Model
Huidong Cheng
2012-01-01
Full Text Available According to the integrated pest management strategies, a Holling type I functional response predator-prey system concerning state-dependent impulsive control is investigated. By using differential equation geometry theory and the method of successor functions, we prove the existence of order one periodic solution, and the attractivity of the order one periodic solution by sequence convergence rules and qualitative analysis. Numerical simulations are carried out to illustrate the feasibility of our main results which show that our method used in this paper is more efficient than the existing ones for proving the existence and attractiveness of order one periodic solution.
Time-periodic and stationary solutions to the compressible Hall-magnetohydrodynamic system
Cheng, Ming
2017-04-01
We are concerned with the 3-D compressible Hall-magnetohydrodynamic system with a time-periodic external force in a periodic domain, and establish the existence of a strong time-periodic solution under some smallness and symmetry assumptions by adapting a new approach. The basic idea of the proof is the following. First, we prove the existence of a time-periodic solution to the linearized system by applying the Tychonoff fixed point theorem combined with the energy method and the decay estimates. From the details of the proof, we see that the initial data of the time-periodic solution to the linearized system lies in some convex hull. Then, we construct a set-value function, such that the fixed point of this function is a time-periodic solution of the compressible Hall-magnetohydrodynamic system. The existence of the fixed point is obtained by the Kakutani fixed point theorem. Moreover, we establish the uniqueness of the time-periodic solution and the existence of the stationary solution.
Comment on the uncertainty relation with periodic boundary conditions
Fujikawa, Kazuo
2010-01-01
The Kennard-type uncertainty relation $\\Delta x\\Delta p >\\frac{\\hbar}{2}$ is formulated for a free particle with given momentum $ inside a box with periodic boundary conditions in the large box limit. Our construction of a free particle state is analogous to that of the Bloch wave in a periodic potential. A simple Robertson-type relation, which minimizes the effect of the box boundary and may be useful in some practical applications, is also presented.
ANTI-PERIODIC SOLUTIONS FOR FIRST AND SECOND ORDER NONLINEAR EVOLUTION EQUATIONS IN BANACH SPACES
WEI Wei; XIANG Xiaoling
2004-01-01
In this paper, a new existence theorem of anti-periodic solutions for a class ofstrongly nonlinear evolution equations in Banach spaces is presentedThe equations con-tain nonlinear monotone operators and a nonmonotone perturbationMoreover, throughan appropriate transformation, the existence of anti-periodic solutions for a class of second-order nonlinear evolution equations is verifiedOur abstract results are illustrated by anexample from quasi-linear partial differential equations with time anti-periodic conditionsand an example from quasi-linear anti-periodic hyperbolic differential equations.
Bifurcation of Periodic Solutions and Numerical Simulation for the Viscoelastic Belt
Jing Li
2014-04-01
Full Text Available We study the bifurcation of periodic solutions for viscoelastic belt with integral constitutive law in 1: 1 internal resonance. At the beginning, by applying the nonsingular linear transformation, the system is transformed into another system whose unperturbed system is composed of two planar systems: one is a Hamiltonian system and the other has a focus. Furthermore, according to the Melnikov function, we can obtain the sufficient condition for the existence of periodic solutions and make preparations for studying the stability of the periodic solution and the invariant torus. Eventually, we need to give the phase diagrams of the solutions under different parameters to verify the analytical results and obtain which parameters the existence and the stability of the solution are based on. The conclusions not only enrich the behaviors of nonlinear dynamics about viscoelastic belt but also have important theoretical significance and application value on noise weakening and energy loss.
EXISTENCE OF PERIODIC SOLUTIONS TO THIRD-ORDER NONLINEAR DELAY DIFFERENTIAL EQUATION
A.M.A.Abou-El-Ela; A.I.Sadek; R.O.A.Taie
2011-01-01
By means of the continuation theorem of the coincidence degree theory and analysis techniques,sufficient conditions for the existence of periodic solutions to a kind of third-order neutral delay functional differential equation with deviating arguments are obtained.
2T-PERIODIC SOLUTION FOR m ORDER NEUTRAL TYPE DIFFERENTIAL EQUATIONS WITH TIME DELAYS
张保生; 朱光辉
2002-01-01
Periodic solution of m order linear neutral equations with constant coefficient and time delays was studied. Existence and uniqueness of 2 T-periodic solutions for the equation were discussed by using the method of Fourier series. Some new necessary and sufficient conditions of existence and uniqueness of 2 T-periodic solutions for the equation are obtained. The main result is used widely. It contains results in some correlation paper for its special case, improves and extends the main results in them. Existence of periodic solution for the equation in larger number of particular case can be checked by using the result, but cannot be checked in another paper. In other words, the main result in this paper is most generalized for (1), the better result cannot be found by using the same method.
Existence and Uniqueness of Periodic Solutions for Second Order Differential Equations
Yuanhong Wei
2014-01-01
We study some second order ordinary differential equations. We establish the existence and uniqueness in some appropriate function space. By using Schauder’s fixed-point theorem, new results on the existence and uniqueness of periodic solutions are obtained.
Reithmeier, Eduard
1991-01-01
Limit cycles or, more general, periodic solutions of nonlinear dynamical systems occur in many different fields of application. Although, there is extensive literature on periodic solutions, in particular on existence theorems, the connection to physical and technical applications needs to be improved. The bifurcation behavior of periodic solutions by means of parameter variations plays an important role in transition to chaos, so numerical algorithms are necessary to compute periodic solutions and investigate their stability on a numerical basis. From the technical point of view, dynamical systems with discontinuities are of special interest. The discontinuities may occur with respect to the variables describing the configuration space manifold or/and with respect to the variables of the vector-field of the dynamical system. The multiple shooting method is employed in computing limit cycles numerically, and is modified for systems with discontinuities. The theory is supported by numerous examples, mainly fro...
Existence and uniqueness of periodic solutions for forced Liénard-type equations
LIU Bing-wen
2008-01-01
By using topological degree theory and some analysis skill, some sufficient conditions for the existence and uniqueness of periodic solutions for a class of forced Liénard-type equations are obtained.
TWIN POSITIVE PERIODIC SOLUTIONS OF FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAY
无
2006-01-01
In this paper, the author studies a class of nonlinear functional differential equation. By using a fixed point theorem in cones, sufficient conditions are established for the existence of twin positive periodic solutions.
Darboux coordinates for periodic solutions of the sinh-Gordon equation
Knopf, Markus
2016-12-01
We study the space of periodic solutions of the elliptic sinh-Gordon equation by means of spectral data consisting of a Riemann surface Y and a divisor D and prove the existence of certain Darboux coordinates.
ON THE EXISTENCE OF POSITIVE ALMOST PERIODIC SOLUTIONS TO AN IMPULSIVE NEURAL NETWORKS WITH DELAY
无
2012-01-01
In this paper,Hopfield neural networks with delays and impulses are considered.By means of mathematical analysis techniques,some sufficient conditions for the existence of positive almost periodic solutions are obtained.
Yongkun Li
2005-01-01
Full Text Available We study the existence and exponential attractivity of periodic solutions to Cohen-Grossberg neural network with distributed delays. Our results are obtained by applying the continuation theorem of coincidence degree theory and a general Halanay inequality.
Positive Almost Periodic Solutions for a Time-Varying Fishing Model with Delay
Xia Li
2011-01-01
Full Text Available This paper is concerned with a time-varying fishing model with delay. By means of the continuation theorem of coincidence degree theory, we prove that it has at least one positive almost periodic solution.
EXISTENCE OF PERIODIC SOLUTIONS TO A LINARD EQUATION WITH MULTIPLE DELAYS
无
2011-01-01
In this paper,by a coincidence degree theory,the existence of periodic solutions to a Linard equation with multiple delays is established,which substantially extends some results in the previous literatures.
EXISTENCE OF POSITIVE PERIODIC SOLUTIONS TO A SECOND-ORDER DIFFERENTIAL INCLUSION
无
2012-01-01
In this paper,the existence of positive periodic solutions to a second-order differential inclusion is considered.Some existence results are established by the fixed-point theorem for multivalued operators and Sobolev constant.
EXISTENCE OF PERIODIC SOLUTIONS TO A KIND OF n-ORDER NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATION
无
2009-01-01
By means of the continuation theorem of coincidence degree theory, we study a kind of n-order neutral functional differential equation. Some new results on the existence of periodic solutions are obtained.
Shi Ping LU; Wei Gao GE
2005-01-01
By means of the continuation theorem of coincidence degree theory, some new results on the non-existence, existence and unique existence of periodic solutions for a kind of second order neutral functional differential equation are obtained.
Existence of infinitely many periodic solutions for second-order nonautonomous Hamiltonian systems
Wen Guan
2015-04-01
Full Text Available By using minimax methods and critical point theory, we obtain infinitely many periodic solutions for a second-order nonautonomous Hamiltonian systems, when the gradient of potential energy does not exceed linear growth.
LIU Shi-Kuo; GAO Bin; FU Zun-Tao; LIU Shi-Da
2009-01-01
In this paper, applying the dependent and independent variables transformations as well as the Jacobi elliptic function expansion method, the envelope periodic solutions to one-dimensional Gross-Pitaevskii equation in Bose-Einstein condensates are obtained.
POSITIVE PERIODIC SOLUTIONS TO NEUTRAL RATIO-DEPENDENT PREDATOR-PREY SYSTEM
无
2012-01-01
Using Mawhin's continuation theorem of coincidence degree theory,the existenceof periodic solutions to a neutral ratio-dependent predator-prey system is considered.The results in this paper generalize the corresponding results of the known literature.
Periodic Wave Solutions of Generalized Derivative Nonlinear Schr(o)dinger Equation
ZHA Qi-Lao; LI Zhi-Bin
2008-01-01
A Darboux transformation of the generalized derivative nonlinear Schr(o)dinger equation is derived. As an application, some new periodic wave solutions of the generalized derivative nonlinear Schr(o)dinger equation are explicitly given.
Bifurcations of Invariant Tori and Subharmonic Solutions for Periodic Perturbed Systems
韩茂安
1994-01-01
The time-periodic perturbations of planar Hamiltonian systems are investigated.A necessary condition for the existence of an invariant torus,a sufficient condition for the bifurcation of a unique invariant torus and a subharmonic solution are obtained.
EXISTENCE OF PERIODIC SOLUTIONS OF THE BURGERS-GINZBURG-LANDAU EQUATIONS
黄海洋
2004-01-01
In this paper, the existence of the periodic solutions for a forced Burgers equation coupled to a non-homogeneous Ginzburg-Landau equation is proved by LeraySchauder fixed point theorem and Galerkin method under appropriate conditions.
Zheng-qiu ZHANG; Zhi-cheng WANG
2007-01-01
In this paper, the existence of two positive periodic solutions for a generalized delayed population model with an exploited term is established by using the continuation theorem of the coincidence degree theory.
Periodic Solutions for Some Second-order Differential System with p(t)-Laplacian
WANG Qi; LU Di-cheng; MA Qi; DAI Jin
2015-01-01
In this article, we investigate the existence of periodic solutions for a class of nonautonomous second-order differential systems with p(t)-Laplacian. Some multiplicity results are obtained by using critical point theory, which extend some known results.
Stability analysis for periodic solutions of the Van der Pol-Duffing forced oscillator
Cui, Jifeng; Liang, Jiaming; Lin, Zhiliang
2016-01-01
Based on the homotopy analysis method (HAM), the high accuracy frequency response curve and the stable/unstable periodic solutions of the Van der Pol-Duffing forced oscillator with the variation of the forced frequency are obtained and studied. The stability of the periodic solutions obtained is analyzed by use of Floquet theory. Furthermore, the results are validated in the light of spectral analysis and bifurcation theory.
无
2007-01-01
In this paper, global exponential stability of almost periodic solution of cellular neural networks with time-varing delays (CNNVDs) is considered. By using the methods of the topological degree theory and generalized Halanay inequality, a few new applicable criteria are established for the existence and global exponential stability of almost periodic solution. Some previous results are improved and extended in this letter and one example is given to illustrate the effectiveness of the new results.
Positive Almost Periodic Solution on a Nonlinear Logistic Biological Model with Grazing Rates
NI Hua; TIAN Li-xin
2013-01-01
In this paper,we study the following nonlinear biological model dx(t)/dt =x(t)[a(t)-b(t)xα(t)] + f(t,xt),by using fixed pointed theorem,the sufficient conditions of the existence of unique positive almost periodic solution for the above system are obtained,by using the theories of stability,the sufficient conditions which guarantee the stability of the positive almost periodic solution are derived.
Positive solutions for a nonlinear periodic boundary-value problem with a parameter
Jingliang Qiu
2012-08-01
Full Text Available Using topological degree theory with a partially ordered structure of space, sufficient conditions for the existence and multiplicity of positive solutions for a second-order nonlinear periodic boundary-value problem are established. Inspired by ideas in Guo and Lakshmikantham [6], we study the dependence of positive periodic solutions as a parameter approaches infinity, $$ lim_{lambdao +infty}|x_{lambda}|=+infty,quadhbox{or}quad lim_{lambdao+infty}|x_{lambda}|=0. $$
Xiao-Bao Shu
2013-06-01
Full Text Available In this article, we study the existence of an infinite number of subharmonic periodic solutions to a class of second-order neutral nonlinear functional differential equations. Subdifferentiability of lower semicontinuous convex functions $varphi(x(t,x(t-au$ and the corresponding conjugate functions are constructed. By combining the critical point theory, Z2-group index theory and operator equation theory, we obtain the infinite number of subharmonic periodic solutions to such system.
S-asymptotically -periodic Solutions of R-L Fractional Derivative-Integral Equation
WANG Bing
2015-01-01
The aim of this paper is to study the S-asymptotically ω-periodic solutions of R-L fractional derivative-integral equation:is a linear densely defined operator of sectorial type on a completed Banach space X, f is a continuous function satisfying a suitable Lipschitz type condition. We will use the contraction mapping theory to prove problem (1) and (2) has a unique S-asymptotically ω-periodic solution if the function f satisfies Lipshcitz condition.
New Exact Travelling Wave and Periodic Solutions of Discrete Nonlinear Schr(o)dinger Equation
YANG Qin; DAI Chao-Qing; ZHANG Jie-Fang
2005-01-01
Some new exact travelling wave and period solutions of discrete nonlinear Schrodinger equation are found by using a hyperbolic tangent function approach, which was usually presented to find exact travelling wave solutions of certain nonlinear partial differential models. Now we can further extend the new algorithm to other nonlinear differentialdifferent models.
The periodic wave solutions for two systems of nonlinear wave equations
王明亮; 王跃明; 张金良
2003-01-01
The periodic wave solutions for the Zakharov system of nonlinear wave equations and a long-short-wave interaction system are obtained by using the F-expansion method, which can be regarded as an overall generalization of Jacobi elliptic function expansion proposed recently. In the limit cases, the solitary wave solutions for the systems are also obtained.
EXISTENCE AND MULTIPLICITY OF POSITIVE SOLUTIONS TO THIRD-ORDER PERIODIC BOUNDARY VALUE PROBLEM
无
2011-01-01
The existence and multiplicity of positive solutions to a periodic boundary value problem for nonlinear third-order ordinary differential equation are established, based on the zero point theorem concerning cone expansion and compression of order type. Our main approach is different from the previous papers on the existence of multiple positive solutions to the similar problem.
EXISTENCE OF SOLUTIONS TO 2m-ORDER PERIODIC BOUNDARY VALUE PROBLEM
无
2012-01-01
In this paper, we are concerned with the existence of nontrivial solutions to a 2m-order nonlinear periodic boundary value problem. By the infinite dimensional Morse theory, under some conditions on nonlinear term, we obtain that there exist at least two nontrivial solutions.
BIFURCATIONS OF SUBHARMONIC SOLUTIONS IN PERIODIC PERTURBATION OF A HYPERBOLIC LIMIT CYCLE
韩茂安; 顾圣士
2002-01-01
Bifurcations of subharmonic solutions of order m of a planar periodic perturbed system near a hyperbolic limit cycle are discussed. By using a Poincare map and the method of rescaling a discriminating condition for the existence of subharmonic solutions of order m is obtained. An example is given in the end of the paper.
Solution to the initial value problem of the ultradiscrete periodic Toda equation
Idzumi, Makoto [Department of Mathematics, Faculty of Education, Shimane University, Matsue, Shimane 690-8504 (Japan); Iwao, Shinsuke; Tokihiro, Tetsuji [Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Tokyo 153-8914 (Japan); Mada, Jun [College of Industrial Technology, Nihon University, 2-11-1 Shin-ei, Narashino, Chiba 275-8576 (Japan)
2009-08-07
We present an expression for the solution to the initial value problem for the ultradiscrete periodic Toda equation. The expression provides explicit forms of all dependent variables of the equation, while the previously known solutions give only half of the dependent variables while the others have to be determined implicitly using the conserved quantities.
The role of periodic solutions in the Falkner-Skan problem for λ > 0
Botta, E.F.T.; Hut, F.J.; Veldman, A.E.P.
1986-01-01
The Falkner-Skan equation f '" + ff" + λ(1 - f'^2) = 0 is discussed for λ > 0. Two types of solutions have been pursued: those satisfying f(0) = f'(0) = 0, f'(∞) = 1 and those being periodic. In both cases, numerical evidence is given for a rich structure of multiple solutions. Branching occurs for
The role of periodic solutions in the Falkner-Skan problem for λ > 0
Botta, E.F.T.; Hut, F.J.; Veldman, A.E.P.
1986-01-01
The Falkner-Skan equation f '" + ff" + λ(1 - f'^2) = 0 is discussed for λ > 0. Two types of solutions have been pursued: those satisfying f(0) = f'(0) = 0, f'(∞) = 1 and those being periodic. In both cases, numerical evidence is given for a rich structure of multiple solutions. Branching occurs for
Shanying Zhu
2009-01-01
This paper deals with the existence of positive solutions to the singular second-order periodic boundary value problem, We obtain the existence results of positive solutions by the fixed point index theory. The results obtained extend and complement some known results.
Exact periodic wave and soliton solutions in two-component Bose-Einstein condensates
Li Hua-Mei
2007-01-01
We present several families of exact solutions to a system of coupled nonlinear Schr(o)dinger equations. The model describes a binary mixture of two Bose-Einstein condensates in a magnetic trap potential. Using a mapping deformation method, we find exact periodic wave and soliton solutions, including bright and dark soliton pairs.
Fonda, Alessandro
2016-01-01
This book provides an up-to-date description of the methods needed to face the existence of solutions to some nonlinear boundary value problems. All important and interesting aspects of the theory of periodic solutions of ordinary differential equations related to the physical and mathematical question of resonance are treated. The author has chosen as a model example the periodic problem for a second order scalar differential equation. In a paedagogical style the author takes the reader step by step from the basics to the most advanced existence results in the field.
Curious interior solutions of general relativity
Kozyrev, S M
2010-01-01
In this article, we provide a discussion on a composite class of exact static spherically symmetric vacuum solutions of Einstein's equations. We construct the composite solution of Einstein field equation by match the interior vacuum metric in Schwarzschild original gauge, to the exterior vacuum metric in isotropic gauge, at a junction surface. This approach allows us to associate rigorously with both gauges as a same "space", which is a unique differentiable manifold M^4
Stabilization of periodic solutions in a tethered satellite system by damping injection
Larsen, Martin Birkelund; Blanke, Mogens
2009-01-01
presents a control design for stabilizing these periodic solutions. The design consists of a control law for stabilizing the open-loop equilibrium and a bias term which forces the system trajectory away from the equilibrium. The tether needs to be positioned away from open-loop equilibrium for the tether...... to affect the orbit parameters. An approximation of the periodic solutions of the closed loop system is found as a series expansion in the parameter plane spanned by the controller gain and the bias term. The stability of the solutions is investigated using linear Floquet analysis of the variational...
Toka Diagana
2011-02-01
Full Text Available First we show that if the doubly-weighted Bohr spectrum of an almost periodic function exists, then it is either empty or coincides with the Bohr spectrum of that function. Next, we investigate the existence of doubly-weighted pseudo-almost periodic solutions to some non-autonomous abstract differential equations.
A Newton-Picard collocation method for periodic solutions of delay differential equations
Verheyden, Koen; Lust, Kurt
This paper presents a collocation method with an iterative linear system solver to compute periodic solutions of a system of autonomous delay differential equations (DDEs). We exploit the equivalence of the linearized collocation system and the discretization of the linearized periodic boundary
Unique Existence Theorem of Solution of Almost Periodic Differential Equations on Time Scales
Meng Hu
2012-01-01
Full Text Available By using the theory of calculus on time scales and M-matrix theory, the unique existence theorem of solution of almost periodic differential equations on almost periodic time scales is established. The result can be used to a large of dynamic systems.
Unique Existence Theorem of Solution of Almost Periodic Differential Equations on Time Scales
Meng Hu; Lili Wang
2012-01-01
By using the theory of calculus on time scales and M-matrix theory, the unique existence theorem of solution of almost periodic differential equations on almost periodic time scales is established. The result can be used to a large of dynamic systems.
Zheyan Zhou
2011-01-01
Full Text Available We propose a discrete multispecies cooperation and competition predator-prey systems. For general nonautonomous case, sufficient conditions which ensure the permanence and the global stability of the system are obtained; for periodic case, sufficient conditions which ensure the existence of a globally stable positive periodic solution of the system are obtained.
Almost Periodic Solutions of Prey-Predator Discrete Models with Delay
Itokazu Tomomi
2009-01-01
Full Text Available Abstract The purpose of this article is to investigate the existence of almost periodic solutions of a system of almost periodic Lotka-Volterra difference equations which are a prey-predator system and a competitive system , by using certain stability properties, which are referred to as -weakly uniformly asymptotic stable in hull and -totally stable.
Periodic Solutions of a Delayed Predator-Prey Model with Stage Structure for Prey
Rui Xu; Lan-sun Chen; Fei-long Hao
2004-01-01
A periodic predator-prey model with stage structure for prey and time delays due to negative feedbackand gestation of predator is proposed. By using Gaines and Mawhin's continuation theorem of coincidencedegree theory, su.cient conditions are derived for the existence of positive periodic solutions to the proposedmodel. Numerical simulations are presented to illustrate the feasibility of our main result.
PERIODIC SOLUTIONS FOR A DISCRETE TIME RATIO-DEPENDENT TWO PREDATOR-ONE PREY SYSTEM
柏灵; 范猛; 王克
2004-01-01
In this paper, we consider a three-species ratio-dependent predator-prey model governed by difference equations with periodic coefficients. By using the method of coincidence degree, we discuss the existence of positive periodic solutions of this system, a set of easily verifiable sufficient conditions are derived.
Positive Periodic Solutions of Cooperative Systems with Delays and Feedback Controls
Tursuneli Niyaz
2013-01-01
Full Text Available This paper studies a class of periodic n species cooperative Lotka-Volterra systems with continuous time delays and feedback controls. Based on the continuation theorem of the coincidence degree theory developed by Gaines and Mawhin, some new sufficient conditions on the existence of positive periodic solutions are established.
ALMOST PERIODIC SOLUTION OF A NONAUTONOMOUS DIFFUSIVE FOOD CHAIN SYSTEM OF THREE SPECIES
LuoGuilie
1999-01-01
In this paper,the almost periodic nonautonomous diffusive food chain system of threespecies is discussed. By using the comparison theorem and V-function method,the author provesthe existence and uniqueness of a positive almost periodic solution,and its stability under disturbances from the hull.
Global Attractivity of Positive Periodic Solutions for a Survival Model of Red Blood Cells
Xin-min Wu; Jing-wen Li
2007-01-01
In this paper, we deal with a model for the survival of red blood cells with periodic coefficients x′(t)=- μ(t)x(t)+P(t)e-γ(t)x(t-(τ))＞0. (*)A new sufficient condition for global attractivity of positive periodic solutions of Eq.(*) is obtained. Our criterion improves corresponding result obtained by Li and Wang in 2005.
Jia Junguo [Department of Applied Mathematics, Xi' an Jiaotong University, Xi' an 710049 (China) and Department of Mathematics, Zhengzhou University, Zhengzhou, Henan 450001 (China)]. E-mail: jungjia2@zzu.edu.cn; Wang Miansen [Department of Applied Mathematics, Xi' an Jiaotong University, Xi' an 710049 (China); Li Meili [Department of Applied Mathematics, Xi' an Jiaotong University, Xi' an 710049 (China)
2007-05-15
In this paper, a two-dimensional non-autonomous system with impulse that arises in plankton allelopathy involving discrete time delays and periodic environmental factors is studied. By the theory of the coincidence degree we obtain the conditions for the existence of periodic solution of this system.
Deep water periodic waves as Hamiltonian relative equilibria
van Groesen, Embrecht W.C.; Lie She Liam, L.S.L.; Lakhturov, I.; Andonowati, A.; Biggs, N.
2007-01-01
We use a recently derived KdV-type of equation for waves on deep water to study Stokes waves as relative equilibria. Special attention is given to investigate the cornered Stokes-120 degree wave as a singular solution in the class of smooth steady wave profiles.
Botello-Smith, Wesley M.; Luo, Ray
2016-01-01
Continuum solvent models have been widely used in biomolecular modeling applications. Recently much attention has been given to inclusion of implicit membrane into existing continuum Poisson-Boltzmann solvent models to extend their applications to membrane systems. Inclusion of an implicit membrane complicates numerical solutions of the underlining Poisson-Boltzmann equation due to the dielectric inhomogeneity on the boundary surfaces of a computation grid. This can be alleviated by the use of the periodic boundary condition, a common practice in electrostatic computations in particle simulations. The conjugate gradient and successive over-relaxation methods are relatively straightforward to be adapted to periodic calculations, but their convergence rates are quite low, limiting their applications to free energy simulations that require a large number of conformations to be processed. To accelerate convergence, the Incomplete Cholesky preconditioning and the geometric multi-grid methods have been extended to incorporate periodicity for biomolecular applications. Impressive convergence behaviors were found as in the previous applications of these numerical methods to tested biomolecules and MMPBSA calculations. PMID:26389966
Grout Spread and Injection Period of Silica Solution and Cement Mix in Rock Fractures
El Tani, Mohamed; Stille, Håkan
2017-09-01
A systematic presentation of the analytic relations of grout spread to the time period is established. They are divided following the nature of the flow, the property of the mix and the driving process. This includes channel flow between parallel plates and radial flow between parallel discs, nonlinear Newtonian fluids like silica solution, polyurethane and epoxy, and Bingham material like cement-based grout, and three grouting processes at a constant flow rate, constant pressure and constant energy. The analytic relations for the constant energy process are new and complete the relations of the constant flow rate and constant pressure processes. The well-known statement that refusal cannot be obtained during finite time for any injected material at a constant flow rate or constant injection pressure is extended to include the energy process. The term refusal pressure or energy cannot be supported for stop criteria. Stop criteria have to be defined considering confirmed relation of the spread to the time period and of the flow rate to the pressure and spread. It is shown that it is always possible to select a grouting process along which the work will exceed any predefined energy, the consequence of which is that jacking is related to the applied forces and not to the injected energy. Furthermore, a clarification is undertaken concerning the radial flow rate of a Bingham material since there are two different formulations. Their difference is explained and quantified. Finally, it is shown that the applied Lugeon theory is not supported by the analytic relations and needs to be substantially modified.
SDP-based approximation of stabilising solutions for periodic matrix Riccati differential equations
Gusev, Sergei V.; Shiriaev, Anton S.; Freidovich, Leonid B.
2016-07-01
Numerically finding stabilising feedback control laws for linear systems of periodic differential equations is a nontrivial task with no known reliable solutions. The most successful method requires solving matrix differential Riccati equations with periodic coefficients. All previously proposed techniques for solving such equations involve numerical integration of unstable differential equations and consequently fail whenever the period is too large or the coefficients vary too much. Here, a new method for numerical computation of stabilising solutions for matrix differential Riccati equations with periodic coefficients is proposed. Our approach does not involve numerical solution of any differential equations. The approximation for a stabilising solution is found in the form of a trigonometric polynomial, matrix coefficients of which are found solving a specially constructed finite-dimensional semidefinite programming (SDP) problem. This problem is obtained using maximality property of the stabilising solution of the Riccati equation for the associated Riccati inequality and sampling technique. Our previously published numerical comparisons with other methods shows that for a class of problems only this technique provides a working solution. Asymptotic convergence of the computed approximations to the stabilising solution is proved below under the assumption that certain combinations of the key parameters are sufficiently large. Although the rate of convergence is not analysed, it appeared to be exponential in our numerical studies.
Murashige, Sunao
This paper considers numerical methods for stability analyses of periodic solutions of ordinary differential equations. Stability of a periodic solution can be determined by the corresponding monodromy matrix and its eigenvalues. Some commonly used numerical methods can produce inaccurate results of them in some cases, for example, near bifurcation points or when one of the eigenvalues is very large or very small. This work proposes a numerical method using a periodic boundary condition for vector fields, which preserves a critical property of the monodromy matrix. Numerical examples demonstrate effectiveness and a drawback of this method.
Periodic Solutions of Duffing Equation with an Asymmetric Nonlinearity and a Deviating Argument
Zaihong Wang
2013-01-01
Full Text Available We study the existence of periodic solutions of the second-order differential equation x′′+ax+-bx-+g(x(t-τ=p(t, where a,b are two constants satisfying 1/a+1/b=2/n, n∈N, τ is a constant satisfying 0≤τ<2π, g,p:R→R are continuous, and p is 2π-periodic. When the limits limx→±∞g(x=g(±∞ exist and are finite, we give some sufficient conditions for the existence of 2π-periodic solutions of the given equation.
Hui-Sheng Ding
2013-04-01
Full Text Available In this paper, we first introduce a new class of pseudo almost periodic type functions and investigate some properties of pseudo almost periodic type functions; and then we discuss the existence of pseudo almost periodic solutions to the class of abstract partial functional differential equations $x'(t=Ax(t+f(t,x_t$ with finite delay in a Banach space X.
The cubic period-distance relation for the Kate reversible pendulum
Rossi, Michele; Zaninetti, Lorenzo
2005-12-01
We describe the correct cubic relation between the mass configuration of a Kater reversible pendulum and its period of oscillation. From an analysis of its solutions we conclude that there could be as many as three distinct mass configurations for which the periods of small oscillations about the two pivots of the pendulum have the same value. We also discuss a real compound Kater pendulum that realizes this property.
The cubic period-distance relation for the Kater reversible pendulum
Rossi, Michele; Zaninetti, Lorenzo
2005-01-01
We describe the correct cubic relation between the mass configuration of a Kater reversible pendulum and its period of oscillation. From an analysis of its solutions we conclude that there could be as many as three distinct mass configurations for which the periods of small oscillations about the two pivots of the pendulum have the same value. We also discuss a real compound Kater pendulum that realizes this property.
Near Periodic solution of the Elliptic RTBP for the Jupiter Sun system
Perdomo, Oscar M
2016-01-01
Let us consider the elliptic restricted three body problem (Elliptic RTBP) for the Jupiter Sun system with eccentricity $e=0.048$ and $\\mu=0.000953339$. Let us denote by $T$ the period of their orbits. In this paper we provide initial conditions for the position and velocity for a spacecraft such that after one period $T$ the spacecraft comes back to the same place, with the same velocity, within an error of 4 meters for the position and 0.2 meters per second for the velocity. Taking this solution as periodic, we present numerical evidence showing that this solution is stable. In order to compare this periodic solution with the motion of celestial bodies in our solar system, we end this paper by providing an ephemeris of the spacecraft motion from February 17, 2017 to December 28, 2028.
Kuiper, Logan K
2016-01-01
An approximate solution to the two dimensional Navier Stokes equation with periodic boundary conditions is obtained by representing the x any y components of fluid velocity with complex Fourier basis vectors. The chosen space of basis vectors is finite to allow for numerical calculations, but of variable size. Comparisons of the resulting approximate solutions as they vary with the size of the chosen vector space allow for extrapolation to an infinite basis vector space. Results suggest that such a solution, with the full basis vector space and which would give the exact solution, would fail for certain initial velocity configurations when initial velocity and time t exceed certain limits.
New period-luminosity and period-color relations of classical Cepheids: III. Cepheids in SMC
Sandage, A; Reindl, B
2008-01-01
The photometric data for 460 classical, fundamental-mode Cepheids in the SMC with log P > 0.4 measured by Udalski et al. have been analyzed for their P-C and P-L relations, and for the variation of amplitude across the instability strip in a similar way that was done in Papers I and II of this series. The SMC Cepheids are bluer in (B-V) at a given period than for both the Galaxy and the LMC. Their P-C relation in (B-V) is best fit by two lines intersecting at P=10 d. Their break must necessarily exist also in the P-L relations in B and/or V, but remains hidden in the magnitude scatter. An additional pronounced break of the P-L relations in B, V, and I occurs at P=2.5 d. The observed slope of the lines of constant period in the HR diagram agrees with the theoretical expectation from the pulsation equation. The largest amplitude Cepheids for periods less than 13 days occur near the blue edge of the instability strip. The sense is reversed in the period interval from 13 to 20 days, as in the Galaxy and the LMC. ...
Koprivica, Slavica; Siller, Martin; Hosoya, Takashi; Roggenstein, Walter; Rosenau, Thomas; Potthast, Antje
2016-04-21
A method for easy and fast regeneration of aqueous periodate solutions from dialdehyde cellulose (DAC) production by ozone treatment is presented, along with a direct and reliable simultaneous quantification of iodate and periodate by reversed-phase HPLC. The influence of iodate and ozone concentration, solution pH, and reaction time on the regeneration efficiency was studied, as well as the reaction kinetics. Regeneration of spent periodate solutions by ozone was successfully performed in alkaline medium, which favors the formation of free (.) OH radicals, as supported by the addition of radical scavengers and quantum mechanical calculations. At pH 13 and an ozone concentration of approximately 150 mg L(-1) , periodate was completely regenerated from a 100 mm solution of iodate within 1 h at room temperature. A cyclic process of cellulose oxidation and subsequent regeneration of spent periodate with 90 % efficiency has been developed. So far, commercial applications of DAC have been hampered by difficulties in reusing the costly periodate. This work overcomes this hurdle and presents a highly efficient, clean, and low-cost protocol for the preparation of DAC with integrated periodate recycling, with the possibility of scaling the process up.
Dehghan, Mehdi [Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No. 424, Hafez Ave., Tehran (Iran, Islamic Republic of)]. E-mail: mdehghan@aut.ac.ir; Mazrooei-Sebdani, Reza [Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No. 424, Hafez Ave., Tehran (Iran, Islamic Republic of)]. E-mail: mazrooei@aut.ac.ir
2007-05-15
We obtain some results about the global attractivity of bounded solutions of difference equation x{sub n+1}=f(x{sub n},x{sub n-1},...,x{sub n-k}), n=0,1,... where f is non-increasing or non-decreasing in each argument and every point in I is an equilibrium point of above equation where I is an invariant interval for this equation. By our results we prove that when k is an odd positive integer and p>=1 is a real number, every positive solution ofx{sub n+1}=p+x{sub n-k}1+x{sub n},n=0,1,...converges to a period-two solution of this equation. We also apply our results to the rational difference equationx{sub n+1}=1+x{sub n-2k+1}x{sub n-2l},n=0,1,...where k,l-bar {l_brace}0,1,...{r_brace}, and we show that every positive solution of this equation converges to a period-two solution of this equation.
Maria Clara da Silva Valadão
2015-10-01
Full Text Available ABSTRACT OBJECTIVE: To compare two electrolyte maintenance solutions in the postoperative period in children undergoing appendectomy, in relation to the occurrence of hyponatremia and water retention. METHODS: A randomized clinical study involving 50 pediatric patients undergoing appendectomy, who were randomized to receive 2,000 mL/m2/day of isotonic (Na 150 mEq/L or 0.9% NaCl or hypotonic (Na 30 mEq/L NaCl or 0.18% solution. Electrolytes, glucose, urea, and creatinine were measured at baseline, 24 h, and 48 h after surgery. Volume infused, diuresis, weight, and water balance were analyzed. RESULTS: Twenty-four patients had initial hyponatremia; in this group, 13 received hypotonic solution. Seventeen patients remained hyponatremic 48 h after surgery, of whom ten had received hypotonic solution. In both groups, sodium levels increased at 24 h (137.4 ± 2.2 and 137.0 ± 2.7 mmol/L, with no significant difference between them (p = 0.593. Sodium levels 48 h after surgery were 136.6 ± 2.7 and 136.2 ± 2.3 mmol/L in isotonic and hypotonic groups, respectively, with no significant difference. The infused volume and urine output did not differ between groups during the study. The water balance was higher in the period before surgery in patients who received hypotonic solution (p = 0.021. CONCLUSIONS: In the post-appendectomy period, the use of hypotonic solution (30 mEq/L, 0.18% did not increase the risk of hyponatremia when compared to isotonic saline. The use of isotonic solution (150 mEq/L, 0.9% did not favor hypernatremia in these patients. Children who received hypotonic solution showed higher cumulative fluid balance in the preoperative period.
Ma Hong-Cai; Ge Dong-Jie; Yu Yao-Dong
2008-01-01
Based on the B(a)cklund method and the multilinear variable separation approach (MLVSA), this paper finds a general solution including two arbitrary functions for the (2+1)-dimensional Burgers equations. Then a class of new doubly periodic wave solutions for (2+1)-dimensional Burgers equations is obtained by introducing appropriate Jacobi elliptic functions, Weierstrass elliptic functions and their combination in the general solutions (which contains two arbitrary functions). Two types of limit cases are considered. Firstly, taking one of the moduli to be unity and the other zero, it obtains particular wave (called semi-localized) patterns, which is periodic in one direction, but localized in the other direction. Secondly, if both moduli are tending to 1 as a limit, it derives some novel localized excitations (two-dromion solution).
Existence of positive periodic solution of mutualism system with several delays
Wu Haihui [College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350002 (China); Department of Computer Science and Technology, Sunshine College, Fuzhou University, Fuzhou 350002 (China); Xia Yonghui [College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350002 (China)], E-mail: yhxia@fzu.edu.cn; Lin Muren [College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350002 (China)
2008-04-15
In this paper, by using Mawhin coincidence degree, some sufficient conditions are obtained for the global existence of positive periodic solutions of a mutualism systems with bounded and unbounded delays. Our results generalize significantly improve those of Gopalsamy and He [Gopalsamy K, He XZ. Persistence, attractivity, and delay in facultative mutualism. J Math Anal Appl 1997;215:154-73], Yang et al. [Yang F, Jiang D, Ying A. Existence of positive solution of multidelays facultative mutualism system. J Eng Math 2002;3:64-8], Chen et al. [Chen FD, Shi JL, Chen XX. Periodicity in Lotka-Volterra facultative mutualism system with several delays. J Eng Math 2004;21(3)] and Xia and Lin [Xia YH, Lin M, Existence of positive periodic solution of mutualism system with infinite delays. Ann Diff Eqs 2005;21(3):448-53].
Bifurcations and Periodic Solutions for an Algae-Fish Semicontinuous System
Chuanjun Dai
2013-01-01
Full Text Available We propose an algae-fish semicontinuous system for the Zeya Reservoir to study the control of algae, including biological and chemical controls. The bifurcation and periodic solutions of the system were studied using a Poincaré map and a geometric method. The existence of order-1 periodic solution of the system is discussed. Based on previous analysis, we investigated the change in the location of the order-1 periodic solution with variable parameters and we described the transcritical bifurcation of the system. Finally, we provided a series of numerical results to illustrate the feasibility of the theoretical results. These results may help to facilitate a better understanding of algal control in the Zeya Reservoir.
Phenomena in late period of seeded precipitation of sodium aluminate solution
LI Xiao-bin; FENG Gang-tao; ZHOU Qiu-sheng; PENG Zhi-hong; LIU Gui-hua
2006-01-01
Aiming at seeded precipitation of aluminate solution with high caustic ratio(αk＞2.4), corresponding to the late period of seeded precipitation, the influence of different types of seed on precipitation ratio was explained with respect to solution structure in the interface of seed and the evolution of Al(OH)3 growth units in this layer. The effects of solid content and seed size on agglomeration were determined by calculating the particle number of product. The results imply that the solution structure in the interface of seed imposes a notable significance on the process in the late period of seeded precipitation. Agglomeration still exists in this period. However, the agglomeration bodies break in the case of prolonging precipitation due to the mechanical effect, which results in the increase of particle number.
Extended F-Expansion Method and Periodic Wave Solutions for Klein-Gordon-Schr(o)dinger Equations
LI Xiao-Yan; LI Xiang-Zheng; WANG Ming-Liang
2006-01-01
We present an extended F-expansion method for finding periodic wave solutions of nonlinear evolution equations in mathematical physics. By using extended F-expansion method, many periodic wave solutions expressed by various Jacobi elliptic functions for the Klein-Gordon-Schrodinger equations are obtained. In the limit cases, the solitary wave solutions and trigonometric function solutions for the equations are also obtained.
Exact solutions to plaquette Ising models with free and periodic boundaries
Mueller, Marco; Johnston, Desmond A.; Janke, Wolfhard
2017-01-01
An anisotropic limit of the 3d plaquette Ising model, in which the plaquette couplings in one direction were set to zero, was solved for free boundary conditions by Suzuki (1972) [1], who later dubbed it the fuki-nuke, or "no-ceiling", model. Defining new spin variables as the product of nearest-neighbour spins transforms the Hamiltonian into that of a stack of (standard) 2d Ising models and reveals the planar nature of the magnetic order, which is also present in the fully isotropic 3d plaquette model. More recently, the solution of the fuki-nuke model was discussed for periodic boundary conditions, which require a different approach to defining the product spin transformation, by Castelnovo et al. (2010) [2]. We clarify the exact relation between partition functions with free and periodic boundary conditions expressed in terms of original and product spin variables for the 2d plaquette and 3d fuki-nuke models, noting that the differences are already present in the 1d Ising model. In addition, we solve the 2d plaquette Ising model with helical boundary conditions. The various exactly solved examples illustrate how correlations can be induced in finite systems as a consequence of the choice of boundary conditions.
Anti-periodic solutions of Liénard equations with state dependent impulses
Belley, J.-M.; Bondo, É.
2016-10-01
Subject to a priori bounds, Liénard equations with state dependent impulsive forcing are shown to admit a unique absolutely continuous anti-periodic solution with first derivative of bounded variation on finite intervals. The point-wise convergence of a sequence of iterates to the solution is obtained, along with a bound for the rate of convergence. The results are applied to Josephson's and van der Pol's equations.
VANGQUANYI
1997-01-01
This paper deals with the problems on the existence and uniqueness and stability of almostperiodic solutions for functional differential equations with infinite delays. The author obtainssome sufficient conditions which ganrantee the existence and uniqueness and stability of almost periodic solutions with module containment. The results extend all the results of the paper[1] and solve the two open problems proposed in [1] under much weaker conditions than that proposed in [1].
Explicit Soliton and Periodic Solutions to Three-Wave System with Quadratic and Cubic Nonlinearities
LIN Ji; ZHAO Li-Na; LI Hua-Mei
2011-01-01
Lie group theoretical method and the equation of the Jacobi elliptic function are used to study the three wave system that couples two fundamental frequency (FF) and a single second harmonic (SH) one by competing x(2)(quadratic) and x(3) (cubic) nonlinearities and birefringence.This system shares some of the nice properties of soliton system.On the phase-locked condition, we obtain large families of analytical solutions as the soliton, kink and periodic solutions of this system.
Exact Solitary Wave and Periodic Wave Solutions of a Class of Higher-Order Nonlinear Wave Equations
Lijun Zhang
2015-01-01
Full Text Available We study the exact traveling wave solutions of a general fifth-order nonlinear wave equation and a generalized sixth-order KdV equation. We find the solvable lower-order subequations of a general related fourth-order ordinary differential equation involving only even order derivatives and polynomial functions of the dependent variable. It is shown that the exact solitary wave and periodic wave solutions of some high-order nonlinear wave equations can be obtained easily by using this algorithm. As examples, we derive some solitary wave and periodic wave solutions of the Lax equation, the Ito equation, and a general sixth-order KdV equation.
Wei-guo Zhang; Shao-wei Li; Wei-zhong Tian; Lu Zhang
2008-01-01
By means of the undetermined assumption method, we obtain some new exact solitary-wave solutions with hyperbolic secant function fractional form and periodic wave solutions with cosine function form for the generalized modified Bonssinesq equation. We also discuss the boundedness of these solutions. More over,we study the correlative characteristic of the solitary-wave solutions and the periodic wave solutions along with the travelling wave velocity's variation.
J. Rodrigues Dias
2006-11-01
Full Text Available Systems with different lifetime distributions, associated with increasing, decreasing, constant, and bathtub-shaped hazard rates, are examined in this paper. It is assumed that a failure is only detected if systems are inspected. New approximate solutions for the inspection period and for the expected duration of hidden faults are presented, on the basis of the assumption that only periodic and perfect inspections are carried out. By minimizing total expected cost per unit of time, on the basis of numerical results and a range of comparisons, the conclusion is drawn that these new approximate solutions are extremely useful and simple to put into practice.
Periodic solutions for a two-species nonautonomous competition system with diffusion and impulses
Dong Lingzhen [Department of Mathematics, Taiyuan University of Technology, Taiyuan 030024 (China)]. E-mail: linzhen_dong@yahoo.com.cn; Chen Lansun [Department of Applied Mathematics, Dalian University of Technology, Dalian 116023 (China); Shi Peilin [Department of Mathematics, Taiyuan University of Technology, Taiyuan 030024 (China)
2007-06-15
By re-estimating the upper bound of {integral}{sub 0}{sup {omega}}e{sup u{sub i}}{sup (t)}dt (i=1,2), we generalize a result about the existence of a positive periodic solution for a two-species nonautonomous patchy competition system with time delay. Based on that system, we consider the impulsive harvesting and stocking, and establish a two-species nonautonomous competition Lotka-Volterra system with diffusion and impulsive effects. With the continuation theorem of coincidence degree theory, we obtain the existence of a positive periodic solution for such a system. At last, two examples are given to demonstrate our results.
Quasi-periodic solutions for d-dimensional beam equation with derivative nonlinear perturbation
Mi, Lufang, E-mail: milufang@126.com [Department of Mathematics, Binzhou University, Shandong 256600 (China); Cong, Hongzi, E-mail: conghongzi@dlut.edu.cn [School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024 (China)
2015-07-15
In this paper, we consider the d-dimensional beam equation with convolution potential under periodic boundary conditions. We will apply the Kolmogorov-Arnold-Moser theorem in Eliasson and Kuksin [Ann. Math. 172, 371-435 (2010)] into this system and obtain that for sufficiently small ε, there is a large subset S′ of S such that for all s ∈ S′, the solution u of the unperturbed system persists as a time-quasi-periodic solution which has all Lyapunov exponents equal to zero and whose linearized equation is reducible to constant coefficients.
Analytical Structuring of Periodic and Regular Cascading Solutions in Self-Pulsing Lasers
Belkacem Meziane
2008-01-01
Full Text Available A newly proposed strong harmonic-expansion method is applied to the laser-Lorenz equations to analytically construct a few typical solutions, including the first few expansions of the well-known period-doubling cascade that characterizes the system in its self-pulsing regime of operation. These solutions are shown to evolve in accordance with the driving frequency of the permanent solution that we recently reported to illustrate the system. The procedure amounts to analytically construct the signal Fourier transform by applying an iterative algorithm that reconstitutes the first few terms of its development.
Global search of non-linear systems periodic solutions: A rotordynamics application
Sarrouy, Emmanuelle; Thouverez, Fabrice
2010-01-01
International audience; Introducing non-linearities into models contributes towards a better reality description but leads to systems having multiple solutions. It is then legitimate to look for all the solutions of such systems, that is to have a global analysis approach. However no effective method can be found in literature for systems described by more than two or three degrees of freedom. We propose in this paper a way to find all T-periodic solutions--where T is known--of a non-linear d...
Gumowski, I
1977-01-01
A class of differential equations with pure delay and a hyperbolic nonlinearity, analogous to the Michaelis-Menten term in chemical reaction kinetics, is examined. Conditions for the existence of periodic solutions are established. The amplitude and period dependences on the equation parameters are estimated analytically. A mixed analytico-numerical approach is used in the computations, because a straightforward integration of the equations is numerically ill conditioned. (11 refs).
Periodic Solutions for n-Species Lotka-Volterra Competitive Systems with Pure Delays
Ahmadjan Muhammadhaji
2015-01-01
Full Text Available We study a class of periodic general n-species competitive Lotka-Volterra systems with pure delays. Based on the continuation theorem of the coincidence degree theory and Lyapunov functional, some new sufficient conditions on the existence and global attractivity of positive periodic solutions for the n-species competitive Lotka-Volterra systems are established. As an application, we also examine some special cases of the system, which have been studied extensively in the literature.
Liu Su-Hua; Tang Jia-Shi; Qin Jin-Qi; Yin Xiao-Bo
2008-01-01
Bifurcation characteristics of the Langford system in a general form are systematically analysed,and nonlinear controls of periodic solutions changing into invariant tori in this system are achieved.Analytical relationship between control gain and bifurcation parameter is obtained.Bifurcation diagrams are drawn,showing the results of control for secondary Hopf bifurcation and sequences of bifurcations route to chaos.Numerical simulations of quasi-periodic tori validate analytic predictions.
Almost Periodic Solution of a Multispecies Discrete Mutualism System with Feedback Controls
Hui Zhang
2015-01-01
Full Text Available We consider an almost periodic multispecies discrete Lotka-Volterra mutualism system with feedback controls. We firstly obtain the permanence of the system by utilizing the theory of difference equation. By means of constructing a suitable Lyapunov function, sufficient conditions are obtained for the existence of a unique positive almost periodic solution which is uniformly asymptotically stable. An example together with numerical simulation indicates the feasibility of the main result.
POSITIVE PERIODIC SOLUTIONS OF FIRST AND SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS
LI YONGXIANG
2004-01-01
In this paper the existence results of positive ω-periodic solutions are obtained for second order ordinary differential equation -u″(t) = f(t, u(t)) (t ∈ R), and also for first order ordinary differential equation u′(t) = f(t, u(t)) (t ∈ R), where f: R × R+ → R is a continuous function which is ω-periodic in t. The discussion is based on the fixed point index theory in cones.
Observations and light curve solutions of four ultrashort-period binaries
Kjurkchieva D.
2016-01-01
Full Text Available The paper presents light curve solutions of our observations of four new ultrashort-period eclipsing binaries with MS components. Two of them have periods almost at the upper limit (0.22 days of the ultrashort-period binaries, while the periods of around 0.18 days of CSS J171508.5+350658 and CSS J214633.8+120016 are amongst the shortest known orbital periods. CSS J171410.0+ 445850, CSS J214633.8+120016 and CSS J224326.0+154532 are over contact binaries with fill out factors around 0.25 while CSS J171508.5+350658 is a semidetached system. The two targets with shortest periods consist of M dwarfs.
Egging, R.G.
2010-11-15
This dissertation develops deterministic and stochastic multi-period mixed complementarity problems (MCP) for the global natural gas market, as well as solution approaches for large-scale stochastic MCP. The deterministic model is unique in the combination of the level of detail of the actors in the natural gas markets and the transport options, the detailed regional and global coverage, the multi-period approach with endogenous capacity expansions for transportation and storage infrastructure, the seasonal variation in demand and the representation of market power according to Nash-Cournot theory. The model is applied to several scenarios for the natural gas market that cover the formation of a cartel by the members of the Gas Exporting Countries Forum, a low availability of unconventional gas in the United States, and cost reductions in long-distance gas transportation. The results provide insights in how different regions are affected by various developments, in terms of production, consumption, traded volumes, prices and profits of market participants. The stochastic MCP is developed and applied to a global natural gas market problem with four scenarios for a time horizon until 2050 with nineteen regions and containing 78,768 variables. The scenarios vary in the possibility of a gas market cartel formation and varying depletion rates of gas reserves in the major gas importing regions. Outcomes for hedging decisions of market participants show some significant shifts in the timing and location of infrastructure investments, thereby affecting local market situations. A first application of Benders decomposition (BD) is presented to solve a large-scale stochastic MCP for the global gas market with many hundreds of first-stage capacity expansion variables and market players exerting various levels of market power. The largest problem solved successfully using BD contained 47,373 variables of which 763 first-stage variables, however using BD did not result in
Multi-period natural gas market modeling Applications, stochastic extensions and solution approaches
Egging, Rudolf Gerardus
This dissertation develops deterministic and stochastic multi-period mixed complementarity problems (MCP) for the global natural gas market, as well as solution approaches for large-scale stochastic MCP. The deterministic model is unique in the combination of the level of detail of the actors in the natural gas markets and the transport options, the detailed regional and global coverage, the multi-period approach with endogenous capacity expansions for transportation and storage infrastructure, the seasonal variation in demand and the representation of market power according to Nash-Cournot theory. The model is applied to several scenarios for the natural gas market that cover the formation of a cartel by the members of the Gas Exporting Countries Forum, a low availability of unconventional gas in the United States, and cost reductions in long-distance gas transportation. 1 The results provide insights in how different regions are affected by various developments, in terms of production, consumption, traded volumes, prices and profits of market participants. The stochastic MCP is developed and applied to a global natural gas market problem with four scenarios for a time horizon until 2050 with nineteen regions and containing 78,768 variables. The scenarios vary in the possibility of a gas market cartel formation and varying depletion rates of gas reserves in the major gas importing regions. Outcomes for hedging decisions of market participants show some significant shifts in the timing and location of infrastructure investments, thereby affecting local market situations. A first application of Benders decomposition (BD) is presented to solve a large-scale stochastic MCP for the global gas market with many hundreds of first-stage capacity expansion variables and market players exerting various levels of market power. The largest problem solved successfully using BD contained 47,373 variables of which 763 first-stage variables, however using BD did not result in
Solutions with intersecting p-branes related to Toda chains
Ivashchuk, V D
2000-01-01
Solutions in multidimensional gravity with m p-branes related to Toda-like systems (of general type) are obtained. These solutions are defined on a product of n+1 Ricci-flat spaces M_0 x M_1 x...x M_n and are governed by one harmonic function on M_0. The solutions are defined up to the solutions of Laplace and Toda-type equations and correspond to null-geodesics of the (sigma-model) target-space metric. Special solutions relating to A_m Toda chains (e.g. with m =1,2) are considered.
Variable Separation Solution for （1＋1）-Dimensional Nonlinear Models Related to Schroedinger Equation
XUChang-Zhi; ZHANGJie-Fang
2004-01-01
A variable separation approach is proposed and successfully extended to the (1+1)-dimensional physics models. The new exact solution of (1+1)-dimensional nonlinear models related to Schr6dinger equation by the entrance of three arbitrary functions is obtained. Some special types of soliton wave solutions such as multi-soliton wave solution,non-stable soliton solution, oscillating soliton solution, and periodic soliton solutions are discussed by selecting the arbitrary functions appropriately.
XU Chang-Zhi; ZHANG Jie-Fang
2004-01-01
A variable separation approach is proposed and successfully extended to the (1+1)-dimensional physics models. The new exact solution of (1+ 1)-dimensional nonlinear models related to Schrodinger equation by the entrance of three arbitrary functions is obtained. Some special types of soliton wave solutions such as multi-soliton wave solution,non-stable soliton solution, oscillating soliton solution, and periodic soliton solutions are discussed by selecting the arbitrary functions appropriately.
Analytical Solutions of Time Periodic Electroosmotic Flow in a Semicircular Microchannel
Shaowei Wang
2015-01-01
Full Text Available The time periodic electroosmotic flow of Newtonian fluids through a semicircular microchannel is studied under the Debye–Hückel approximation. Analytical series of solutions are found, and they consist of a time-dependent oscillating part and a time-dependent generating or transient part. Some new physical phenomena are found. The electroosmotic flow driven by an alternating electric field is not periodic in time, but quasi-periodic. There is a phase shift between voltage and flow, which is only dependent on the frequency of external electric field.
Stabilization of Periodic Solutions in a Thedered Satellite System by Damping Injection
Larsen, Martin Birkelund; Blanke, Mogens
2009-01-01
presents a control design for stabilizing these periodic solutions. The design consists of a control law for stabilising the open-loo equibrilibrium and a bias term which forces the system trajectory away from the equilibrium. The tether needs to be positioned away from open-loop equilibrium for the tether...
Periodic Solutions for a Class of Singular Hamiltonian Systems on Time Scales
Xiaofang Meng
2014-01-01
Full Text Available We are concerned with a class of singular Hamiltonian systems on time scales. Some results on the existence of periodic solutions are obtained for the system under consideration by means of the variational methods and the critical point theory.
Existence and Uniqueness of Periodic Solutions for Second Order Differential Equations
Yuanhong Wei
2014-01-01
Full Text Available We study some second order ordinary differential equations. We establish the existence and uniqueness in some appropriate function space. By using Schauder’s fixed-point theorem, new results on the existence and uniqueness of periodic solutions are obtained.
Almost Periodic Solutions to Dynamic Equations on Time Scales and Applications
Yongkun Li
2012-01-01
equations on time scales. Then, as an application, using these concepts and results, we establish sufficient conditions for the existence and exponential stability of almost periodic solution to a class of Hopfield neural networks with delays. Finally, two examples and numerical simulations given to illustrate our results are plausible and meaningful.
Zhinan Xia
2015-07-01
Full Text Available In this article, we show sufficient conditions for the existence, uniqueness and attractivity of piecewise weighted pseudo almost periodic classical solution of nonlinear impulsive integro-differential equations. The working tools are based on the fixed point theorem and fractional powers of operators. An application to impulsive integro-differential equations is presented.
On the periodic mild solutions to complete higher order differential equations on Banach spaces
Lan Nguyen
2011-08-01
Full Text Available For the complete higher order differential equation u(n(t=∑k=0n-1Aku(k(t+f(t, 0 ≤ t ≤ T, on a Banach space E, we give necessary and sufficient conditions for the periodicity of mild solutions. The results, which are proved in a simple manner, generalize some well-known ones.
Stabilization of periodic solutions in a tethered satellite system by damping injection
Larsen, Martin Birkelund; Blanke, Mogens
2009-01-01
presents a control design for stabilizing these periodic solutions. The design consists of a control law for stabilizing the open-loop equilibrium and a bias term which forces the system trajectory away from the equilibrium. The tether needs to be positioned away from open-loop equilibrium for the tether...
无
2010-01-01
By the generalized Borsuk theorem in coincidence degree theory, a p-Laplacian neutral functional differential equation is studied. A new result on the existence of periodic solution is obtained. The interest is that some coeffcient in it is not a constant function and its sign can be changeable, which is different from that in the known literatures.
Dynamical stability of quasi-periodic response solutions in planar conservative systems
Hanssmann, H.|info:eu-repo/dai/nl/107757435; Simo, Carles
2011-01-01
We study non-autonomous planar Hamiltonian or reversible vector fields that vanish at the origin. The time-dependence is quasi-periodic with strongly non-resonant frequencies. First we give a simple criterion in terms of the averaged system for the trivial solution to be dynamically stable. Then we
Existence of positive almost periodic solutions for delay Lotka-Volterra cooperative systems
Kaihong Zhao
2013-07-01
Full Text Available In this article, we study a Lotka-Volterra cooperative system of equations with time-varying delays and distributed delays. By using Mawhin's continuation theorem of coincidence degree theory, we obtain sufficient conditions for the existence of positive almost periodic solutions. Also we present an example to illustrate our results.
Permanence and Positive Periodic Solutions of a Discrete Delay Competitive System
Wenjie Qin
2010-01-01
coincidence degree theory and constructing a suitable Lyapunov discrete function, sufficient conditions which guarantee the existence and global attractivity of positive periodic solutions are obtained. As an application, examples and their numerical simulations are presented to illustrate the feasibility of our main results.
Almost periodic solution of shunting inhibitory cellular neural networks with time-varying delay
Huang Xia; Cao Jinde
2003-07-28
Several sufficient conditions are obtained for the existence of almost periodic solution and its attractivity of shunting inhibitory cellular neural networks with time-varying delay based on the fixed point method and Halanay inequality technique. Some previous results are improved and extended in this Letter and two examples are given to illustrate the effectiveness of the new results.
Zhao Hongyong [Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016 (China)]. E-mail: hongyongz@126.com; Ding Nan [Department of Mathematics, Xinjiang Normal University, Urumqi 830054 (China)
2006-07-15
In this paper, Lotka-Volterra competition-predator system with variable delays is considered. Some sufficient conditions ensuring the existence and global attractivity of periodic solution for this system are obtained by using coincidence degree theory and Lyapunov functional method. An example is also worked out to demonstrate the advantages of our results.
Multiple periodic solutions for a class of second-order nonlinear neutral delay equations
2006-01-01
Full Text Available By means of a variational structure and Z 2 -group index theory, we obtain multiple periodic solutions to a class of second-order nonlinear neutral delay equations of the form0, au>0$"> x ″ ( t − τ + λ ( t f ( t , x ( t , x ( t − τ , x ( t − 2 τ = x ( t , λ ( t > 0 , τ > 0 .
Periodic Solution of Weakly Damped 3D Schrodinger-Boussinesq Equations
GUANMei-jiao; LIYong-sheng
2003-01-01
In this paper the authors consider a model of the interaction of a nonlinear complex Schrodinger field and a real Boussinesq field in a 3D domain with the weakly damping which arises in the laser and plasma physics and prove the existence of the periodic solution.
Existence of Positive Periodic Solutions to -Species Nonautonomous Food Chains with Harvesting Terms
Li Yongkun
2010-01-01
Full Text Available By using Mawhin's continuation theorem of coincidence degree theory and some skills of inequalities, we establish the existence of at least positive periodic solutions for -species nonautonomous Lotka-Volterra type food chains with harvesting terms. An example is given to illustrate the effectiveness of our results.
Dynamical stability of quasi-periodic response solutions in planar conservative systems
Hanssmann, H.; Simo, Carles
2011-01-01
We study non-autonomous planar Hamiltonian or reversible vector fields that vanish at the origin. The time-dependence is quasi-periodic with strongly non-resonant frequencies. First we give a simple criterion in terms of the averaged system for the trivial solution to be dynamically stable. Then we
Periodic Solution to BAM-type Cohen-Grossberg Neural Network with Time-varying Delays
An-ping Chen; Qun-hua Gu
2011-01-01
By using the continuation theorem of Mawhin's coincidence degree theory and the Liapunov functional method, some sufficient conditions are obtained to ensure the existence, uniqueness and the global exponential stability of the periodic solution to the BAM-type Cohen-Grossberg neural networks involving time-varying delays.
On periodic and stable solutions of the Lasota equation in different phase spaces
Antoni Leon Dawidowicz
2008-01-01
Full Text Available We study properties of the Lasota partial differential equation in two different spaces: \\(V_{\\alpha}\\ (Hölder continuous functions and \\(L^p\\. The aim of this paper is to generalize the results of [Z. Brzeźniak, A. L. Dawidowicz, On the periodic solution to the von Foerster-Lasota equation, to appear in Semigroup Forum].
Laser Flash Photolysis and Pulse Radiolysis of Iodate and Periodate in Aqueous Solution
Kläning, U K; Sehested, Knud; Wolff, Thomas
1981-01-01
Species containing iodine in oxidation state six are formed by photolysis and radiolysis of aqueous iodate and periodate solutions in the following reactions: IO3–+ O–→ IO42–; IO3–+ OH → IO3; IVII+ eaq–→ IeVI and IVII [graphic omitted] I0VI+ O–(or OH). The present pulse radiolysis and laser flash...
Xinggui Liu
2011-01-01
Full Text Available In this paper, by using Mawhin's continuation theorem of coincidence degree theory, we establish the existence of at least four positive periodic solutions for a discrete time Lotka-Volterra competitive system with harvesting terms. An example is given to illustrate the effectiveness of our results.
PERIODIC SOLUTION TO A DELAYED PREDATOR-PREY SYSTEM WITH STAGE STRUCTURE AND DISPERSION
无
2011-01-01
In this paper,a delayed two-species predator-prey system with stage structure and diffiusion is investigated. Based on the continuation theorem of coincidence degree theory,the suficient conditions for the existence of positive ω-periodic solution to the system are derived. The numerical simulation of an example verifies our main result.
S-asymptotically periodic solutions for partial differential equations with finite delay
William Dimbour
2011-09-01
Full Text Available In this article, we give some sufficient conditions for the existence and uniqueness of S-asymptotically periodic (mild solutions for some partial functional differential equations. To illustrate our main result, we study a diffusion equation with delay.
Periodic solutions of delayed predator-prey model with the Beddington-DeAngelis functional response
Huo Haifeng [Institute of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu 730050 (China)]. E-mail: hfhuo@lut.cn; Li Wantong [Department of Mathematics, Lanzhou University Lanzhou, Gansu 730000 (China)]. E-mail: wtli@lzu.edu.cn; Nieto, Juan J. [Departamento de Analisis Matematico, Facultad de Matematicas, Universidad de Santiago de Compostela 15782 (Spain)]. E-mail: amnieto@usc.es
2007-07-15
By using the continuation theorem based on Gaines and Mawhin's coincidence degree, sufficient and realistic conditions are obtained for the global existence of positive periodic solutions for a delayed predator-prey model with the Beddington-DeAngelis functional response. Our results are applicable to state dependent and distributed delays.
Periodic solutions of a 2nth-order nonlinear difference equation
无
2010-01-01
In this paper, a 2 nth-order nonlinear difference equation is considered.Using the critical point theory, we establish various sets of sufficient conditions of the nonexistence and existence of periodic solutions.Results obtained complement or improve the existing ones.
THE EXISTENCE OF PERIODIC SOLUTIONS TO SECOND ORDER SELF-ADJOINT DIFFERENCE EQUATIONS
无
2010-01-01
In this paper, we consider the existence of periodic solutions to a class of second order self-adjoint difference equations. By the least action principle and saddle point theorem in the critical point theory, some new results are obtained. As an application, we also give two examples to demonstrate our main results.
MULTIPLE POSITIVE PERIODIC SOLUTIONS TO SINGULAR DIFFERENTIAL EQUATION WITH STATE-DEPENDENT DELAY
无
2008-01-01
By virtue of the fixed point indices, we discuss the existence of the multiple positive periodic solutions to singular differential equation with state-dependent delay under the conditions concerning the first eigenvalue of the relevant linear operator. The results in this paper are optimal and totally generalize many present results.
Existence of periodic and subharmonic solutions for second-order superlinear difference equations
郭志明; 庾建设
2003-01-01
By critical point theory, a new approach is provided to study the existence and multiplicity results of periodic and subharmonic solutions for difference equations. For secord-order difference equations △2xn-1 + f(n,xn) = 0,some new results are obtained for the above problems when f(t, z) has superlinear growth at zero and at infinity in z.
Periodic and subharmonic solutions for fourth-order p-Laplacian difference equations
Xia Liu
2014-01-01
Full Text Available Using critical point theory, we obtain criteria for the existence and multiplicity of periodic and subharmonic solutions to fourth-order p-Laplacian difference equations. The proof is based on the Linking Theorem in combination with variational technique. Recent results in the literature are generalized and improved.
A Periodic Solution of the Generalized Forced Liénard Equation
Zahra Goodarzi
2014-01-01
Full Text Available We consider the generalized forced Liénard equation as follows: (ϕp(x′′+(f(x+k(xx′x′+g(x=p(t+s. By applying Schauder's fixed point theorem, the existence of at least one periodic solution of this equation is proved.
Liu, Yuxiang; Barnett, Alex H.
2016-11-01
We present a high-order accurate boundary-based solver for three-dimensional (3D) frequency-domain scattering from a doubly-periodic grating of smooth axisymmetric sound-hard or transmission obstacles. We build the one-obstacle solution operator using separation into P azimuthal modes via the FFT, the method of fundamental solutions (with N proxy points lying on a curve), and dense direct least-squares solves; the effort is O (N3 P) with a small constant. Periodizing then combines fast multipole summation of nearest neighbors with an auxiliary global Helmholtz basis expansion to represent the distant contributions, and enforcing quasiperiodicity and radiation conditions on the unit cell walls. Eliminating the auxiliary coefficients, and preconditioning with the one-obstacle solution operator, leaves a well-conditioned square linear system that is solved iteratively. The solution time per incident wave is then O (NP) at fixed frequency. Our scheme avoids singular quadratures, periodic Green's functions, and lattice sums, and its convergence rate is unaffected by resonances within obstacles. We include numerical examples such as scattering from a grating of period 13 λ × 13 λ comprising highly-resonant sound-hard "cups" each needing NP = 64800 surface unknowns, to 10-digit accuracy, in half an hour on a desktop.
Yigang Sun
2008-02-01
Full Text Available We establish the existence of multiple positive solutions for a singular nonlinear third-order periodic boundary value problem. We are mainly interested in the semipositone case. The proof relies on a nonlinear alternative principle of Leray-Schauder, together with a truncation technique.
Hongxia Fan
2011-01-01
Full Text Available By means of the fixed point theory of strict set contraction operators, we establish a new existence theorem on multiple positive solutions to a singular boundary value problem for second-order impulsive differential equations with periodic boundary conditions in a Banach space. Moreover, an application is given to illustrate the main result.
Massimiliano Ferrara
2016-01-01
Full Text Available This paper discusses the existence of infinitely many periodic solutions for a semilinear fourth-order impulsive differential inclusion with a perturbed nonlinearity and two parameters. The approach is based on a critical point theorem for nonsmooth functionals.
Zhenguo Luo
2013-01-01
Full Text Available By using a fixed-point theorem of strict-set-contraction, we investigate the existence of positive periodic solutions for a class of the following impulsive neutral Lotka-Volterra system with distributed delays: xi′(t=xi(t[ri(t-∑j=1naij(txj(t-∑j=1nbij(t∫-τij0fij(ξxj(t+ξdξ-∑j=1ncij(t∫-σij0gij(ξxj′(t+ξdξ], Δxi(tk=-Iik(xi(tk, i=1,2,…,n, k=1,2,…. Some verifiable criteria are established easily.
Stability of equilibrium and periodic solutions of a delay equation modeling leukemia
Ion, Anca-Veronica
2010-01-01
We consider a delay differential equation that occurs in the study of chronic myelogenous leukemia. After shortly reminding some previous results concerning the stability of equilibrium solutions, we concentrate on the study of stability of periodic solutions emerged by Hopf bifurcation from a certain equilibrium point. We give the algorithm for approximating a center manifold at a typical point (in the parameter space) of Hopf bifurcation (and an unstable manifold in the vicinity of such a point, where such a manifold exists). Then we find the normal form of the equation restricted to the center manifold, by computing the first Lyapunov coefficient. The normal form allows us to establish the stability properties of the periodic solutions occurred by Hopf bifurcation.
Periodic even and odd-harmonic solutions of the equation of the forced pendulum
Schmitt, B. V.; Sari, N.
The periodic solutions of the simple forced-pendulum equation analyzed by Schmitt and Mazzanti (1981), and Schmitt (1982) are investigated numerically, using computer integrations by a fourth-order Runge-Kutta method (Henrici, 1962) with a step corresponding to 25 iterations per solution to explore the initial conditions of the even and odd-harmonic solutions. The variation of these conditions with respect to the parameters omega and b is shown in a series of maps, and the reliability of the results, despite the approximate nature of numerical integration algorithms and the necessary rounding errors, is seen as demonstrated by double-precision computations and calculations of similar problems with known analytical solutions.
Cepheid Period-Luminosity Relation from the AKARI Observations
Ngeow, Chow-Choong; Kanbur, Shashi M; Neilson, Hilding; Onaka, Takashi; Kato, Daisuke
2010-01-01
In this paper, we derive the period-luminosity (P-L) relation for Large Magellanic Cloud (LMC) Cepheids based on mid-infrared AKARI observations. AKARI's IRC sources were matched to the OGLE-III LMC Cepheid catalog. Together with the available I band light curves from the OGLE-III catalog, potential false matches were removed from the sample. This procedure excluded most of the sources in the S7 and S11 bands: hence only the P-L relation in the N3 band was derived in this paper. Random-phase corrections were included in deriving the P-L relation for the single epoch AKARI data, even though the derived P-L relation is consistent with the P-L relation without random-phase correction, though there is a \\sim 7 per-cent improvement in the dispersion of the P-L relation. The final adopted N3 band P-L relation is N3 = -3.246 log(P) + 15.844, with a dispersion of 0.149.
Cepheid period-luminosity relation from the AKARI observations
Ngeow, Chow-Choong; Ita, Yoshifusa; Kanbur, Shashi M.; Neilson, Hilding; Onaka, Takashi; Kato, Daisuke
2010-10-01
In this paper, we derive the period-luminosity (P-L) relation for Large Magellanic Cloud (LMC) Cepheids based on mid-infrared AKARI observations. AKARI's Infrared Camera sources were matched to the Optical Gravitational Lensing Experiment-III (OGLE-III) LMC Cepheid catalogue. Together with the available I-band light curves from the OGLE-III catalogue, potential false matches were removed from the sample. This procedure excluded most of the sources in the S7 and S11 bands; hence, only the P-L relation in the N3 band is derived in this paper. Random-phase corrections were included in deriving the P-L relation for the single-epoch AKARI data; even though the derived P-L relation is consistent with the P-L relation without random-phase correction, however there is an ~7 per cent improvement in the dispersion of the P-L relation. The final adopted N3-band P-L relation is N3 = -3.246 log(P) + 15.844, with a dispersion of 0.149.
Approximate solutions of non-linear circular orbit relative motion in curvilinear coordinates
Bombardelli, Claudio; Gonzalo, Juan Luis; Roa, Javier
2016-07-01
A compact, time-explicit, approximate solution of the highly non-linear relative motion in curvilinear coordinates is provided under the assumption of circular orbit for the chief spacecraft. The rather compact, three-dimensional solution is obtained by algebraic manipulation of the individual Keplerian motions in curvilinear, rather than Cartesian coordinates, and provides analytical expressions for the secular, constant and periodic terms of each coordinate as a function of the initial relative motion conditions or relative orbital elements. Numerical test cases are conducted to show that the approximate solution can be effectively employed to extend the classical linear Clohessy-Wiltshire solution to include non-linear relative motion without significant loss of accuracy up to a limit of 0.4-0.45 in eccentricity and 40-45° in relative inclination for the follower. A very simple, quadratic extension of the classical Clohessy-Wiltshire solution in curvilinear coordinates is also presented.
Approximate solutions of non-linear circular orbit relative motion in curvilinear coordinates
Bombardelli, Claudio; Gonzalo, Juan Luis; Roa, Javier
2017-01-01
A compact, time-explicit, approximate solution of the highly non-linear relative motion in curvilinear coordinates is provided under the assumption of circular orbit for the chief spacecraft. The rather compact, three-dimensional solution is obtained by algebraic manipulation of the individual Keplerian motions in curvilinear, rather than Cartesian coordinates, and provides analytical expressions for the secular, constant and periodic terms of each coordinate as a function of the initial relative motion conditions or relative orbital elements. Numerical test cases are conducted to show that the approximate solution can be effectively employed to extend the classical linear Clohessy-Wiltshire solution to include non-linear relative motion without significant loss of accuracy up to a limit of 0.4-0.45 in eccentricity and 40-45° in relative inclination for the follower. A very simple, quadratic extension of the classical Clohessy-Wiltshire solution in curvilinear coordinates is also presented.
Zai-hong WANG
2007-01-01
In this paper, we deal with the existence of unbounded orbits of the mapping {θ1 = θ + 2nπ + 1/ρμ(θ) + o(ρ-1),ρ1=ρ+c-μ′(θ)+o(1), ρ→∞,where n is a positive integer, c is a constant and μ(θ) is a 2π-periodic function. We prove that if c ＞ 0 and μ(θ) ≠ 0, θ∈ [0, 2π], then every orbit of the given mapping goes to infinity in the future for ρ large enough; if c ＜ 0 and μ(θ) ≠ 0, θ∈ [0, 2π], then every orbit of the given mapping goes to infinity in the past for ρ large enough. By using this result, we prove that the equation x″+f(x)x′+ax+-bx- +φ(x) =p(t) has unbounded solutions provided that a, b satisfy 1/√a + 1/√b = 2/n and F(x)(= ∫x0 f(s)ds),and φ(x) satisfies some limit conditions. At the same time, we obtain the existence of 2π-periodic solutions of this equation.
Jin Zhen E-mail: jinzhn@263.net; Ma Zhien; Maoan Han
2004-10-01
In this paper, we study the existence of positive periodic solutions of periodic n-species Lotka-Volterra competition systems with impulses. By using the method coincidence degree theorem, a set of easily verifiable sufficient conditions are obtained for the existence of at least one strictly positive periodic solutions. Some known results are improved and generalized.
Mid-IR period-magnitude relations for AGB stars
Glass, I S; Blommaert, J A D L; Sahai, R; Stute, M; Uttenthaler, S
2009-01-01
Asymptotic Giant Branch variables are found to obey period-luminosity relations in the mid-IR similar to those seen at K_S (2.14 microns), even at 24 microns where emission from circumstellar dust is expected to be dominant. Their loci in the M, logP diagrams are essentially the same for the LMC and for NGC6522 in spite of different ages and metallicities. There is no systematic trend of slope with wavelength. The offsets of the apparent magnitude vs. logP relations imply a difference between the two fields of 3.8 in distance modulus. The colours of the variables confirm that a principal period with log P > 1.75 is a necessary condition for detectable mass-loss. At the longest observed wavelength, 24 microns, many semi-regular variables have dust shells comparable in luminosity to those around Miras. There is a clear bifurcation in LMC colour-magnitude diagrams involving 24 micron magnitudes.
THE EXISTENCE OF POSITIVE PERIODIC SOLUTIONS IN A LOGISTIC DIFFERENCE MODEL WITH A FEEDBACK CONTROL
刘智钢; 陈安平
2004-01-01
Consider the following nonautonomous delayed periodic logistic difference model with feedback control term N(k+1)=N(k)exp[r(k)-a1(k)N(k)-a2(k)N(k-τ(k))-c(k)u(k)],Δu(k)=-a(k)u(k)+b(k)N(k-τ(k)), which describes the evolution of a single species. The existence of a positive periodic solution is established by using the method of Mawhin's coincidence degree. This work has important significance in both theory and applications.
Huang Zhenkun [Department of Mathematics, School of Sciences, Zhejiang University, Hangzhou, Zhejiang 310027 (China) and School of Sciences, Jimei University, Xiamen, Fujian 361021 (China)]. E-mail: huangdoc@tom.com; Wang Xinghua [Department of Mathematics, School of Sciences, Zhejiang University, Hangzhou, Zhejiang 310027 (China); Gao Feng [School of Sciences, Jimei University, Xiamen, Fujian 361021 (China)
2006-02-06
In this Letter, we discuss discrete-time analogue of a continuous-time cellular neural network. Sufficient conditions are obtained for the existence of a unique almost periodic sequence solution which is globally attractive. Our results demonstrate dynamics of the formulated discrete-time analogue as mathematical models for the continuous-time cellular neural network in almost periodic case. Finally, a computer simulation illustrates the suitability of our discrete-time analogue as numerical algorithms in simulating the continuous-time cellular neural network conveniently.
On the existence of a periodic solution of a nonlinear ordinary differential equation
Hsin Chu; Sunhong Ding
1998-01-01
Consider a planar forced system of the following form {dxdt=μ(x,y)+h(t)dydt=−ν(x,y)+g(t), where h(t) and g(t) are 2π-periodic continuous functions, t∈(−∞,∞) and μ(x,y) and ν(x,y) are continuous and satisfy local Lipschitz conditions. In this paper, by using the Poincáre's operator we show that if we assume the condltions, (C1), (C2) and (C3) (see Section 2), then there is at least one 2π-periodic solution. In conclusion, we provide an explicit example w...
Global stability, periodic solutions, and optimal control in a nonlinear differential delay model
Anatoli F. Ivanov
2010-09-01
Full Text Available A nonlinear differential equation with delay serving as a mathematical model of several applied problems is considered. Sufficient conditions for the global asymptotic stability and for the existence of periodic solutions are given. Two particular applications are treated in detail. The first one is a blood cell production model by Mackey, for which new periodicity criteria are derived. The second application is a modified economic model with delay due to Ramsey. An optimization problem for a maximal consumption is stated and solved for the latter.
Mitchell, K. E.; Dutton, J. A.
1981-01-01
The considered investigation is concerned with periodic solutions in the context of a forced, dissipative, barotropic spectral model truncated to three complex coefficients with constant forcing on only the intermediate scale. It is found that determining a periodic solution of this three-coefficient model also reduces to finding the algebraic roots of a real polynomial. In the derivation of this polynomial, a class of hydrodynamic spectral systems is described for which a periodic solution might be similarly specified. The existence of periodic solutions of the three-coefficient model is controlled by the roots of the stability polynomial of the basic stationary solution, which represents the simplest response to the constant forcing. When the forcing exceeds a critical value, the basic solution becomes unstable. Owing to the nature of the roots of the stability polynomial at critical forcing, bifurcation theory guarantees the existence of a periodic solution.
Barker, Blake; Noble, Pascal; Rodrigues, L Miguel; Zumbrun, Kevin
2012-01-01
In this paper we consider the spectral and nonlinear stability of periodic traveling wave solutions of a generalized Kuramoto-Sivashinsky equation. In particular, we resolve the long-standing question of nonlinear modulational stability by demonstrating that spectrally stable waves are nonlinearly stable when subject to small localized (integrable) perturbations. Our analysis is based upon detailed estimates of the linearized solution operator, which are complicated by the fact that the (necessarily essential) spectrum of the associated linearization intersects the imaginary axis at the origin. We carry out a numerical Evans function study of the spectral problem and find bands of spectrally stable periodic traveling waves, in close agreement with previous numerical studies of Frisch-She-Thual, Bar-Nepomnyashchy, Chang-Demekhin-Kopelevich, and others carried out by other techniques. We also compare predictions of the associated Whitham modulation equations, which formally describe the dynamics of weak large s...
On some single-hump solutions of the short-pulse equation and their periodic generalizations
Shen, Y.; Williams, F.; Whitaker, N. [Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003-4515 (United States); Kevrekidis, P.G., E-mail: kevrekid@gmail.co [Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003-4515 (United States); Saxena, A. [Center for Nonlinear Studies and Theoretical Division, MS B262, Los Alamos National Laboratory, Los Alamos, NM 87545 (United States); Frantzeskakis, D.J. [Department of Physics, University of Athens, Panepistimiopolis, Zografos, Athens 15784 (Greece)
2010-06-28
In the present work, we consider both localized (e.g. peakon and breather) and extended waveforms (peakon-lattice and breather-lattice, as well as some periodic ones) that arise in the context of the short-pulse equation, as emanating from their sine-Gordon equation analogs. Through direct numerical simulations, we find that the most robust solution is the breather, although some of the single-hump variants of the periodic solutions may be preserved upon the time dynamics as well. Multi-peakon, as well as multi-breather and multi-hump profiles more generally are found to be subject to symmetry-breaking instabilities and are, thus, less robust.
Anti-periodic traveling wave solution to a forced two-dimensional generalized KdV-Burgers equation
TAN Junyu
2003-01-01
The anti-periodic traveling wave solutions to a forced two-dimensional generalized KdV-Burgers equation are studied.Some theorems concerning the boundness, existence and uniqueness of the solution to this equation are proved.
Periodic Solutions for Duffing Type p-Laplacian Equation with Multiple Constant Delays
Hong Zhang
2012-01-01
Full Text Available Using inequality techniques and coincidence degree theory, new results are provided concerning the existence and uniqueness of periodic solutions for the Duffing type p-Laplacian equation with multiple constant delays of the form (φp(x′(t′+Cx′(t+g0(t,x(t+∑k=1ngk(t,x(t-τk=e(t. Moreover, an example is provided to illustrate the effectiveness of the results in this paper.
On quasi-periodic solutions for generalized Boussinesq equation with quadratic nonlinearity
Shi, Yanling; Xu, Junxiang; Xu, Xindong
2015-02-01
In this paper, one-dimensional generalized Boussinesq equation: utt - uxx + (u2 + uxx)xx = 0 with boundary conditions ux(0, t) = ux(π, t) = uxxx(0, t) = uxxx(π, t) = 0 is considered. It is proved that the equation admits a Whitney smooth family of small-amplitude quasi-periodic solutions with 2-dimensional Diophantine frequencies. The proof is based on an infinite dimensional Kolmogorov-Arnold-Moser theorem and Birkhoff normal form.
Validation of Finite Element Solutions of Nonlinear, Periodic Eddy Current Problems
Plasser René
2014-12-01
Full Text Available An industrial application is presented to validate a finite element analysis of 3-dimensional, nonlinear eddy-current problems with periodic excitation. The harmonic- balance method and the fixed-point technique are applied to get the steady state solution using the finite element method. The losses occurring in steel reinforcements underneath a reactor due to induced eddy-currents are computed and compared to measurements.
Periodic solutions of fully nonlinear autonomous equations of Benjamin-Ono type
Baldi, Pietro
2012-01-01
We prove the existence of time-periodic, small amplitude solutions of autonomous quasilinear or fully nonlinear completely resonant pseudo-PDEs of Benjamin-Ono type in Sobolev class. The result holds for frequencies in a Cantor set that has asymptotically full measure as the amplitude goes to zero. At the first order of amplitude, the solutions are the superposition of an arbitrarily large number of waves that travel with different velocities (multimodal solutions). The equation can be considered as a Hamiltonian, reversible system plus a non-Hamiltonian (but still reversible) perturbation that contains derivatives of the highest order. The main difficulties of the problem are: an infinite-dimensional bifurcation equation, and small divisors in the linearized operator, where also the highest order derivatives have nonconstant coefficients. The main technical step of the proof is the reduction of the linearized operator to constant coefficients up to a regularizing rest, by means of changes of variables and co...
Global search of non-linear systems periodic solutions: A rotordynamics application
Sarrouy, E.; Thouverez, F.
2010-08-01
Introducing non-linearities into models contributes towards a better reality description but leads to systems having multiple solutions. It is then legitimate to look for all the solutions of such systems, that is to have a global analysis approach. However no effective method can be found in literature for systems described by more than two or three degrees of freedom. We propose in this paper a way to find all T-periodic solutions—where T is known—of a non-linear dynamical system. This method is compared to three other approaches and is shown to be the most efficient on a Duffing oscillator. As a more complex example, a rotor model including a squeeze-film damper is studied and a second branch of solutions is exhibited.
Discrete doubly periodic and solitary wave solutions for the semi-discrete coupled mKdV equations
Wu Xiao-Fei; Zhu Jia-Min; Ma Zheng-Yi
2007-01-01
In this paper, the improved Jacobian elliptic function expansion approach is extended and applied to constructing discrete solutions of the semi-discrete coupled modified Korteweg de Vries (mKdV) equations with the aid of the symbolic computation system Maple. Some new discrete Jacobian doubly periodic solutions are obtained. When the modulus M → 1, these doubly periodic solutions degenerate into the corresponding solitary wave solutions, including kink-type, bell-type and other types of excitations.
BHARDWAJ S B; SINGH RAM MEHAR; SHARMA KUSHAL; MISHRA S C
2016-06-01
Attempts have been made to explore the exact periodic and solitary wave solutions of nonlinear reaction diffusion (RD) equation involving cubic–quintic nonlinearity along with timedependent convection coefficients. Effect of varying model coefficients on the physical parameters of solitary wave solutions is demonstrated. Depending upon the parametric condition, the periodic,double-kink, bell and antikink-type solutions for cubic–quintic nonlinear reaction-diffusion equation are extracted. Such solutions can be used to explain various biological and physical phenomena.
Fan, M; Wang, K; Jiang, D
1999-08-01
In this paper, we study the existence and global attractivity of positive periodic solutions of periodic n-species Lotka-Volterra competition systems. By using the method of coincidence degree and Lyapunov functional, a set of easily verifiable sufficient conditions are derived for the existence of at least one strictly positive (componentwise) periodic solution of periodic n-species Lotka-Volterra competition systems with several deviating arguments and the existence of a unique globally asymptotically stable periodic solution with strictly positive components of periodic n-species Lotka-Volterra competition system with several delays. Some new results are obtained. As an application, we also examine some special cases of the system we considered, which have been studied extensively in the literature. Some known results are improved and generalized.
Obstructive Sleep Apnea Syndrome, Periodic Limb Movements and Related Factors
Osman Özgür Yalın
2015-09-01
Full Text Available OBJECTIVE: Obstructive sleep apnea syndrome (OSAS is characterized by nocturnal repetitive apnea episodes. Periodic limb movements (PLMs is nocturnal, stereotypic, repetitive movements of the lower extremities. The aim of this study was to investigate the presence of periodic limb movements in OSAS patients and correlation of PLM with OSAS severity. METHODS: One hundred and forty one OSAS suspected patients was enrolled into the study. All subjects’ blood pressure, heart rate measurements and neurologic examinations were made by the same neurologist. Sociodemographic characteristics were recorded. One night polysomnography (PSG was performed to all patients and results were analyzed. Apnea Hypopnea Index (AHI ≥ 5 subjects were accepted as OSAS, and PLM Index (PLMI ≥ 5 subjects were accepted as having PLM. RESULTS: One hundred and two patients were diagnosed as OSAS. The control group consisted of 39 patients who had normal polysomnographic findings. OSAS patients’ were older and body mass index (BMI were higher than the control group. Systolic blood pressure was higher in OSAS group. Alcohol use was determined as a risk factor for OSAS. PLM were more common in OSAS group than the control group (% 30,3 - % 10,2. PLM frequency was associated with the severity of OSAS. CONCLUSION: In OSAS patients presence of PLM was related with OSAS severity, higher systolic and diastolic blood pressure and REM sleep depletion. PLM in OSAS patients could be regarded as an indicator of disease severity and also could aware clinician for increased complication rates.
Metallicity effects on synthetic Cepheid Period-Luminosity relations
Musella, I.
On the basis of new theoretical results (Bono, Marconi & Stellingwerf, 1998, hereafter BMS; Bono, Caputo, Castellani & Marconi, 1998, hereafter BCCM) useful predictions concerning the Period-Luminosity (PLR) and Period-Luminosity-Color (PLCR) relations both for optical and infrared magnitudes are presented. It is shown that, following the dependence of the instability strip on metallicity, there is a non negligible dependence of the PLRs and PLCRs on the metallicity of the pulsating stars, mainly for optical bands. In particular theoretical results predict a dependence of the PLR on metals which is reversed with respect to current empirical evaluations (see for instance Gould 1994, Sasselov et al. 1997, Kennicutt et al. 1998, hereafter K98). To give a possible explanation for this discrepancy the typical observational procedures used to estimate extragalactic distances through Cepheid PLRs are here tested, with the aim of disentangling, if possible, the reddening and metallicity effects. To this purpose, synthetic PLRs for different metallicities were produced and treated as typical observational samples.
Relative Refractory Period in an Excitable Semiconductor Laser
Selmi, F.; Braive, R.; Beaudoin, G.; Sagnes, I.; Kuszelewicz, R.; Barbay, S.
2014-05-01
We report on experimental evidence of neuronlike excitable behavior in a micropillar laser with saturable absorber. We show that under a single pulsed perturbation the system exhibits subnanosecond response pulses and analyze the role of the laser bias pumping. Under a double pulsed excitation we study the absolute and relative refractory periods, similarly to what can be found in neural excitability, and interpret the results in terms of a dynamical inhibition mediated by the carrier dynamics. These measurements shed light on the analogy between optical and biological neurons and pave the way to fast spike-time coding based optical systems with a speed several orders of magnitude faster than their biological or electronic counterparts.
Acupuncture and related techniques during perioperative period: A literature review.
Acar, H Volkan
2016-12-01
Acupuncture has been used in the Far East for more than 2000 years. Since the early 1970s, this technique has been gaining popularity among Western medical community. A number of studies suggest that its mechanism of effect can be explained in biomedical terms. In this context, a number of transmitters and modulators including beta-endorphin, serotonin, substance P, interleukins, and calcitonin gene-related peptide are released. For that reason, acupuncture can be used in a wide variety of clinical conditions. Studies showed that acupuncture may have beneficial effect in perioperative period. It relieves preoperative anxiety, decreases postoperative analgesic requirements, and decreases the incidence of postoperative nausea and vomiting. In this review article, we examine perioperative use of acupuncture for a variety of conditions.
Globular Clusters and the Mira Period-Luminosity Relation
Feast, M W; Menzies, J; Feast, Michael; Whitelock, Patricia; Menzies, John
2002-01-01
A globular cluster distance scale based on Hipparcos parallaxes of subdwarfs has been used to derive estimates of M_K for cluster Miras, including one in the SMC globular cluster NGC121. These lead to a zero-point of the Mira infrared period-luminosity relation, PL(K), in good agreement with that derived from Hipparcos parallaxes of nearby field Miras. The mean of these two estimates together with data on LMC Miras yields an LMC distance modulus of 18.60 +/- 0.10 in evident agreement with a metallicity corrected Cepheid modulus (18.59 +/- 0.10). The use of luminous AGB stars as extragalactic population indicators is also discussed.
无
2001-01-01
The existence and uniqueness of a strong periodic solution of the evolution system describing geophysical flow in bounded domains of RN(N = 3, 4) are proven if external forces are periodic in time and sufficiently small.
Periodic Sturm-Liouville problems related to two Riccati equations of constant coefficients
Khmelnytskaya, K V; González, A
2009-01-01
We consider two closely related Riccati equations of constant parameters whose particular solutions are used to construct the corresponding class of supersymmetrically-coupled second-order differential equations. We solve analytically these parametric periodic problems along the positive real axis. Next, the analytically solved model is used as a case study for a powerful numerical approach that is employed here for the first time in the investigation of the energy band structure of periodic not necessarily regular potentials. The approach is based on the well-known self-matching procedure of James (1949) and implements the spectral parameter power series solutions introduced by Kravchenko (2008). We obtain additionally an efficient series representation of the Hill discriminant based on Kravchenko's series
Positive almost periodic solutions for state-dependent delay Lotka-Volterra competition systems
Yongkun Li
2012-06-01
Full Text Available In this article, using Mawhin's continuation theorem of coincidence degree theory, we obtain sufficient conditions for the existence of positive almost periodic solutions for the system of equations $$ dot{u}_i(t=u_i(tBig[r_i(t-a_{ii}(tu_i(t -sum_{j=1, jeq i}^na_{ij}(tu_jig(t-au_j(t,u_1(t, dots,u_n(tigBig], $$ where $r_i,a_{ii}>0$, $a_{ij}geq0(jeq i$, $i,j=1,2,dots,n$ are almost periodic functions, $au_iin C(mathbb{R}^{n+1},mathbb{R}$, and $au_i(i=1,2,dots,n$ are almost periodic in $t$ uniformly for $(u_1,dots,u_n^Tinmathbb{R}^n$. An example and its simulation figure illustrate our results.
Yang, Xitao; Yuan, Rong
2006-10-01
In the first part of this paper, we obtain a new property on the module containment for almost periodic functions. Based on it, we establish the module containment of an almost periodic solution for a class of differential equations with piecewise constant delays. In the second part, we investigate the existence, uniqueness and exponential stability of a positive almost periodic and quasi-periodic solution for a certain class of logistic differential equations with a piecewise constant delay. The module containment for the almost periodic solution is established.
AN EMPIRICAL FORMULA FOR THE RELATION BETWEEN VISCOSITY OF SOLUTION AND VOLUME OF SOLUTE.
Kunitz, M
1926-07-20
It has been found that the expression See PDF for Equation represents very closely the relation between the volume of the solute and the viscosity of the solution. The formula has been applied to a number of experimental results and found to hold very well for as high concentrations as 50 per cent solutions of such substances as sugars, glycogen, casein, and rubber. In the case of various sugar solutions, and also in the case of sulfur suspensions, the volume of the solute as calculated from the viscosity values agrees with the actual volume of the substance in dry state, as determined from specific gravity measurement, while in the case of caoutchouc solutions in benzene the values of varphi as calculated from the viscosity measurements fit remarkably well in the equation for osmotic pressure.
Asymptotically Almost Periodic Solutions for a Class of Stochastic Functional Differential Equations
Aimin Liu
2014-01-01
Full Text Available This work is concerned with the quadratic-mean asymptotically almost periodic mild solutions for a class of stochastic functional differential equations dxt=Atxt+Ft,xt,xtdt+H(t,xt,xt∘dW(t. A new criterion ensuring the existence and uniqueness of the quadratic-mean asymptotically almost periodic mild solutions for the system is presented. The condition of being uniformly exponentially stable of the strongly continuous semigroup {Tt}t≥0 is essentially removed, which is generated by the linear densely defined operator A∶D(A⊂L2(ℙ,ℍ→L2(ℙ,ℍ, only using the exponential trichotomy of the system, which reflects a deeper analysis of the behavior of solutions of the system. In this case the asymptotic behavior is described through the splitting of the main space into stable, unstable, and central subspaces at each point from the flow’s domain. An example is also given to illustrate our results.
Rothe, R.E.
1996-09-30
A series of 62 critical and critical approach experiments were performed to evaluate a possible novel means of storing large volumes of fissile solution in a critically safe configuration. This study is intended to increase safety and economy through use of such a system in commercial plants which handle fissionable materials in liquid form. The fissile solution`s concentration may equal or slightly exceed the minimum-critical-volume concentration; and experiments were performed for high-enriched uranium solution. Results should be generally applicable in a wide variety of plant situations. The method is called the `Poisoned Tube Tank` because strong neutron absorbers (neutron poisons) are placed inside periodically spaced stainless steel tubes which separate absorber material from solution, keeping the former free of contamination. Eight absorbers are investigated. Both square and triangular pitched lattice patterns are studied. Ancillary topics which closely model typical plant situations are also reported. They include the effect of removing small bundles of absorbers as might occur during inspections in a production plant. Not taking the tank out of service for these inspections would be an economic advantage. Another ancillary topic studies the effect of the presence of a significant volume of unpoisoned solution close to the Poisoned Tube Tank on the critical height. A summary of the experimental findings is that boron compounds were excellent absorbers, as expected. This was true for granular materials such as Gerstley Borate and Borax; but it was also true for the flexible solid composed of boron carbide and rubber, even though only thin sheets were used. Experiments with small bundles of absorbers intentionally removed reveal that quite reasonable tanks could be constructed that would allow a few tubes at a time to be removed from the tank for inspection without removing the tank from production service.
The Energy-Related Inventions Program: Evaluation challenges and solutions
Brown, M.A.
1996-12-31
This paper describes results of evaluation of the Energy-Related Inventions Program (ERIP), focusing on the methodological challenges faced by the evaluators and solutions implemented. Operated jointly by US DOE and NIST, ERIP is one of the longest running commercialization assistance programs in US. The evaluation suggest that ERIP is a cost-effective federal investment. By the end of 1994, 24% of ERIP technologies had entered the market, producing total cumulative sales of $961 million (1994 dollars). With $124 million in program appropriations 1975-94, ERIP has an 8:1 return. At least 757 job-years were directly supported by ERIP technologies in 1994, and 6, 646 job-years of employment have been created over the past decade. The sales and employment supported by ERIP technologies are associated with $4.4 million in 1994 federal tax returns. Many issues must be addressed to fairly appraise public investments in technology commercialization programs, such as the need to track the program participants for extended periods, complexities in accounting for spinoff technologies, determining the validity of program evaluations, and dealing with performance data that are dominated by a small number of highly successful technologies.
Orbital stability of periodic traveling-wave solutions for the log-KdV equation
Natali, Fábio; Pastor, Ademir; Cristófani, Fabrício
2017-09-01
In this paper we establish the orbital stability of periodic waves related to the logarithmic Korteweg-de Vries equation. Our motivation is inspired in the recent work [3], in which the authors established the well-posedness and the linear stability of Gaussian solitary waves. By using the approach put forward recently in [20] to construct a smooth branch of periodic waves as well as to get the spectral properties of the associated linearized operator, we apply the abstract theories in [13] and [25] to deduce the orbital stability of the periodic traveling waves in the energy space.
Yao, Zhijian
2015-01-01
In this paper, impulsive Nicholson’s blowflies model with linear harvesting term is studied. By using the contraction mapping fixed point theorem, we obtain sufficient conditions for the existence of a unique positive almost periodic solution. In addition, the exponential convergence of positive almost periodic solution is investigated.
无
2008-01-01
In this paper, a predator-prey chain system with impulsive effects and Beddington-DeAngelis functional response is studied. We investigate the existence of periodic solu-tion by coincidence degree theory. Sufficient conditions are obtained for the existence of periodic solution.
无
2012-01-01
The positive periodic solutions to a three-species delayed Lotka-Volterra model with dispersion and harvesting terms are studied in this paper. By the coincidence degree theory, the sufficient conditions for existence of eight positive periodic solutions to the model are obtained.
Jiang, Daqing; Zhang, Qiumei; Hayat, Tasawar; Alsaedi, Ahmed
2017-04-01
In this paper, we consider a stochastic non-autonomous competitive Lotka-Volterra model in a polluted environment. We derive sufficient criteria for the existence and global attractivity of the boundary periodic solutions. Furthermore, we obtain conditions for the existence and global attractivity of a nontrivial positive periodic solution. Finally we make simulations to illustrate our analytical results.
An analytic solution for periodic thermally-driven flows over an infinite slope
Zardi, Dino; Serafin, Stefano
2013-04-01
The flow generated along an infinite slope in an unperturbed stably stratified atmosphere at rest by a time periodic surface temperature forcing is examined. Following Defant (1949), a set of equations is derived which extends Prandtl's (1942) theory to allow for nonstationary conditions. Uniform boundary conditions are conducive to an along-slope parallel flow, governed by a periodically reversing local imbalance between along-slope advection and slope-normal fluxes of momentum and heat. Solutions include both a transient part and a subsequent periodic regime. The former can only be expressed in an integral form, whereas the latter is a combination of exponential and sine or cosine functions of time and height normal to the slope. Key parameters are the quantity Nα = N sinα (where α is the slope angle, and N is the Brunt-Väisälä frequency of the unperturbed atmosphere) and the angular frequency of the driving surface temperature cycle, ?. Three different flow regimes may occur, namely subcritical (Nα ?). The properties of the solutions in each regime are examined and discussed. The relationship between the present solutions and the earlier time-dependent slope flow model by Defant (1949) is also discussed. References Defant, F., 1949: Zur Theorie der Hangwinde, nebst Bemerkungen zur Theorie der Berg- und Talwinde. [A theory of slope winds, along with remarks on the theory of mountain winds and valley winds]. Arch. Meteor. Geophys. Bioclimatol., Ser. A, 1, 421-450 (Theoretical and Applied Climatology). [English translation: Whiteman, C.D., and E. Dreiseitl, 1984: Alpine meteorology: Translations of classic contributions by A. Wagner, E. Ekhart and F. Defant. PNL-5141 / ASCOT-84-3. Pacific Northwest Laboratory, Richland, Washington, 121 pp]. Prandtl, L., 1942: Strömungslehre [Flow Studies]. Vieweg und Sohn, Braunschweig, 382 pp.
Yingwei Li
2013-01-01
Full Text Available The global exponential stability issues are considered for almost periodic solution of the neural networks with mixed time-varying delays and discontinuous neuron activations. Some sufficient conditions for the existence, uniqueness, and global exponential stability of almost periodic solution are achieved in terms of certain linear matrix inequalities (LMIs, by applying differential inclusions theory, matrix inequality analysis technique, and generalized Lyapunov functional approach. In addition, the existence and asymptotically almost periodic behavior of the solution of the neural networks are also investigated under the framework of the solution in the sense of Filippov. Two simulation examples are given to illustrate the validity of the theoretical results.
An easy trick to a periodic solution of relativistic harmonic oscillator
Jafar Biazar
2014-04-01
Full Text Available In this paper, the relativistic harmonic oscillator equation which is a nonlinear ordinary differential equation is investigated by Homotopy perturbation method. Selection of a linear operator, which is a part of the main operator, is one of the main steps in HPM. If the aim is to obtain a periodic solution, this choice does not work here. To overcome this lack, a linear operator is imposed, and Fourier series of sines will be used in solving the linear equations arise in the HPM. Comparison of the results, with those of resulted by Differential Transformation and Harmonic Balance Method, shows an excellent agreement.
Time-periodic solutions of massive scalar fields in AdS background: perturbative constructions
Kim, Nakwoo
2014-01-01
We consider scalar fields which are coupled to Einstein gravity with a negative cosmological constant, and construct periodic solutions perturbatively. In particular, we study tachyonic scalar fields whose mass is at or above the Breitenlohner-Freedman bound in four, five, and seven spacetime dimensions. The critical amplitude of the leading order perturbation, for which the perturbative expansion breaks down, increases as we consider less massive fields. We present various examples including a model with a self-interacting scalar field which is derived from a consistent truncation of IIB supergravity.
Kim, Nakwoo, E-mail: nkim@khu.ac.kr
2015-03-06
We consider scalar fields which are coupled to Einstein gravity with a negative cosmological constant, and construct periodic solutions perturbatively. In particular, we study tachyonic scalar fields whose mass is at or above the Breitenlohner–Freedman bound in four, five, and seven spacetime dimensions. The critical amplitude of the leading order perturbation, for which the perturbative expansion breaks down, increases as we consider less massive fields. We present various examples including a model with a self-interacting scalar field which is derived from a consistent truncation of IIB supergravity.
Wu Huaiqin
2009-01-01
Full Text Available This paper considers a new class of additive neural networks where the neuron activations are modelled by discontinuous functions with nonlinear growth. By Leray-Schauder alternative theorem in differential inclusion theory, matrix theory, and generalized Lyapunov approach, a general result is derived which ensures the existence and global asymptotical stability of a unique periodic solution for such neural networks. The obtained results can be applied to neural networks with a broad range of activation functions assuming neither boundedness nor monotonicity, and also show that Forti's conjecture for discontinuous neural networks with nonlinear growth activations is true.
Quasi-periodic solutions of nonlinear beam equation with prescribed frequencies
Chang, Jing [College of Information Technology, Jilin Agricultural University, Changchun 130118 (China); Gao, Yixian, E-mail: gaoyx643@nenu.edu.cn; Li, Yong [School of Mathematics and Statistics, and Center for Mathematics and Interdisciplinary Sciences, Northeast Normal University, Changchun 130024 (China)
2015-05-15
Consider the one dimensional nonlinear beam equation u{sub tt} + u{sub xxxx} + mu + u{sup 3} = 0 under Dirichlet boundary conditions. We show that for any m > 0 but a set of small Lebesgue measure, the above equation admits a family of small-amplitude quasi-periodic solutions with n-dimensional Diophantine frequencies. These Diophantine frequencies are the small dilation of a prescribed Diophantine vector. The proofs are based on an infinite dimensional Kolmogorov-Arnold-Moser iteration procedure and a partial Birkhoff normal form. .
Lessard, Jean-Philippe
2009-01-01
An old conjecture in delay equations states that Wright's equation \\[ y'(t)= - \\alpha y(t-1) [ 1+y(t)], \\alpha \\in \\mathbb{R} \\] has a unique slowly oscillating periodic solution (SOPS) for every parameter value $\\alpha>\\pi/2$. We reformulate this conjecture and we use a method called validated continuation to rigorously compute a global continuous branch of SOPS of Wright's equation. Using this method, we show that a part of this branch does not have any fold point nor does it undergo any secondary bifurcation, partially answering the new reformulated conjecture.
Stationary distribution and periodic solutions for stochastic Holling-Leslie predator-prey systems
Jiang, Daqing; Zuo, Wenjie; Hayat, Tasawar; Alsaedi, Ahmed
2016-10-01
The stochastic autonomous and periodic predator-prey systems with Holling and Leslie type functional response are investigated. For the autonomous system, we prove that there exists a unique stationary distribution, which is ergodic by constructing a suitable Lyapunov function under relatively small white noise. The result shows that, stationary distribution doesn't rely on the existence and the stability of the positive equilibrium in the undisturbed system. Furthermore, for the corresponding non-autonomous system, we show that there exists a positive periodic Markov process under relatively weaker condition. Finally, numerical simulations illustrate our theoretical results.
无
2009-01-01
The carbon nanotubes (CNTs) periodically decorated by high-density polyethylene (HDPE) composites with nanohybrid shish kebabs (NHSK) structures were prepared by CNTs-initiated solution crystalli-zation. The disc-shaped HDPE crystalline lamellae were periodically located on the surface of CNTs in the direction perpendicular to the nanotube axis. Observations from scanning electron microscopy and transmission electron microscopy showed that with the increasing of crystallization temperature, the lateral dimension of the lamellae was decreased and the distance between two neighboring lamellae was increased. However, the thickness of the lamellae did not vary with the crystallization temperature. The formation mechanism of the NHSK structures was also explained. The one-dimensional structure and the ultra-high curved surface of CNTs lead to strong geometry confinement, which plays a main role in the formation of the NHSKs.
Almost Periodic Solutions of Prey-Predator Discrete Models with Delay
Tomomi Itokazu
2009-01-01
Full Text Available The purpose of this article is to investigate the existence of almost periodic solutions of a system of almost periodic Lotka-Volterra difference equations which are a prey-predator system x1(n+1=x1(nexp{b1(n−a1(nx1(n−c2(n∑s=−∞nK2(n−sx2(s}, x2(n+1=x2(nexp{−b2(n−a2(nx2(n+c1(n∑s=−∞nK1(n−sx1(s} and a competitive system xi(n+1=xi(nexp{bi(n−aiixi(n−∑j=1,j≠il∑s=−∞nKij(n−sxj(s}, by using certain stability properties, which are referred to as (K,ρ-weakly uniformly asymptotic stable in hull and (K,ρ-totally stable.
Analytical solutions of weakly coupled map lattices using recurrence relations
Sotelo Herrera, Dolores, E-mail: dsh@dfmf.uned.e [Applied Maths, EUITI, UPM, Ronda de Valencia, 3-28012 Madrid (Spain); San Martin, Jesus [Applied Maths, EUITI, UPM, Ronda de Valencia, 3-28012 Madrid (Spain); Dep. Fisica Matematica y de Fluidos, UNED, Senda del Rey 9-28040 Madrid (Spain)
2009-07-20
By using asymptotic methods recurrence relations are found that rule weakly CML evolution, with both global and diffusive coupling. The solutions obtained from these relations are very general because they do not hold restrictions about boundary conditions, initial conditions and number of oscilators in the CML. Furthermore, oscillators are ruled by an arbitraty C{sup 2} function.
Surface tension and related thermodynamic quantities of aqueous electrolyte solutions
Matubayasi, Norihiro
2013-01-01
Surface tension provides a thermodynamic avenue for analyzing systems in equilibrium and formulating phenomenological explanations for the behavior of constituent molecules in the surface region. While there are extensive experimental observations and established ideas regarding desorption of ions from the surfaces of aqueous salt solutions, a more successful discussion of the theory has recently emerged, which allows the quantitative calculation of the distribution of ions in the surface region. Surface Tension and Related Thermodynamic Quantities of Aqueous Electrolyte Solutions provides a d
Complex Singular Solutions of the 3-d Navier-Stokes Equations and Related Real Solutions
Boldrighini, Carlo; Li, Dong; Sinai, Yakov G.
2017-04-01
By applying methods of statistical physics Li and Sinai (J Eur Math Soc 10:267-313, 2008) proved that there are complex solutions of the Navier-Stokes equations in the whole space R3 which blow up at a finite time. We present a review of the results obtained so far, by theoretical work and computer simulations, for the singular complex solutions, and compare with the behavior of related real solutions. We also discuss the possible application of the techniques introduced in (J Eur Math Soc 10:267-313, 2008) to the study of the real ones.
Complex Singular Solutions of the 3-d Navier-Stokes Equations and Related Real Solutions
Boldrighini, Carlo; Li, Dong; Sinai, Yakov G.
2017-02-01
By applying methods of statistical physics Li and Sinai (J Eur Math Soc 10:267-313, 2008) proved that there are complex solutions of the Navier-Stokes equations in the whole space R3 which blow up at a finite time. We present a review of the results obtained so far, by theoretical work and computer simulations, for the singular complex solutions, and compare with the behavior of related real solutions. We also discuss the possible application of the techniques introduced in (J Eur Math Soc 10:267-313, 2008) to the study of the real ones.
Jia, Shu-Liang; Gao, Yi-Tian; Hu, Lei; Huang, Qian-Min; Hu, Wen-Qiang
2017-02-01
Under investigation in this paper is a (3 + 1)-dimensional Boiti-Leon-Manna-Pempinelli equation in the incompressible fluid. With the aid of the bilinear form, Nth-order soliton-like solutions are obtained via the Pffafian method, rational solutions are derived with the ansätz method and periodic wave solutions are constructed via the Riemann theta function. The analytic solutions obtained via the Pffafian method are similar to the kink solitons, while, the interaction regions with little peaks are different from those of the usual kink solitons. The rational solutions which have one upper lump and one down deep hole are the bright-dark solitary wave solutions. For the rational solutions which combine the kink solitary wave with breather-like wave, asymptotic behaviors show that the breather-like wave disappears with the evolution of t. Relations between the one-soliton solutions and one-periodic wave solutions are analysed, which exhibit the asymptotic behaviors of the periodic waves.
Jian Song
2006-01-01
conditions for the global attractivity of N*(t. Our results imply that under the appropriate periodic impulsive perturbations, the impulsive delay equation preserves the original periodic property of the nonimpulsive delay equation. In particular, our work extends and improves some known results.
Osório, W. R.
2005-12-01
Full Text Available Several metallic materials form spontaneously an oxide film at the surface when is exposed in a corrosive environment. It is well known that the type of corrosive media may develop different results at the material corrosion resistance. The aim of the present paper is to investigate the influence of immersion periods and different solutions upon the corrosion resistance of pure Zn and Al specimens presenting different grain morphologies. The specimens were monitored for several periods in a 3 % NaCl solution at room temperature. Tests were also performed with variations of the 3 % NaCl solution modified by additions of acid and alkaline components. Both the electrochemical impedance spectroscopy (EIS and polarization methods were applied.
Algunos materiales metálicos, cuando se encuentran en un entorno corrosivo, forman espontáneamente una película de óxido en su superficie. Se sabe que los medios corrosivos pueden dar resultados diferentes, según sea la resistencia a la corrosión del material. El propósito del siguiente trabajo es investigar la influencia de los períodos de inmersión en diferentes soluciones sobre la resistencia a la corrosión de probetas de cinc y aluminio puros, con morfologías de grano diferentes. Las probetas fueron ensayadas durante varios períodos de tiempo en soluciones de NaCl 3 % y también con adiciones de ácidos y bases. Se utilizaron las técnicas de espectrometría de impedancia electroquímica (EIS y de polarización.
Melnikov, Andrey
2012-01-01
We prove the existence of solutions to the Sturm-Liouville (SL) equation -y"(x)+q(x)y(x) = s^2 y(x) with periodic and quasi-periodic potential q(x) using theory of SL vessels, implementing a Backlund transformation of SL equation. In this paper quasi-periodic means a finite sum of periodic integrable functions. The solutions for a general s are explicitly constructed in terms of the solutions zn(x), satisfying the SL equation with initial conditions zn(0)=0, zn'(0)=1 for a discrete Levinson set of numbers s=sn, n-natural number. The tau function tau(x) of the corresponding vessel realizes the given potential via the formula q(x)= - 2(ln(tau(x)))". We also prove an analogue of the inverse scattering theorem in this setting too. Using the notion of "KdV evolutionary vessel", we construct a solution of the Korteweg-de-Vries (KdV) equation q'_t = - 3/2 q q'_x + 1/4 q"'_{xxx}, which coincides for t=0 with a given (periodic or quasi-periodic) potential.
PERIODIC SOLUTIONS FOR GENERALIZED PREDATOR-PREY SYSTEMS WITH TIME DELAY AND DIFFUSION
李必文
2004-01-01
A set of easily verifiable sufficient conditions are derived for the existence of positive periodic solutions for delayed generalized predator-prey dispersion system x'1 (t) = x1 (t)g1 (t, x1 (t) ) - a1 (t)y(t)p1 (x1 (t) ) + D1 (t)(x2(t) - x1 (t) ),x'2 (t) = x2 (t)g2 (t, x2 (t) ) - a2 (t)y(t)p2 (x2 (t) ) + D2(t)(x1 (t) - x2 (t)),y' (t) = y(t) {-h(t, y(t) ) + b1 (t)p1 (x1 (t - τ1 ) ) + b2(t)p2(x2(t - τ2))],where ai(t), bi(t) and Di(t)(i = 1, 2) are positive continuous T-periodic functions, gi(t, xi)(i = 1,2) and h(t,y) are continuous and T-periodic with respect to t and h(t,y) ＞ 0 for y ＞ 0, t, y ∈ R, pi(x)(i = 1, 2) are continuous and monotonously increasing functions, and pi(xi) ＞ 0 for xi ＞ 0.
Periodic Solution of a Nonautonomous Diffusive Food Chain System of Three Species with Time Delays
Zheng-qiu Zhang; Xian-wu Zeng; Zhi-cheng Wang
2003-01-01
By using the continuation theorem of coincidence degree theory, the existence of a positive periodic solution for a nonautonomous diffusive food chain system of three species.dx1(t)/dt = xl(t)[r1(t) - a11(t)x1(t) - a12(t)x2(t)] + D1(t)[y(t) - x1(t)],dx2 (t)/dt = x2(t)[-r2(t) + a21(t)x1(t - τ1) - a22(t)x2(t) - a23(t)x3(t)],dx3 (t)/dt = x3(t)[-r3(t) + a32(t)x2(t - τ2) - a33(t)x3(t)],dy(t)/dt = y(t)[r4(t) - a44(t)y(t)] + D2(t)[x1 (t) - y(t)],is established, where ri(t), aii(t) (i= 1, 2, 3, 4), Di(t) (i = 1, 2), a12(t), a21 (t), a23(t) and a32(t) are all positive periodic continuous functions with period w ＞ 0, τi(i = 1, 2) are positive constants.
Local time-decay of solutions to Schroedinger equations with time-periodic potentials
Galtbayar, A; Yajima, K
2002-01-01
Let $H(t)=-\\Delta+V(t,x)$ be a time-dependent Schr\\"{o}dinger operator on $L^2(\\R^3)$. We assume that $V(t,x)$ is $2\\pi$--periodic in time and decays sufficiently rapidly in space. Let $U(t,0)$ be the associated propagator. For $u_0$ belonging to the continuous spectral subspace of $L^2(\\R^3)$ for the Floquet operator $U(2\\pi, 0)$, we study the behavior of $U(t,0)u_0$ as $t\\to\\infty$ in the topology of $x$-weighted spaces, in the form of asymptotic expansions. Generically the leading term is $t^{-3/2}B_1u_0$. Here $B_1$ is a finite rank operator mapping functions of $x$ to functions of $t$ and $x$, periodic in $t$. If $n\\in\\Z$ is an eigenvalue, or a threshold resonance of the corresponding Floquet Hamiltonian $-i\\pa_t + H(t)$, the leading behavior is $t^{-1/2}B_0u_0$. The point spectral subspace for $U(2\\pi, 0)$ is finite dimensional. If $U(2\\pi, 0)\\phi_j = e^{-i2\\pi\\l_j }\\phi_j$, then $U(t, 0)\\phi_j$ represents a quasi-periodic solution.
The core and related solution concepts for infinite assignment games
Llorca, Natividad; Sanchez-Soriano, Joaquin; Tijs, Stef; Timmer, Judith B.
2004-01-01
Assignment problems where both sets of agents that have to be matched are countably infinite, the so-called infinite assignment problems, are studied as well as the related cooperative assignment games. Further, several solution concepts for these assignment games are studied. The first one is the
Photometric solution and period analysis of the contact binary system AH Cnc
Peng, Ying-Jiang; Luo, Zhi-Quan; Zhang, Xiao-Bin; Deng, Li-Cai; Wang, Kun; Tian, Jian-Feng; Yan, Zheng-Zhou; Pan, Yang; Fang, Wei-Jing; Feng, Zhong-Wen; Tang, De-Lin; Liu, Qi-Li; Sun, Jin-Jiang; Zhou, Qiang
2016-10-01
Photometric observations of AH Cnc, a W UMa-type system in the open cluster M67, were carried out by using the 50BiN telescope. About 100 h of time-series B- and V -band data were taken, based on which eight new times of light minima were determined. By applying the Wilson-Devinney method, the light curves were modeled and a revised photometric solution of the binary system was derived. We confirmed that AH Cnc is a deep contact (f = 51%), low mass-ratio (q = 0.156) system. Adopting the distance modulus derived from study of the host cluster, we have re-calculated the physical parameters of the binary system, namely the masses and radii. The masses and radii of the two components were estimated to be respectively 1.188(±0.061) M ⊙, 1.332(±0.063) R ⊙ for the primary component and 0.185(±0.032) M ⊙, 0.592(±0.051) R ⊙ for the secondary. By adding the newly derived minimum timings to all the available data, the period variations of AH Cnc were studied. This shows that the orbital period of the binary is continuously increasing at a rate of dp/dt = 4.29 × 10‑10 d yr‑1. In addition to the long-term period increase, a cyclic variation with a period of 35.26 yr was determined, which could be attributed to an unresolved tertiary component of the system.
Isotropic extensions of the vacuum solutions in general relativity
Molina, C. [Universidade de Sao Paulo (USP), SP (Brazil); Martin-Moruno, Prado [Victoria University of Wellington (New Zealand); Gonzalez-Diaz, Pedro F. [Consejo Superior de Investigaciones Cientificas, Madrid (Spain)
2012-07-01
Full text: Spacetimes described by spherically symmetric solutions of Einstein's equations are of paramount importance both in astrophysical applications and theoretical considerations. And among those, black holes are highlighted. In vacuum, Birkhoff's theorem and its generalizations to non-asymptotically flat cases uniquely fix the metric as the Schwarzschild, Schwarzschild-de Sitter or Schwarzschild-anti-de Sitter geometries, the vacuum solutions of the usual general relativity with zero, positive or negative values for the cosmological constant, respectively. In this work we are mainly interested in black holes in a cosmological environment. Of the two main assumptions of the cosmological principle, homogeneity is lost when compact objects are considered. Nevertheless isotropy is still possible, and we enforce this condition. Within this context, we investigate spatially isotropic solutions close - continuously deformable - to the usual vacuum solutions. We obtain isotropic extensions of the usual spherically symmetric vacuum geometries in general relativity. Exact and perturbative solutions are derived. Maximal extensions are constructed and their causal structures are discussed. The classes of geometries obtained include black holes in compact and non-compact universes, wormholes in the interior region of cosmological horizons, and anti-de Sitter geometries with excess/deficit solid angle. The tools developed here are applicable in more general contexts, with extensions subjected to other constraints. (author)
Multiple periodic solutions for a discrete time model of plankton allelopathy
Zhang Jianbao; Fang Hui
2006-01-01
We study a discrete time model of the growth of two species of plankton with competitive and allelopathic effects on each other N1(k+1) = N1(k)exp{r1(k)-a11(k)N1(k)-a12(k)N2(k)-b1(k)N1(k)N2(k)}, N2(k+1) = N2(k)exp{r2(k)-a21(k)N2(k)-b2(k)N1(k)N1(k)N2(k)}. A set of sufficient conditions is obtained for the existence of multiple positive periodic solutions for this model. The approach is based on Mawhin's continuation theorem of coincidence degree theory as well as some a priori estimates. Some...
Quasi-periodic solutions of the Belov-Chaltikian lattice hierarchy
Geng, Xianguo; Zeng, Xin
Utilizing the characteristic polynomial of Lax matrix for the Belov-Chaltikian (BC) lattice hierarchy associated with a 3 × 3 discrete matrix spectral problem, we introduce a trigonal curve with three infinite points, from which we establish the associated Dubrovin-type equations. The essential properties of the Baker-Akhiezer function and the meromorphic function are discussed, that include their asymptotic behavior near three infinite points on the trigonal curve and the divisor of the meromorphic function. The Abel map is introduced to straighten out the continuous flow and the discrete flow in the Jacobian variety, from which the quasi-periodic solutions of the entire BC lattice hierarchy are obtained in terms of the Riemann theta function.
Exact solution to the steady-state dynamics of a periodically modulated resonator
Momchil Minkov
2017-07-01
Full Text Available We provide an analytic solution to the coupled-mode equations describing the steady-state of a single periodically modulated optical resonator driven by a monochromatic input. The phenomenology of this system was qualitatively understood only in the adiabatic limit, i.e., for low modulation speed. However, both in and out of this regime, we find highly non-trivial effects for specific parameters of the modulation. For example, we show complete suppression of the transmission even with zero detuning between the input and the static resonator frequency. We also demonstrate the possibility for complete, lossless frequency conversion of the input into the sideband frequencies, as well as for optimizing the transmitted signal towards a given target temporal waveform. The analytic results are validated by first-principle simulations.
Zhenguo Luo
2014-01-01
Full Text Available By using a fixed point theorem of strict-set-contraction, which is different from Gaines and Mawhin's continuation theorem and abstract continuation theory for k-set contraction, we established some new criteria for the existence of positive periodic solution of the following generalized neutral delay functional differential equation with impulse: x'(t=x(t[a(t-f(t,x(t,x(t-τ1(t,x(t,…,x(t-τn(t,x(t,x'(t-γ1(t,x(t,…,x'(t-γm(t,x(t], t≠tk, k∈Z+; x(tk+=x(tk-+θk(x(tk, k∈Z+. As applications of our results, we also give some applications to several Lotka-Volterra models and new results are obtained.
Multiple periodic solutions for a discrete time model of plankton allelopathy
Zhang Jianbao; Fang Hui
2006-01-01
We study a discrete time model of the growth of two species of plankton with competitive and allelopathic effects on each other N1(k+1) = N1(k)exp{r1(k)-a11(k)N1(k)-a12(k)N2(k)-b1(k)N1(k)N2(k)}, N2(k+1) = N2(k)exp{r2(k)-a21(k)N2(k)-b2(k)N1(k)N1(k)N2(k)}. A set of sufficient conditions is obtained for the existence of multiple positive periodic solutions for this model. The approach is based on Mawhin's continuation theorem of coincidence degree theory as well as some a priori estimates. Some...
FAN Hong-Yi; ZHU Jia-Min; WANG Tong-Tong; LU Zhi-Ming; LIU Yu-Lu
2008-01-01
One of the advantages of the variational iteration method is the free choice of initial guess. In this paper we use the basic idea of the Jacobian-function method to construct a generalized trial function with some unknown parameters. The Jaulent-Miodek equations are used to illustrate effectiveness and convenience of this method, some new explicit exact travelling wave solutions have been obtained, which include bell-type soliton solution, kink-type soliton solutions, solitary wave solutions, and doubly periodic wave solutions.
ZHAO Qiang; LIU Shi-Kuo; FU Zun-Tao
2004-01-01
The (2+ 1)-dimensional Boussinesq equation and (3+ 1)-dimensional KP equation are studied by using the extended Jacobi elliptic-function method. The exact periodic-wave solutions for the two equations are obtained.
Yan Lv; Wei Lv; Jian-hua Sun
2007-01-01
By using the continuation theorem of coincidence degree theory, the sufficient conditions to guarantee the existence of positive periodic solutions are established for nonautonomous predator-prey systems with discrete and continuously distributed delays.
无
2012-01-01
In this paper,the existence of eight periodic solutions to a Michaelis-Menten-type predator-prey system with delay and harvesting in patch environment is established using the analytical techniques and Mawhin's coincidence degree theory.
无
2006-01-01
Using a fixed point theorem in a cone, we obtain some optimal existence results for single and multiple positive periodic solutions to a functional difference system with feedback control. Moreover, we apply our results to a population model.
BOOK AND EARLY PERIOD FORMS – PLATE AND DESIGN RELATION
Mesude Hülya (ŞANES DOĞRU
2015-04-01
Full Text Available The Koran, main book of the Islam civilization takes place in base of various art forms. The book elements such as superscription, interior face of binder, title, epilogue, heading of sura (section of the Koran applied during the centuries by the ornamentation are available in all scientific, historical and literary artworks. These forms of the ornamentation within the book as well as periods and changed styles had also continued their improvement. The ornamentation and the script in its center had met in the books firstly and this togetherness had demonstrated a full compliance at the classic period. Presentation wish of the script and the ornamentation getting out of the book pages and targeting more independent and more persons was also a precipitating of improvement in the script and the ornamentation. The cuts and murakka which could be accepted as early period forms other than books had enabled to presentation of the calligraphy and the illumination as a plate with their ornamentation concepts resembling books but becoming free. The tughras and illuminated edicts which were the basis of the Turkish-Islam plate concept are considered. At ornamentation of the tughras, it is possible to see the ornamentation in the certificate which sent by the Sultan was thought for a nice presentation of an entire artwork. While the style difference which is in view at any time are evaluated in any way, big change in the forms and presentation style must not be overlooked. If it is possible to see a plate as the interior decoration of the architecture or a space, of course we must also count inscriptions and ornamentations among basic concepts which constitute such style. While some forms such as hilye’s, mosque scripts were starting the plate tradition, improvement of the apparent scripts and aesthetic caught by the calligraphers at this field had encountered to the periods when the Turkish ornamentation had under the influence of the west. The master
Yongzhi Liao
2012-01-01
Full Text Available By applying Mawhin’s continuation theorem of coincidence degree theory, we study the existence of multiple positive periodic solutions for a Gilpin-Ayala competition predator-prey system with harvesting terms and obtain some sufficient conditions for the existence of multiple positive periodic solutions for the system under consideration. The result of this paper is completely new. An example is employed to illustrate our result.
Bíró, Oszkár; Koczka, Gergely; Preis, Kurt
2014-05-01
An efficient finite element method to take account of the nonlinearity of the magnetic materials when analyzing three-dimensional eddy current problems is presented in this paper. The problem is formulated in terms of vector and scalar potentials approximated by edge and node based finite element basis functions. The application of Galerkin techniques leads to a large, nonlinear system of ordinary differential equations in the time domain. The excitations are assumed to be time-periodic and the steady-state periodic solution is of interest only. This is represented either in the frequency domain as a finite Fourier series or in the time domain as a set of discrete time values within one period for each finite element degree of freedom. The former approach is the (continuous) harmonic balance method and, in the latter one, discrete Fourier transformation will be shown to lead to a discrete harmonic balance method. Due to the nonlinearity, all harmonics, both continuous and discrete, are coupled to each other. The harmonics would be decoupled if the problem were linear, therefore, a special nonlinear iteration technique, the fixed-point method is used to linearize the equations by selecting a time-independent permeability distribution, the so-called fixed-point permeability in each nonlinear iteration step. This leads to uncoupled harmonics within these steps. As industrial applications, analyses of large power transformers are presented. The first example is the computation of the electromagnetic field of a single-phase transformer in the time domain with the results compared to those obtained by traditional time-stepping techniques. In the second application, an advanced model of the same transformer is analyzed in the frequency domain by the harmonic balance method with the effect of the presence of higher harmonics on the losses investigated. Finally a third example tackles the case of direct current (DC) bias in the coils of a single-phase transformer.
ZHANG Li-Hua; LIU Xi-Qiang; BAI Cheng-Lin
2006-01-01
In this paper, the generalized tanh function method is extended to (2+1)-dimensional canonical generalized KP (CGKP) equation with variable coefficients. Taking advantage of the Riccati equation, many explicit exact solutions,which contain multiple soliton-like and periodic solutions, are obtained for the (2+1)-dimensional CGKP equation with variable coefficients.
Qi Wang
2012-01-01
Full Text Available By using critical point theory and variational methods, we investigate the subharmonic solutions with prescribed minimal period for a class of second-order impulsive functional differential equations. The conditions for the existence of subharmonic solutions are established. In the end, we provide an example to illustrate our main results.
陈怀堂; 张鸿庆
2003-01-01
A new generalized Jacobi elliptic function method is used to construct the exact travelling wave solutions of nonlinear partial differential equations (PDEs) in a unified way. The main idea of this method is to take full advantage of the elliptic equation which has more new solutions. More new doubly periodic and multiple soliton solutions are obtained for the generalized (3+1)-dimensional Kronig-Penny (KP) equation with variable coefficients. This method can be applied to other equations with variable coefficients.
Xu, Yanlong
2015-08-01
The coupled mode theory with coupling of diffraction modes and waveguide modes is usually used on the calculations of transmission and reflection coefficients for electromagnetic waves traveling through periodic sub-wavelength structures. In this paper, I extend this method to derive analytical solutions of high-order dispersion relations for shear horizontal (SH) wave propagation in elastic plates with periodic stubs. In the long wavelength regime, the explicit expression is obtained by this theory and derived specially by employing an effective medium. This indicates that the periodical stubs are equivalent to an effective homogenous layer in the long wavelength. Notably, in the short wavelength regime, high-order diffraction modes in the plate and high-order waveguide modes in the stubs are considered with modes coupling to compute the band structures. Numerical results of the coupled mode theory fit pretty well with the results of the finite element method (FEM). In addition, the band structures\\' evolution with the height of the stubs and the thickness of the plate shows clearly that the method can predict well the Bragg band gaps, locally resonant band gaps and high-order symmetric and anti-symmetric thickness-twist modes for the periodically structured plates. © 2015 Elsevier B.V.
GNSS related periodic signals in coordinate time-series from Precise Point Positioning
Abraha, K. E.; Teferle, F. N.; Hunegnaw, A.; Dach, R.
2017-03-01
In Global Navigation Satellite System (GNSS) coordinate time-series unrecognized errors and unmodelled (periodic) effects may bias nonlinear motions induced by geophysical signals. Hence, understanding and mitigating these errors is vital to reducing biases and on revealing subtle geophysical signals. To assess the nature of periodic signals in coordinate time-series Precise Point Positioning (PPP) solutions for the period 2008-2015 are generated. The solutions consider Global Positioning System (GPS), GLObalnaya NAvigatsionnaya Sputnikovaya Sistema (GLONASS) or combined GPS+GLONASS (GNSS) observations. We assess the periodic signals of station coordinates computed using the combined International GNSS Service (IGS) and four of its Analysis Centers (ACs) products. Furthermore, we make use of different filtering methods to investigate the sources of the periodic signals. A faint fortnightly signal in our PPP solution based on Jet Propulsion Laboratory (JPL) products and the existence of an 8 d period for those ACs generating combined GPS+GLONASS products are the main features in the GPS-only solutions. The existence of the 8 d period in the GPS-only solution indicates that GPS orbits computed in a combined GNSS solution contain GLONASS-specific signals. The GLONASS-only solution shows highly elevated powers at the third draconitic harmonic (˜120 d period), at the 8 d period and its harmonics (4 d, 2.67 d) besides the well-known annual, semi-annual and other draconitic harmonics. We show that the GLONASS constellation gaps before December 2011 contribute to the power at some of the frequencies. However, the well-known fortnightly signal in GPS-only solutions is not discernible in the GLONASS-only solution. The combined GNSS solution contains periodic signals from both systems, with most of the powers being reduced when compared to the single-GNSS solutions. A 52 per cent reduction for the horizontal components and a 36 per cent reduction for the vertical component
Huanhe Dong
2014-01-01
Full Text Available We introduce how to obtain the bilinear form and the exact periodic wave solutions of a class of (2+1-dimensional nonlinear integrable differential equations directly and quickly with the help of the generalized Dp-operators, binary Bell polynomials, and a general Riemann theta function in terms of the Hirota method. As applications, we solve the periodic wave solution of BLMP equation and it can be reduced to soliton solution via asymptotic analysis when the value of p is 5.
Mei Yue JIANG
2005-01-01
In this paper, we give a Landesman-Lazer type theorem for periodic solutions of the asymmetric 1-dimensional p-Laplacian equation-(|x'|p-2x')' ＝λ|x|p-2x+ + μ|x|p-2x_ + f(t, x)with periodic boundary value.
Cuimei ZHANG; Wencheng CHEN; Yu YANG
2006-01-01
In this paper, we study the existence and global asymptotic stability of positive periodic solutions of a delayed periodic predator-prey system with Holling Ⅱ type functional response. By use of the continuation theorem of coincidence degree theory and the method of Lyapunov function, some sufficient conditions are obtained.
Li, Meili; Han, Maoan; Kou, Chunhai
2008-10-01
In this paper, the existence of positive periodic solutions of a class of periodic -species Gilpin-Ayala impulsive competition systems is studied. By using the continuation theorem of coincidence degree theory, a set of easily verifiable sufficient conditions is obtained. Our results are general enough to include some known results in this area.
Exact solutions to plaquette Ising models with free and periodic boundaries
Marco Mueller
2017-01-01
We clarify the exact relation between partition functions with free and periodic boundary conditions expressed in terms of original and product spin variables for the 2d plaquette and 3d fuki-nuke models, noting that the differences are already present in the 1d Ising model. In addition, we solve the 2d plaquette Ising model with helical boundary conditions. The various exactly solved examples illustrate how correlations can be induced in finite systems as a consequence of the choice of boundary conditions.
Abbasbandy, S.; Van Gorder, R. A.; Hajiketabi, M.; Mesrizadeh, M.
2015-10-01
We consider traveling wave solutions to the Casimir equation for the Ito system (a two-field extension of the KdV equation). These traveling waves are governed by a nonlinear initial value problem with an interesting nonlinearity (which actually amplifies in magnitude as the size of the solution becomes small). The nonlinear problem is parameterized by two initial constant values, and we demonstrate that the existence of solutions is strongly tied to these parameter values. For our interests, we are concerned with positive, bounded, periodic wave solutions. We are able to classify parameter regimes which admit such solutions in full generality, thereby obtaining a nice existence result. Using the existence result, we are then able to numerically simulate the positive, bounded, periodic solutions. We elect to employ a group preserving scheme in order to numerically study these solutions, and an outline of this approach is provided. The numerical simulations serve to illustrate the properties of these solutions predicted analytically through the existence result. Physically, these results demonstrate the existence of a type of space-periodic structure in the Casimir equation for the Ito model, which propagates as a traveling wave.
Qin, Chun-Yan; Tian, Shou-Fu; Wang, Xiu-Bin; Zhang, Tian-Tian
2016-07-01
Under investigation in this paper is a fifth-order Korteweg-de Vries type (fKdV-type) equation with time-dependent coefficients, which can be used to describe many nonlinear phenomena in fluid mechanics, ocean dynamics and plasma physics. The binary Bell polynomials are employed to find its Hirota’s bilinear formalism with an extra auxiliary variable, based on which its N-soliton solutions can be also directly derived. Furthermore, by considering multi-dimensional Riemann theta function, a lucid and straightforward generalization of the Hirota-Riemann method is presented to explicitly construct the multiperiodic wave solutions of the equation. Finally, the asymptotic properties of these periodic wave solutions are strictly analyzed to reveal the relationships between periodic wave solutions and soliton solutions.
Algebro-Geometric Quasi-Periodic Finite-Gap Solutions of the Toda and Kac-van Moerbeke Hierarchies
Bulla, W; Holden, H; Teschl, G
1997-01-01
Combining algebro-geometric methods and factorization techniques for finite difference expressions we provide a complete and self-contained treatment of all real-valued quasi-periodic finite-gap solutions of both the Toda and Kac-van Moerbeke hierarchies. In order to obtain our principal new result, the algebro-geometric finite-gap solutions of the Kac-van Moerbeke hierarchy, we employ particular commutation methods in connection with Miura-type transformations which enable us to transfer whole classes of solutions (such as finite-gap solutions) from the Toda hierarchy to its modified counterpart, the Kac-van Moerbeke hierarchy, and vice versa.
POSITIVE PERIODIC SOLUTION OF ANINTEGRO-DIFFERENTIAL PREDATOR-PREY SYSTEM WITH INFINITE DELAYS
孙德献; 陈凤德
2004-01-01
With the help of a continuation theorem based on Gaines and Mawhin's coincidence degree, easily verifiable criteria are established for the global existence of positive periodic solutions of a differential-integral predator-prey system with infinite delay dN1(t)/dt=N1(t)[b1(t)-a1(t)∫(-∞,t)K1(t-u)N1(u)du-α(t)∫(-∞,t)K2(t-u)N2(u)/(1+mN1(u))du,dN2(t)/dt=N2(t)[-b2(t)+a2(t)∫(-∞,t)K3(t-u)N1(u)/(1+mN1(u))du] where N1(t),N2(t)satisfy N1(t)=Ф1(t),N2(t)=Ф2(t),Фi∈BC((-∞,0],R+),Фi(0)>0,i=1,2∫(0,+∞)Ki(s)ds=1,i=1,2,3.
Stability of periodic solutions in series arrays of Josephson junctions with internal Capacitance
Watanabe, S; Watanabe, Shinya; Swift, James W.
1996-01-01
A mystery surrounds the stability properties of the splay-phase periodic solutions to a series array of N Josephson junction oscillators. Contrary to what one would expect from dynamical systems theory, the splay state appears to be neutrally stable for a wide range of system parameters. It has been explained why the splay state must be neutrally stable when the Stewart-McCumber parameter beta is zero. In this paper we complete the explanation of the apparent neutral stability; we show that the splay state is typically hyperbolic -- either asymptotically stable or unstable -- when beta > 0. We conclude that there is only a single unit Floquet multiplier, based on accurate and systematic computations of the Floquet multipliers for beta ranging from 0 to 10. However, N-2 multipliers are extremely close to 1 for beta larger than about 1. In addition, two more Floquet multipliers approach 1 as beta becomes large. We visualize the global dynamics responsible for these nearly degenerate multipliers, and then estima...
Quittner, Pavol
2016-02-01
We consider positive solutions of cooperative parabolic Lotka-Volterra systems with equal diffusion coefficients, in bounded and unbounded domains. The systems are complemented by the Dirichlet or Neumann boundary conditions. Under suitable assumptions on the coefficients of the reaction terms, these problems possess both global solutions and solutions which blow up in finite time. We show that any solution (u , v) defined on the time interval (0 , T) satisfies a universal estimate of the form
Ankiewicz, Adrian
2016-07-01
Analysis of short-pulse propagation in positive dispersion media, e.g., in optical fibers and in shallow water, requires assorted high-order derivative terms. We present an infinite-order "dark" hierarchy of equations, starting from the basic defocusing nonlinear Schrödinger equation. We present generalized soliton solutions, plane-wave solutions, and periodic solutions of all orders. We find that "even"-order equations in the set affect phase and "stretching factors" in the solutions, while "odd"-order equations affect the velocities. Hence odd-order equation solutions can be real functions, while even-order equation solutions are complex. There are various applications in optics and water waves.
Propofol-Related Infusion Syndrome in the Peripartum Period
Eziefule, Akwugo A.; Elshatanoufy, Solafa; Thakur, Mili; Rocha, Frederico G.
2016-01-01
Background Propofol is a widely known, commonly used drug. Complications can occur with the use of this drug, including propofol-related infusion syndrome (PRIS). PRIS, in the obstetric population, has not been documented; however, we report a case of a patient who developed PRIS after an emergent cesarean delivery of a preterm infant. Case Study A 35-year-old multigravida woman presented complaining of leakage of fluid and decreased fetal movement. Her pregnancy was complicated by methadone maintenance therapy due to a history of opioid abuse. Complications after admission for prolonged monitoring and a prolonged fetal heart tone deceleration was noted with no recovery despite intrauterine resuscitation. An emergent cesarean delivery was performed using general anesthesia and endotracheal intubation after which she developed aspiration pneumonia. She was admitted to the intensive care unit and reintubation and sedation were required secondary to respiratory distress. Sedation was achieved using propofol infusion. She subsequently developed changes in her electrocardiogram, an increase of her serum creatinine, creatinine protein kinase, lipase, amylase, and triglycerides, making the diagnosis of PRIS. Conclusion PRIS should be included in the differential diagnosis of intubated or postoperative patients in the obstetric population. PMID:27738550
The periodic standing-wave approximation: computations in full general relativity
Hernandez, Napoleon
2008-01-01
The periodic standing wave method studies circular orbits of compact objects coupled to helically symmetric standing wave gravitational fields. From this solution an approximation is extracted for the strong field, slowly inspiralling motion of binary black holes and binary neutron stars. Previous work on this project has developed a method using a few multipoles of specially adapted coordinates well suited both to the radiation and the source regions. This method had previously been applied to linear and nonlinear scalar field models, to linearized gravity, and to a post-Minkowski approximation. Here we present the culmination of this approach: the application of the method in full general relativity. The fundamental equations had previously been developed and the challenge presented by this step is primarily a computational one which was approached with an innovative technique. The numerical results of these computations are compared with the corresponding results from linearized and post-Minkowksi computat...
Light curve solution and orbital period analysis of the contact binary V842 Herculis
Selam, S. O.; Albayrak, B.; Şenavci, H. V.; Aksu, O.
2005-10-01
New photoelectric BV light curves were obtained for the neglected eclipsing binary V842 Her at the TÜB{İTAK National Observatory (TUG) and studied for the first time in detail to determine the orbital parameters and geometry of the system. The solutions obtained simultaneously for the new light curves and the radial velocity curves in the literature by using the Wilson-Devinney code reveal a typical W-type contact system. The light curves exhibit the so-called O'Connell effect which the level of the primary maxima being higher than that of the secondary ones in both pass-bands. The O'Connell effect in the light curves is explained in terms of a dark-spot located on the more massive component which makes the more massive larger component slightly cooler than the less massive smaller one. The O-C diagram constructed for all available times of minima of V842 Her exhibits a cyclic character superimposed on a quadratic variation. The quadratic character yields a orbital period increase with a rate of dP/dt=7.76×10-7 days yr-1 which can be attributed to the mass exchange/loss mechanism in the system. By assuming the presence of a gravitationally bound third body in the system, the analysis of the cyclic nature in the O-C diagram revealed a third body with mass of 0.4M\\sun orbiting around the eclipsing pair. The possibility of magnetic activity cycle effect as a cause for the observed cyclic variation in the O-C diagram was also discussed.
Xiaokui Yue
2014-01-01
Full Text Available A numerical approach for obtaining periodic orbits of satellite relative motion is proposed, based on using the time domain collocation (TDC method to search for the periodic solutions of an exact J2 nonlinear relative model. The initial conditions for periodic relative orbits of the Clohessy-Wiltshire (C-W equations or Tschauner-Hempel (T-H equations can be refined with this approach to generate nearly bounded orbits. With these orbits, a method based on the least-squares principle is then proposed to generate projected closed orbit (PCO, which is a reference for the relative motion control. Numerical simulations reveal that the presented TDC searching scheme is effective and simple, and the projected closed orbit is very fuel saving.
郭抗抗; 曹树谦
2014-01-01
A modified Lindstedt-Poincaré (LP) method for obtaining the resonance periodic solutions of nonlinear non-autonomous vibration systems is proposed in this paper. In the modified method, nonlinear non-autonomous equa-tions are converted into a group of linear ordinary differential equations by introducing a set of simple transformations. An approximate resonance solution for the original equation can then be obtained. The periodic solutions of primary, super-harmonic, sub-harmonic, zero-frequency and combination resonances can be solved effectively using the modi-fied method. Some examples, such as damped cubic nonlinear systems under single and double frequency excitation, and damped quadratic nonlinear systems under double frequency excitation, are given to illustrate its convenience and effectiveness. Using the modified LP method, the first-order approximate solutions for each equation are obtained. By comparison, the modified method proposed in this paper produces the same results as the method of multiple scales.
Li, Hongfei; Jiang, Haijun; Hu, Cheng
2016-03-01
In this paper, we investigate a class of memristor-based BAM neural networks with time-varying delays. Under the framework of Filippov solutions, boundedness and ultimate boundedness of solutions of memristor-based BAM neural networks are guaranteed by Chain rule and inequalities technique. Moreover, a new method involving Yoshizawa-like theorem is favorably employed to acquire the existence of periodic solution. By applying the theory of set-valued maps and functional differential inclusions, an available Lyapunov functional and some new testable algebraic criteria are derived for ensuring the uniqueness and global exponential stability of periodic solution of memristor-based BAM neural networks. The obtained results expand and complement some previous work on memristor-based BAM neural networks. Finally, a numerical example is provided to show the applicability and effectiveness of our theoretical results.
Bounded Solutions of KdV and Non-Periodic One-Gap Potentials in Quantum Mechanics
Zakharov, Dmitry V.; Dyachenko, Sergey A.; Zakharov, Vladimir E.
2016-06-01
We describe a broad new class of exact solutions of the KdV hierarchy. In general, these solutions do not vanish at infinity, and are neither periodic nor quasi-periodic. This class includes algebro-geometric finite-gap solutions as a particular case. The spectra of the corresponding Schrödinger operators have the same structure as those of N-gap periodic potentials, except that the reflectionless property holds only in the infinite band. These potentials are given, in a non-unique way, by 2 N real positive functions defined on the allowed bands. In this letter we restrict ourselves to potentials with one allowed band on the negative semi-axis; however, our results apply in general. We support our results with numerical calculations.
Periodic Solutions for a Semi-Ratio-Dependent Predator-Prey System with Delays on Time Scales
Xiaoquan Ding
2012-01-01
Full Text Available This paper is devoted to the existence of periodic solutions for a semi-ratio-dependent predator-prey system with time delays on time scales. With the help of a continuation theorem based on coincidence degree theory, we establish necessary and sufficient conditions for the existence of periodic solutions. Our results show that for the most monotonic prey growth such as the logistic, the Gilpin, and the Smith growth, and the most celebrated functional responses such as the Holling type, the sigmoidal type, the Ivlev type, the Monod-Haldane type, and the Beddington-DeAngelis type, the system always has at least one periodic solution. Some known results are shown to be special cases of the present paper.
无
2010-01-01
In this paper,we discuss the multi-scale homogenization theory for the second order elliptic problems with small periodic coefficients of the form xi(aij(xε) uεx(jx)) = f(x).Assuming n = 2 and u0 ∈ W 1,∞(Ω),we present an error estimate between the homogenization solution u0(x) and the exact solution uε(x) on the Sobolev space L∞(Ω).
Liu, Zhijun; Chen, Lansun
2006-12-01
The main purpose of this paper is to investigate a discrete time non-autonomous difference system of plankton allelopathy with delays. By employing continuous theorem proposed by Gains and Mawhin and some new techniques, a set of verifiable sufficient criteria are established for the existence of at least one strictly positive (componentwise) periodic solution, and as an application, we also examine some special case, showing that these conditions are similar to those of continuous differential system. It is also shown that the time delays are harmless for the existence of positive periodic solutions of system.
A Probabilistic Approach to Fitting Period-Luminosity Relations and Validating Gaia Parallaxes
Sesar, Branimir; Price-Whelan, Adrian M; Bailer-Jones, Coryn A L; Gould, Andy; Rix, Hans-Walter
2016-01-01
Pulsating stars, such as Cepheids, Miras, and RR Lyrae stars, are important distance indicators and calibrators of the "cosmic distance ladder", and yet their period-luminosity-metallicity (PLZ) relations are still constrained using simple statistical methods that cannot take full advantage of available data. To enable optimal usage of data provided by the Gaia mission, we present a probabilistic approach that simultaneously constrains parameters of PLZ relations and uncertainties in Gaia parallax measurements. We demonstrate this approach by constraining PLZ relations of RR Lyrae stars in near-infrared W1 and W2 bands, using Tycho-Gaia Astrometric Solution (TGAS) parallax measurements for a sample of 123 RR Lyrae stars located within 2.5 kpc of the Sun. The fitted PLZ relations are consistent with previous studies, and in combination with other data, deliver distances precise to 6% (once various sources of uncertainty are taken into account). To a precision of 0.03 mas ($1\\sigma$), we do not find a statistic...
Charged Analogues of Henning Knutsen Type Solutions in General Relativity
Gupta, Y. K.; Kumar, Sachin; Pratibha
2011-11-01
In the present article, we have found charged analogues of Henning Knutsen's interior solutions which join smoothly to the Reissner-Nordstrom metric at the pressure free interface. The solutions are singularity free and analyzed numerically with respect to pressure, energy-density and charge-density in details. The solutions so obtained also present the generalization of A.L. Mehra's solutions.
Liu Chunping
2003-06-02
Using a direct algebraic method, more new exact solutions of the Kolmogorov-Petrovskii-Piskunov equation are presented by formula form. Then a theorem concerning the relation between the kink-type solution and the kink-bell-type solution of nonlinear evolution equations is given. Finally, the applications of the theorem to several well-known equations in physics are also discussed.
D Manzoori
2009-12-01
Full Text Available The solutions of photometric BV light curves for the Algol like system UV Leo were obtained using Wilson-Devinney code. The physical and orbital parameters along with absolute dimensions of the system were determined. It has been found that to best fit the V light curve of the system, assumptions of three dark spots were necessary two on the secondary and one on the primary. The absolute visual magnitudes (Mv of the individual components i.e., primary and secondary were estimated to 4.41 and 4.43, respectively, through the color curve analysis. The period analysis of the system presented elsewhere, indicated a cyclic period change of 12 yr duration, which was attributed to magnetic activity cycle, as a main cause of period variation in the system, through the Applegate mechanism. To verify the Applegate model I preformed calculations of some related parameters barrowed from Apllegate and Kalimeris. Values of all the calculated parameters were in accordance to those obtained for similar systems by Applegate. The differential magnitudes Δ B and Δ V, along with corresponding values of Δ(B-V color index. The cyclic variations in brightness are quite clear. There are three predictions of Applegate's theory concerning effects of cyclic magnetic changes on the period variations, which can be checked through the observations, these are as follows: I The long term variations in mean brightness (at outside of eclipses and cyclic changes of orbital period, vary with the same period. II The active star gets bluer as it gets brightened and/or the brightness and color variations are to be in phase. III Changes in luminosity due to changes in quadrupole moment should be of the order 0.1 mag. All the above mentioned predictions of Applegate’s theory are verified. These results combined with cyclic character of P(E presented elsewhere and also consistency of parameters which are obtained in this paper, led me to conclude that one the main causes of period
Periodic solutions ofWick-type stochastic Korteweg–de Vries equations
JIN HYUK CHOI; DAEHO LEE; HYUNSOO KIM
2016-10-01
Nonlinear stochastic partial differential equations have a wide range of applications in science and engineering. Finding exact solutions of the Wick-type stochastic equation will be helpful in the theories and numerical studies of such equations. In this paper, Kudrayshov method together with Hermite transform isimplemented to obtain exact solutions of Wick-type stochastic Korteweg–de Vries equation. Further, graphical illustrations in two- and three-dimensional plots of the obtained solutions depending on time and space are also given with white noise functionals.
Qian, Ying-Jing; Yang, Xiao-Dong; Zhai, Guan-Qiao; Zhang, Wei
2017-08-01
Innovated by the nonlinear modes concept in the vibrational dynamics, the vertical periodic orbits around the triangular libration points are revisited for the Circular Restricted Three-body Problem. The ζ -component motion is treated as the dominant motion and the ξ and η -component motions are treated as the slave motions. The slave motions are in nature related to the dominant motion through the approximate nonlinear polynomial expansions with respect to the ζ -position and ζ -velocity during the one of the periodic orbital motions. By employing the relations among the three directions, the three-dimensional system can be transferred into one-dimensional problem. Then the approximate three-dimensional vertical periodic solution can be analytically obtained by solving the dominant motion only on ζ -direction. To demonstrate the effectiveness of the proposed method, an accuracy study was carried out to validate the polynomial expansion (PE) method. As one of the applications, the invariant nonlinear relations in polynomial expansion form are used as constraints to obtain numerical solutions by differential correction. The nonlinear relations among the directions provide an alternative point of view to explore the overall dynamics of periodic orbits around libration points with general rules.
无
2008-01-01
In this paper, by the theory of Fourier series, Bernoulli number theory and continu-ation theorem of coincidence degree theory, we study a kind of higher order functional differential equation with two deviating arguments. Some new results on the existence of periodic solutions are obtained.
Yuanfu Shao
2014-01-01
Full Text Available By constructing a suitable Lyapunov functional, the global attractivity of positive periodic solutions for a delayed predator-prey system with diffusion and impulses is studied in this paper. Finally, an example and numerical analysis are given to show the effectiveness of the main results.
Kaihong Zhao
2011-04-01
Full Text Available Using Mawhin's continuation theorem of coincidence degree theory, we establish the existence of $2^{n+m}$ positive periodic solutions for a non-autonomous Lotka-Volterra network-like predator-prey system with harvesting terms. Here n and m denote the number of prey and predator species respectively. An example is given to illustrate our results.
Yongkun Li
2010-01-01
Full Text Available By using Mawhin's continuation theorem of coincidence degree theory and some skills of inequalities, we establish the existence of at least 2n positive periodic solutions for n-species nonautonomous Lotka-Volterra type food chains with harvesting terms. An example is given to illustrate the effectiveness of our results.
无
2008-01-01
By using Gaines and Mawhin's continuation theorem of coincidence degree theory and constructing Lyapunov functionals,a set of easily verifiable sufficient conditions are derived for the existence and global attractivity of a positive periodic solution to a predator-prey system with delays and impulses.
Jiwei He
2007-07-01
Full Text Available In this paper, we consider a nonautonomous multispecies competition predator-prey system with Holling's type III functional response and prey supplement. It is proved that the system is uniformly persistent under some conditions. Furthermore, we show that the system has a unique positive periodic solution which is globally asymptotically stable.
LiuQiming; XuRui
2005-01-01
A delayed one-predator and two-prey system with Holling type-Ⅱ functional response is investigated. By using Gaines and Mawhin's continuation theorem of coincidence degree theory and by constructing suitable Lyapunov functional, a set of easily verifiable sufficient conditions are derived for the existence and global attractivity of positive periodic solutions to the system.
Yimin Zhang
2009-01-01
Full Text Available By the continuation theorem of coincidence degree and M-matrix theory, we obtain some sufficient conditions for the existence and exponential stability of periodic solutions for a class of generalized neural networks with arbitrary delays, which are milder and less restrictive than those of previous known criteria. Moreover our results generalize and improve many existing ones.
Ni Hua
2012-01-01
Full Text Available With the help of the variable substitution and applying the fixed point theorem, we derive the sufficient conditions which guarantee the existence of the positive almost periodic solutions for a class of Lotka-Volterra type system. The main results improve and generalize the former corresponding results.
Rostworowski, Andrzej
2017-06-01
Motivated by the problem of stability of anti-de Sitter (AdS) spacetime, we discuss nonlinear gravitational perturbations of maximally symmetric solutions of vacuum Einstein equations in general and the case of AdS in particular. We present the evidence that, similarly to the self-gravitating scalar field at spherical symmetry, the negative cosmological constant allows for the existence of globally regular asymptotically AdS, time-periodic solutions of vacuum Einstein equations whose frequencies bifurcate from linear eigenfrequencies of AdS. Interestingly, our preliminary results indicate that the number of one-parameter families of time-periodic solutions bifurcating from a given eigenfrequency equals the multiplicity of this eigenfrequency.
Existence of the time periodic solution for damped Schroedinger-Boussinesq equation
BolingGUO; XianyunDU
2000-01-01
In this paper, we study the time priodic solution for the weakly damped Schroedinger-Boussinesq equation, by Galerkin method, and prove the existence and uniqueness of the equations under some appropriate conditions.
Ambrose, David M.; Wilkening, Jon
2008-12-11
We classify all bifurcations from traveling waves to non-trivial time-periodic solutions of the Benjamin-Ono equation that are predicted by linearization. We use a spectrally accurate numerical continuation method to study several paths of non-trivial solutions beyond the realm of linear theory. These paths are found to either re-connect with a different traveling wave or to blow up. In the latter case, as the bifurcation parameter approaches a critical value, the amplitude of the initial condition grows without bound and the period approaches zero. We propose a conjecture that gives the mapping from one bifurcation to its counterpart on the other side of the path of non-trivial solutions. By experimentation with data fitting, we identify the form of the exact solutions on the path connecting two traveling waves, which represents the Fourier coefficients of the solution as power sums of a finite number of particle positions whose elementary symmetric functions execute simple orbits in the complex plane (circles or epicycles). We then solve a system of algebraic equations to express the unknown constants in the new representation in terms of the mean, a spatial phase, a temporal phase, four integers (enumerating the bifurcation at each end of the path) and one additional bifurcation parameter. We also find examples of interior bifurcations from these paths of already non-trivial solutions, but we do not attempt to analyze their algebraic structure.
Existence of lattice solutions to semilinear elliptic systems with periodic potential
Nicholas D. Alikakos
2012-01-01
Full Text Available Under the assumption that the potential W is invariant under a general discrete reflection group $G'=TG$ acting on $mathbb{R}^n$, we establish existence of G'-equivariant solutions to $Delta u - W_u(u = 0$, and find an estimate. By taking the size of the cell of the lattice in space domain to infinity, we obtain that these solutions converge to G-equivariant solutions connecting the minima of the potential W along certain directions at infinity. When particularized to the nonlinear harmonic oscillator $u''+alpha sin u=0$, $alpha>0$, the solutions correspond to those in the phase plane above and below the heteroclinic connections, while the G-equivariant solutions captured in the limit correspond to the heteroclinic connections themselves. Our main tool is the G'-positivity of the parabolic semigroup associated with the elliptic system which requires only the hypothesis of symmetry for W. The constructed solutions are positive in the sense that as maps from $mathbb{R}^n$ into itself leave the closure of the fundamental alcove (region invariant.
Li, Fang; Liang, Xing; Shen, Wenxian
2016-08-01
In this series of papers, we investigate the spreading and vanishing dynamics of time almost periodic diffusive KPP equations with free boundaries. Such equations are used to characterize the spreading of a new species in time almost periodic environments with free boundaries representing the spreading fronts. In the first part of the series, we showed that a spreading-vanishing dichotomy occurs for such free boundary problems (see [16]). In this second part of the series, we investigate the spreading speeds of such free boundary problems in the case that the spreading occurs. We first prove the existence of a unique time almost periodic semi-wave solution associated to such a free boundary problem. Using the semi-wave solution, we then prove that the free boundary problem has a unique spreading speed.
Families of asymmetric periodic solutions in the restricted four-body problem
Papadakis, K. E.
2016-12-01
Very recently, we presented five of the basic families of the network of periodic orbits of the restricted four-body problem which are simple, i.e. one intersection with the horizontal x-axis at the half period, symmetric with respect to the same axis and asymmetric with respect to the vertical y-axis. In the present work, using these families, we found series of asymmetric critical orbits for various values of the primaries m2 and m3. From these critical orbits we calculate and present five new families of simple periodic orbits which are asymmetric with respect to both the x- and y-axis. Additionally, we describe a grid method in the (x0, dot{x}0) plane and we obtain initial conditions for new asymmetric double-periodic orbits. We determine ten families of asymmetric double-periodic orbits from the bifurcations of the previous five asymmetric families using the special generating horizontally critical periodic orbits. The stability of each calculated asymmetric periodic orbit is also studied. Characteristic curves as well as stability diagrams of these families are illustrated. In the last section we present the evolution of the five basic families of simple asymmetric periodic orbits when the primaries are the Sun the Jupiter and the 2797 Teucer Asteroid.
Anh Tuan Trinh
2013-11-01
Full Text Available The existence of positive periodic solutions of a periodic Lotka-Volterra type competition system with delays and feedback controls is studied by applying the continuation theorem of coincidence degree theory. By contracting a suitable Liapunov functional, a set of sufficient conditions for the global asymptotic stability of the positive periodic solution of the system is given. A counterexample is given to show that the result on the existence of positive periodic solution in [4] is incorrect.
Relation between non uniform magnetic field and close binary systems period
M Zahedi
2011-12-01
Full Text Available Magnetic activity of one or both components of close binary systems can cause orbital period variation of the systems.Variation in gravitational quadropole moment will change the orbital period of the systems. In this article, we suppose that magnetic field is poloidal-troidal according to dynamo theory, and finds its relation with period change in the systems.
Sazonov, V. V.
2013-03-01
We investigated periodic motions of the axis of symmetry of a model satellite of the Earth, which are similar to the motions of the longitudinal axes of the Mir orbital station in 1999-2001 and the Foton-M3 satellite in 2007. The motions of these spacecraft represented weakly disturbed regular Euler precession with the angular momentum vector of motion relative to the center of mass close to the orbital plane. The direction of this vector during the motion was not practically changed. The model satellite represents an axisymmetric gyrostat with gyrostatic moment directed along the axis of symmetry. The satellite moves in a circular orbit and undergoes the action of the gravitational torque. The motion of the axis of symmetry of this satellite relative to the absolute space is described by fourth-order differential equations with periodic coefficients. The periodic solutions to this system with special symmetry properties are constructed using analytical and numerical methods.
EXISTENCE AND UNIQUENESS OF PERIODIC SOLUTIONS FOR GRADIENT SYSTEMS IN FINITE DIMENSIONAL SPACES
Sahbi BOUSSANDEL
2016-01-01
This paper deals with an abstract periodic gradient system in which the gradient is taken with respect to a variable metric. We obtain an existence and uniqueness result via the application of a global inverse theorem.
ANTI-PERIODIC SOLUTIONS FOR DIFFERENTIAL INCLUSIONS IN BANACH SPACES AND THEIR APPLICATIONS
Liu Guifang; Liu Yiliang
2012-01-01
We deal with anti-periodic problems for differential inclusions with nonmonotone perturbations.The main tools in our study are the maximal monotone property ofthe derivative operator with anti-periodic conditions and the theory of pseudomonotone perturbations of maximal monotone mappings.We then apply our results to evolution hemivariational inequalities and parabolic equations with nonmonotone discontinuities,which generalize and extend previously known theorems.
Solitons and periodic solutions to a couple of fractional nonlinear evolution equations
M Mirzazadeh; M Eslami; Anjan Biswas
2014-03-01
This paper studies a couple of fractional nonlinear evolution equations using first integral method. These evolution equations are foam drainage equation and Klein–Gordon equation (KGE), the latter of which is considered in (2 + 1) dimensions. For the fractional evolution, the Jumarie’s modified Riemann–Liouville derivative is considered. Exact solutions to these equations are obtained.
高承华
2014-01-01
In this paper, we consider the existence of three nontrivial solutions for a discrete non-linear multiparameter periodic problem involving the p-Laplacian. By using the similar method for the Dirichlet boundary value problems in [G. Bonanno and P. Candito, Appl. Anal., 88(4) (2009), pp. 605-616], we construct two new strong maximum principles and obtain that the boundary value problem has three positive solutions for λ and µ in some suitable intervals. The approaches we use are the critical point theory.
Hongmei Zhang; Fawang Liu
2007-01-01
In this paper, the space-time Riesz fractional partial differential equations with periodic conditions are considered. The equations are obtained from the integral partial differential equation by replacing the time derivative with a Caputo fractional derivative and the space derivative with Riesz potential. The fundamental solutions of the space Riesz fractional partial differential equation (SRFPDE) and the space-time Riesz fractional partial differential equation (STRFPDE) are discussed, respectively. Using methods of Fourier series expansion and Laplace transform, we derive the explicit expressions of the fundamental solutions for the SRFPDE and the STRFPDE, respectively.
Meng, Xinzhu; Chen, Lansun
2006-12-21
This paper studies a non-autonomous Lotka-Volterra almost periodic predator-prey dispersal system with discrete and continuous time delays which consists of n-patches, the prey species can disperse among n-patches, but the predator species is confined to one patch and cannot disperse. By using comparison theorem and delay differential equation basic theory, we prove the system is uniformly persistent under some appropriate conditions. Further, by constructing suitable Lyapunov functional, we show that the system is globally asymptotically stable under some appropriate conditions. By using almost periodic functional hull theory, we show that the almost periodic system has a unique globally asymptotical stable strictly positive almost periodic solution. The conditions for the permanence, global stability of system and the existence, uniqueness of positive almost periodic solution depend on delays, so, time delays are "profitless". Finally, conclusions and two particular cases are given. These results are basically an extension of the known results for non-autonomous Lotka-Volterra systems.
Gabella, W.E.; Ruth, R.D.; Warnock, R.L.
1988-05-01
Periodic solutions of the Hamilton-Jacobi equation determine invariant tori in phase space. The Fourier spectrum of a torus with respect to angular coordinates gives useful information about nonlinear resonances and their potential for causing instabilities. We describe a method to solve the Hamilton-Jacobi equation for an arbitrary accelerator lattice. The method works with Fourier modes of the generating functions, and imposes periodicity in the machine azimuth by a shooting method. We give examples leading to three-dimensional plots in a surface of section. It is expected that the technique will be useful in lattice optimization. 14 refs., 6 figs., 1 tab.
M. R. Astaraki
2012-01-01
Full Text Available In the present study analytical solution for forced convection heat transfer in a circular duct with a special boundary condition has been presented, because the external wall temperature is a periodic function of axial direction. Local energy balance equation is written with reference to the fully developed regime. Also governing equations are two-dimensionally solved, and the effect of duct wall thickness has been considered. The temperature distribution of fluid and solid phases is assumed as a periodic function of axial direction and finally temperature distribution in the flow field, solid wall, and local Nusselt number, is obtained analytically.
Liu, Yingyuan; Zhang, Xiaolan; Zhou, Tiejun
2014-01-01
The paper studies a periodic and delayed predator-prey system with non-monotonic functional responses and stage structure. In the system, both the predator and prey are divided into immature individuals and mature individuals by two fixed ages. It is assumed that the immature predators cannot attack preys, and the case of the mature predators attacking the immature preys is also ignored. Based on Mawhin's coincidence degree, sufficient conditions are obtained for the existence of two positive periodic solutions of the system. An example is presented to illustrate the feasibility of the main results.
Ferri, A. A.; Dowell, E. H.
1985-01-01
The anticipated low damping level in large space structures (LSS) has been a major concern for the designers of these structures. Low damping degrades the free response and complicates the design of shape and attitude controllers for flexible spacecraft. Dry friction damping has been considered as a means of increasing the passive damping of LSS, by placing it in the joints and connecting junctures of structures. However, dry friction is highly nonlinear and, hence, analytical investigations are difficult to perform. Here, a multi-harmonic, frequency domain solution technique is developed and applied to a multi-DOF, dry friction damped system. It is seen that the multi-harmonic method is much more accurate than traditional, one harmonic solution methods. The method also compares well with time integration. Finally, comparisons are made with experimental results.
Ferruzzo Correa, Diego P.; Bueno, Átila M.; Castilho Piqueira, José R.
2017-04-01
In this paper we investigate stability conditions for small-amplitude periodic solutions emerging near symmetry-preserving Hopf bifurcations in a time-delayed fully-connected N-node PLL network. The study of this type of systems which includes the time delay between connections has attracted much attention among researchers mainly because the delayed coupling between nodes emerges almost naturally in mathematical modeling in many areas of science such as neurobiology, population dynamics, physiology and engineering. In a previous work it has been shown that symmetry breaking and symmetry preserving Hopf bifurcations can emerge in the parameter space. We analyze the stability along branches of periodic solutions near fully-synchronized Hopf bifurcations in the fixed-point space, based on the reduction of the infinite-dimensional space onto a two-dimensional center manifold in normal form. Numerical results are also presented in order to confirm our analytical results.
Liu Zhengrong
2011-01-01
study the periodic wave solutions and their limit forms for the KdV-like equation ut+a(1+buuux+uxxx=0, and PC-like equation vtt - vttxx - (a1v+a2v2+a3v3xx=0, respectively. Via some special phase orbits, we obtain some new explicit periodic wave solutions which are called trigonometric function periodic wave solutions because they are expressed in terms of trigonometric functions. We also show that the trigonometric function periodic wave solutions can be obtained from the limits of elliptic function periodic wave solutions. It is very interesting that the two equations have similar periodic wave solutions. Our work extend previous some results.
SQUEEZE-E: The optimal solution for molecular simulations with periodic boundary conditions
Wassenaar, T.A.; de Vries, S.J.; Bonvin, A.M.J.J.; Bekker, H.
2012-01-01
In molecular simulations of macromolecules, it is desirable to limit the amount of solvent in the system to avoid spending computational resources on uninteresting solvent−solvent interactions. As a consequence, periodic boundary conditions are commonly used, with a simulation box chosen as small as
SQUEEZE-E : The Optimal Solution for Molecular Simulations with Periodic Boundary Conditions
Wassenaar, Tsjerk A.; de Vries, Sjoerd; Bonvin, Alexandre M. J. J.; Bekker, Henk
2012-01-01
In molecular simulations of macromolecules, it is desirable to limit the amount of solvent in the system to avoid spending computational resources on uninteresting solvent−solvent interactions. As a consequence, periodic boundary conditions are commonly used, with a simulation box chosen as small as
SINGLE-PERIOD TWO-PRODUCT INVENTORY MODEL WITH SUBSTITUTION:SOLUTION AND PROPERTIES
Lianqiao CAI; Jian CHEN; Houmin YAN
2004-01-01
In this paper, we study a single-period two-product inventory model with stochastic demands and downward substitution. The optimal order quantities are presented and some properties are provided. Comparing with newsboy model, we prove that both the profit and the fill rate can be improved by using the substitution policy.
Positive almost periodic solutions for a predator-prey Lotka-Volterra system with delays
Yuan Ye
2012-08-01
where $a_i,r_j, a_{il}, b_{ij},d_{jl},e_{jh}\\in C(\\mathbb{R},(0,\\infty\\sigma_{il},\\tau_{ij},\\delta_{jl},\\theta_{jh}\\in C(\\mathbb{R},\\mathbb{R}(i,l=1,\\ldots,n, j,h=1,\\ldots,m$ are almost periodic functions.
Periodic solutions of a multi-DOF beam system with impact
Vorst, E.L.B. van de; Campen, D.H. van; Kraker, A. de; Fey, R.H.B
1996-01-01
The steady state behaviour is analyzed of a periodically driven multi-DOF beam system which has an elastic stop at its middle. The elastic stop is modelled in a continuous way by using the contact law of Hertz. The beam is modelled by using finite elements and subsequently reduced by using a compone
Chang-Bo Yang
2013-01-01
Full Text Available By M-matrix theory, inequality techniques, and Lyapunov functional method, certain sufficient conditions are obtained to ensure the existence, uniqueness, and global exponential stability of periodic solution for a new type of high-order BAM neural networks with continuously distributed delays and impulses. These novel conditions extend and improve some previously known results in the literature. Finally, an illustrative example and its numerical simulation are given to show the feasibility and correctness of the derived criteria.
无
2012-01-01
In this paper,a class of bidirectional associative memory(BAM) recurrent neural networks with delays are studied.By a fixed point theorem and a Lyapunov functional,some new sufficient conditions for the existence,uniqueness and global exponential stability of the almost periodic solutions are established.These conditions are easy to be verified and our results complement the previous known results.
Edgardo Alvarez
2016-10-01
Full Text Available We study weighted pseudo almost automorphic solutions for the nonlinear fractional difference equation $$ \\Delta^{\\alpha}u(n=Au(n+1+f(n, u(n,\\quad n\\in \\mathbb{Z}, $$ for $0<\\alpha \\leq 1$, where A is the generator of an $\\alpha$-resolvent sequence $\\{S_{\\alpha}(n\\}_{n\\in\\mathbb{N}_0}$ in $\\mathcal{B}(X$. We prove the existence and uniqueness of a weighted pseudo almost automorphic solution assuming that f(.,. is weighted almost automorphic in the first variable and satisfies a Lipschitz (local and global type condition in the second variable. An analogous result is also proved for $\\mathcal{S}$-asymptotically $\\omega$-periodic solutions.
Blended learning as a solution to practice-related problems in vocational schools
Kjærgaard, Hanne Wacher; Duch, Henriette Skjærbæk; Mark, Lene
2013-01-01
Four different types of vocational schools have experimented with blended learning as a way of dealing with problems faced in their students’ theoretical and practical training and the interplay between these. A large part of this has involved the need for differentiated teaching...... as will be illustrated through selected cases. The foci of the cases are: •How can students be part of school-based teaching and learning during periods of practical training? •How can authentic practice be brought into school-based practical training? •How may blended learning assist and support students who...... are otherwise challenged in terms of meeting the prescribed competence goals? Methodologically, scenarios have been employed as a tool for defining the practice-related problems teachers meet in their practice and describing ways in which blended learning may present solutions. Subsequently, the solutions have...
Kudryavtseva, Elena A
2012-01-01
We study the partial case of the planar $N+1$ body problem, $N\\ge2$, of the type of planetary system with satellites. We assume that one of the bodies (the Sun) is much heavier than the other bodies ("planets" and "satellites"), moreover the planets are much heavier than the satellites, and the "years" are much longer than the "months". We prove that, under a nondegeneracy condition which in general holds, there exist at least $2^{N-2}$ smooth 2-parameter families of symmetric periodic solutions in a rotating coordinate system such that the distances between each planet and its satellites are much shorter than the distances between the Sun and the planets. We describe generating symmetric periodic solutions and prove that the nondegeneracy condition is necessary. We give sufficient conditions for some periodic solutions to be orbitally stable in linear approximation. Via the averaging method, the results are extended to a class of Hamiltonian systems with fast and slow variables close to the systems of semi-d...
Haas, C; Drenth, J; Wilson, WW
1999-01-01
Tn recent publications it was pointed out that there is a correlation between the observed values of the solubility of proteins in aqueous solutions and the second virial coefficient of the solution. In this paper we give a theoretical explanation of this relation. The derived theoretical expression
Haas, C; Drenth, J; Wilson, WW
1999-01-01
Tn recent publications it was pointed out that there is a correlation between the observed values of the solubility of proteins in aqueous solutions and the second virial coefficient of the solution. In this paper we give a theoretical explanation of this relation. The derived theoretical expression
Anca Visinescu
2011-04-01
Full Text Available Using the multiple scales method, the interaction between two bright and one dark solitons is studied. Provided that a long wave-short wave resonance condition is satisfied, the two-component Zakharov-Yajima-Oikawa (ZYO completely integrable system is obtained. By using a Madelung fluid description, the one-soliton solutions of the corresponding ZYO system are determined. Furthermore, a discussion on the interaction between one bright and two dark solitons is presented. In particular, this problem is reduced to solve a one-component ZYO system in the resonance conditions.
Stability and Fourier-series periodic solution in the binary stellar systems
Mia, Rajib
2016-01-01
In this paper, we use the restricted three body problem in the binary stellar systems, taking photogravitational effects of both the stars. The aim of this study is to investigate the motion of the infinitesimal mass in the vicinity of the Lagrangian points. We have computed semi-analytical expressions for the locations of the collinear points with the help of the perturbation technique. The stability of the triangular points is studied in stellar binary systems Kepler-34, Kepler-35, Kepler-413 and Kepler-16. To investigate the stability of the triangular points, we have obtained the expressions for critical mass which depends on the radiation of both primaries. Fourier-series method is applied to obtain periodic orbits of the infinitesimal mass around triangular points in binary stellar systems. We have obtained Fourier expansions of the periodic orbits around triangular points upto third order terms. A comparison is made between periodic orbits obtained by Fourier-series method and with Runge-Kutta integrat...
Kinetics and mechanism of the oxidation of bromide by periodate in aqueous acidic solution.
Szél, Viktor; Csekő, György; Horváth, Attila K
2014-11-13
The periodate–bromide reaction has been studied spectrophotometrically mainly in excess of bromide ion, monitoring the formation of the total amount of bromine at 450 nm at acidic buffered conditions and at a constant ionic strength in the presence of a phosphoric acid/dihydrogen phosphate buffer. The stoichiometry of the reaction was established to be strictly IO4(–) + 2Br(–) + 2H(+) → Br2 + IO3(–) + H2O. The formal kinetic order of the reactants was found to be perfectly one and two in the cases of periodate and bromide, respectively, but that of the hydrogen ion lies between one and two. We have also provided experimental evidence that dihydrogen phosphate accelerates the formation of bromine, suggesting the appearance of strong buffer assistance. On the basis of the experiments, a simple two-step kinetic model is proposed involving BrIO3 as a key intermediate that perfectly explains all of the experimental findings. Furthermore, we have also shown that in huge excess of bromide, the apparent rate coefficient obtained from the individual curve fitting method of the absorbance–time series is necessarily independent of the initial periodate concentration that may falsely be interpreted as the rate of bromine formation is also independent of the concentration of periodate.
N. N. Nefedov
2016-01-01
Full Text Available Parabolic singularly perturbed problems have been actively studied in recent years in connection with a large number of practical applications: chemical kinetics, synergetics, astrophysics, biology, and so on. In this work a singularly perturbed periodic problem for a parabolic reaction-diﬀusion equation is studied in the two-dimensional case. The case when there is an internal transition layer under unbalanced nonlinearity is considered. The internal layer is localised near the so called transitional curve. An asymptotic expansion of the solution is constructed and an asymptotics for the transitional curve is determined. The asymptotical expansion consists of a regular part, an interior layer part and a boundary part. In this work we focus on the interior layer part. In order to describe it in the neighborhood of the transition curve the local coordinate system is introduced and the stretched variables are used. To substantiate the asymptotics thus constructed, the asymptotic method of diﬀerential inequalities is used. The upper and lower solutions are constructed by suﬃciently complicated modiﬁcation of the asymptotic expansion of the solution. The Lyapunov asymptotical stability of the solution was proved by using the method of contracting barriers. This method is based on the asymptotic comparison principle and uses the upper and lower solutions which are exponentially tending to the solution to the problem. As a result, the solution is locally unique.The article is published in the authors’ wording.
A Novel Method for Optimal Solution of Fuzzy Chance Constraint Single-Period Inventory Model
Anuradha Sahoo
2016-01-01
Full Text Available A method is proposed for solving single-period inventory fuzzy probabilistic model (SPIFPM with fuzzy demand and fuzzy storage space under a chance constraint. Our objective is to maximize the total profit for both overstock and understock situations, where the demand D~j for each product j in the objective function is considered as a fuzzy random variable (FRV and with the available storage space area W~, which is also a FRV under normal distribution and exponential distribution. Initially we used the weighted sum method to consider both overstock and understock situations. Then the fuzziness of the model is removed by ranking function method and the randomness of the model is removed by chance constrained programming problem, which is a deterministic nonlinear programming problem (NLPP model. Finally this NLPP is solved by using LINGO software. To validate and to demonstrate the results of the proposed model, numerical examples are given.
Wu, Shu-Hua; Hao, Jian-Hong; Xu, Hai-Bo
2010-02-01
In the case where the knowledge of goal states is not known, the controllers are constructed to stabilize unstable steady states for a coupled dynamos system. A delayed feedback control technique is used to suppress chaos to unstable focuses and unstable periodic orbits. To overcome the topological limitation that the saddle-type steady state cannot be stabilized, an adaptive control based on LaSalle's invariance principle is used to control chaos to unstable equilibrium (i.e. saddle point, focus, node, etc.). The control technique does not require any computer analysis of the system dynamics, and it operates without needing to know any explicit knowledge of the desired steady-state position.
Thin-Layer Solutions of the Helmholtz and Related Equations
Ockendon, J. R.
2012-01-01
This paper concerns a certain class of two-dimensional solutions to four generic partial differential equations-the Helmholtz, modified Helmholtz, and convection-diffusion equations, and the heat conduction equation in the frequency domain-and the connections between these equations for this particular class of solutions.S pecifically, we consider thin-layer solutions, valid in narrow regions across which there is rapid variation, in the singularly perturbed limit as the coefficient of the Laplacian tends to zero.F or the wellstudied Helmholtz equation, this is the high-frequency limit and the solutions in question underpin the conventional ray theory/WKB approach in that they provide descriptions valid in some of the regions where these classical techniques fail.E xamples are caustics, shadow boundaries, whispering gallery, and creeping waves and focusing and bouncing ball modes.It transpires that virtually all such thin-layer models reduce to a class of generalized parabolic wave equations, of which the heat conduction equation is a special case. Moreover, in most situations, we will find that the appropriate parabolic wave equation solutions can be derived as limits of exact solutions of the Helmholtz equation.W e also show how reasonably well-understood thin-layer phenomena associated with any one of the four generic equations may translate into less well-known effects associated with the others.In addition, our considerations also shed some light on the relationship between the methods of matched asymptotic, WKB, and multiple-scales expansions. © 2012 Society for Industrial and Applied Mathematics.
MULTIPLE SOLUTIONS OF NONHOMOGENEOUS FOR RELATED CHOQUARD'S EQUATION
无
2000-01-01
This paper considers the existence of solutions for the following problem: where v(x) be a continuous function on R3,v(x)<0,～v(x)-→0, (as |x|-→∞); g(x)0,g(x)q0 and g(x) ∈H-1(R3). The author proves that there exists a constant C, such that |g(x)|H{-1 C,then there are at least two solutions for the above problem.
New solutions of initial conditions in general relativity
Tafel, J
2013-01-01
We find new classes of exact solutions of the initial momentum constraint for vacuum Einstein's equations. They are either axially symmetric or the exterior curvature tensor has a simple algebraic structure. In general the mean curvature $H$ is non-constant and initial metric is not conformally flat. Solutions depend on several free functions. The conformal method of Lichnerowicz, Choquet-Bruhat and York is used to prove solvability of the Hamiltonian constraint if $H$ vanishes. The existence of marginally trapped surfaces in initial manifold is discussed.
Solution aversion: On the relation between ideology and motivated disbelief.
Campbell, Troy H; Kay, Aaron C
2014-11-01
There is often a curious distinction between what the scientific community and the general population believe to be true of dire scientific issues, and this skepticism tends to vary markedly across groups. For instance, in the case of climate change, Republicans (conservatives) are especially skeptical of the relevant science, particularly when they are compared with Democrats (liberals). What causes such radical group differences? We suggest, as have previous accounts, that this phenomenon is often motivated. However, the source of this motivation is not necessarily an aversion to the problem, per se, but an aversion to the solutions associated with the problem. This difference in underlying process holds important implications for understanding, predicting, and influencing motivated skepticism. In 4 studies, we tested this solution aversion explanation for why people are often so divided over evidence and why this divide often occurs so saliently across political party lines. Studies 1, 2, and 3-using correlational and experimental methodologies-demonstrated that Republicans' increased skepticism toward environmental sciences may be partly attributable to a conflict between specific ideological values and the most popularly discussed environmental solutions. Study 4 found that, in a different domain (crime), those holding a more liberal ideology (support for gun control) also show skepticism motivated by solution aversion.
Christopoulou, P.-E.; Papageorgiou, A. [Department of Physics, University of Patras, 26500 Patra (Greece); Kleidis, S. [Helliniki Astronomiki Enosi, Athens (Greece); Tsantilas, S. [Department of Astrophysics, Astronomy and Mechanics, Faculty of Physics, Athens University, Panepistimiopolis, Zografos 15784, Athens (Greece)
2012-02-15
We present the first multicolor CCD photometry for the eclipsing binary V380 Cassiopeia (V380 Cas) observed on 34 nights in 2009 and 2010 at the University of Patras Observatory. The PHOEBE program based on the Wilson-Devinney algorithm was used to analyze the first complete BVR{sub c} I{sub c} light curves. It was found that V380 Cas was misclassified and it is a well-detached system consisting of two main-sequence stars. A range of solutions found to give satisfactory fits to the observations is also investigated. The first orbital solution based on the photometric mass ratio q = 1.08 of almost equal temperatures and masses and orbital inclination of i = 86.{sup 0}57 was obtained. In addition, based on all available times of light minima, including 12 new ones, a new orbital period of P = 2.714539884 days is given.
Refined rotational period, pole solution, and shape model for (3200) Phaethon
Ansdell, Megan; Meech, Karen J.; Kaluna, Heather [NASA Astrobiology Institute, Honolulu, HI 96822 (United States); Hainaut, Olivier [European Southern Observatory, Karl Schwarzschild Straße, 85748 Garching bei München (Germany); Buie, Marc W. [Southwest Research Institute, 1050 Walnut Street, Suite 300, Boulder, CO 80302 (United States); Bauer, James [Jet Propulsion Laboratory, 4800 Oak Grove Drive, MS 183-401, Pasadena, CA 91109 (United States); Dundon, Luke, E-mail: mansdell@ifa.hawaii.edu [United States Navy, Washington, DC 20350 (United States)
2014-09-20
(3200) Phaethon exhibits both comet- and asteroid-like properties, suggesting it could be a rare transitional object such as a dormant comet or previously volatile-rich asteroid. This justifies detailed study of (3200) Phaethon's physical properties as a better understanding of asteroid-comet transition objects can provide insight into minor body evolution. We therefore acquired time series photometry of (3200) Phaethon over 15 nights from 1994 to 2013, primarily using the Tektronix 2048 × 2048 pixel CCD on the University of Hawaii 2.2 m telescope. We utilized light curve inversion to (1) refine (3200) Phaethon's rotational period to P = 3.6032 ± 0.0008 hr; (2) estimate a rotational pole orientation of λ = +85° ± 13° and β = –20° ± 10°; and (3) derive a shape model. We also used our extensive light curve data set to estimate the slope parameter of (3200) Phaethon's phase curve as G ∼ 0.06, consistent with C-type asteroids. We discuss how this highly oblique pole orientation with a negative ecliptic latitude supports previous evidence for (3200) Phaethon's origin in the inner main asteroid belt as well as the potential for deeply buried volatiles fueling impulsive yet rare cometary outbursts.
陈凤德
2001-01-01
The aim of this paper is to investigate the existence and uniqueness of almost periodic solutions for the forced Rayleigh equation. By combining the theory of exponential dichotomies with Liapunov functions, we obtain an interesting result on the existence of almost periodic solutions.
Liu Zhenjie
2009-01-01
Full Text Available This paper investigates the existence of periodic solutions of a ratio-dependent predator-prey diffusion system with Michaelis-Menten functional responses and time delays in a two-patch environment on time scales. By using a continuation theorem based on coincidence degree theory, we obtain suffcient criteria for the existence of periodic solutions for the system. Moreover, when the time scale is chosen as or , the existence of the periodic solutions of the corresponding continuous and discrete models follows. Therefore, the methods are unified to provide the existence of the desired solutions for the continuous differential equations and discrete difference equations.
Zhenguo Luo
2013-01-01
Full Text Available Suffiicient and realistic conditions are established in this paper for the existence and global attractivity of a positive periodic solution to the neutral multidelay logarithmic population model with impulse by using the theory of abstract continuous theorem of k-set contractive operator and some inequality techniques. The results improve and generalize the known ones in Li 1999, Lu and Ge 2004, Y. Luo and Z. G. Luo 2010, and Wang et al. 2009. As an application, we also give an example to illustrate the feasibility of our main results.
Li, Bing; Li, Yongkun; Zhang, Xuemei
2016-01-01
In this paper, by using the existence of the exponential dichotomy of linear dynamic equations on time scales and the theory of calculus on time scales, we study the existence and global exponential stability of periodic solutions for a class of n-dimensional neutral dynamic equations on time scales. We also present an example to illustrate the feasibility of our results. The results of this paper are completely new and complementary to the previously known results even in both the case of differential equations (time scale [Formula: see text]) and the case of difference equations (time scale [Formula: see text]).
Mingzhan Huang
2014-01-01
Full Text Available Two predator-prey models with nonmonotonic functional response and state-dependent impulsive harvesting are formulated and analyzed. By using the geometry theory of semicontinuous dynamic system, we obtain the existence, uniqueness, and stability of the periodic solution and analyse the dynamic phenomenon of homoclinic bifurcation of the first system by choosing the harvesting rate β as control parameter. Besides, we also study the homoclinic bifurcation of the second system about parameter δ on the basis of the theory of rotated vector field. Finally, numerical simulations are presented to illustrate the results.
Carvalho, Tiago; Llibre, Jaume
2017-06-01
Lorenz studied the coupled Rosby waves and gravity waves using the differential system U˙ = -VW + bVZ,V˙ = UW - bUZ,Ẇ = -UV,Ẋ = -Z,Ż = bUV + X. This system has the two first integrals H1 = U2 + V2,H 2 = V2 + W2 + X2 + Z2. Our main result shows that in each invariant set {H1 = h1 > 0}∩{H2 = h2 > 0} there are at least four (resp., 2) periodic solutions of the differential system with b≠0 and h2 > h1 (resp., h2 < h1).
Battaglia, J.; Got, J.-L.; Okubo, P.
2003-01-01
We present methods for improving the location of long-period (LP) events, deep and shallow, recorded below Kilauea Volcano by the permanent seismic network. LP events might be of particular interest to understanding eruptive processes as their source mechanism is assumed to directly involve fluid transport. However, it is usually difficult or impossible to locate their source using traditional arrival time methods because of emergent wave arrivals. At Kilauea, similar LP waveform signatures suggest the existence of LP multiplets. The waveform similarity suggests spatially close sources, while catalog solutions using arrival time estimates are widely scattered beneath Kilauea's summit caldera. In order to improve estimates of absolute LP location, we use the distribution of seismic amplitudes corrected for station site effects. The decay of the amplitude as a function of hypocentral distance is used for inferring LP location. In a second stage, we use the similarity of the events to calculate their relative positions. The analysis of the entire LP seismicity recorded between January 1997 and December 1999 suggests that a very large part of the LP event population, both deep and shallow, is generated by a small number of compact sources. Deep events are systematically composed of a weak high-frequency onset followed by a low-frequency wave train. Aligning the low-frequency wave trains does not lead to aligning the onsets indicating the two parts of the signal are dissociated. This observation favors an interpretation in terms of triggering and resonance of a magmatic conduit. Instead of defining fault planes, the precise relocation of similar LP events, based on the alignment of the high-energy low-frequency wave trains, defines limited size volumes. Copyright 2003 by the American Geophysical Union.
CHENYong; WANGQi; LIBiao
2004-01-01
We generalize the algebraic method presented by Fan [J.Phys. A: Math. Gen. 36 (2003) 7009)] to uniformly construct a series of soliton-like solutions and double-like periodic solutions for nonlinear partial differential equations (NPDE). As an application of the method, we choose a (2+1)-dimensional asymmetric Nizhnik Novikov Vesselov equation and successfully construct new and more general solutions including a series of nontraveling wave and coefficient functions'soliton-like solutions, double-like periodic and trigonometric-like function solutions.
CHEN Yong; WANG Qi; LI Biao
2004-01-01
We generalize the algebraic method presented by Fan [J. Phys. A: Math. Gen. 36 (2003) 7009)] to uniformly construct a series of soliton-like solutions and double-like periodic solutions for nonlinear partial differential equations(NPDE). As an application of the method, we choose a (2+1)-dimensional asymmetric Nizhnik-Novikov-Vesselov equation and successfully construct new and more general solutions including a series of nontraveling wave and coefficient functions' soliton-like solutions, double-like periodic and trigonometric-like function solutions.
Farcot, Etienne; Gouzé, Jean-Luc
2009-12-01
This paper concerns periodic solutions of a class of equations that model gene regulatory networks. Unlike the vast majority of previous studies, it is not assumed that all decay rates are identical. To handle this more general situation, we rely on monotonicity properties of these systems. Under an alternative assumption, it is shown that a classical fixed point theorem for monotone, concave operators can be applied to these systems. The required assumption is expressed in geometrical terms as an alignment condition on so-called focal points. As an application, we show the existence and uniqueness of a stable periodic orbit for negative feedback loop systems in dimension 3 or more, and of a unique stable equilibrium point in dimension 2. This extends a theorem of Snoussi, which showed the existence of these orbits only.
Harmonic balance approach to the periodic solutions of the (an)harmonic relativistic oscillator
Belendez, Augusto [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)], E-mail: a.belendez@ua.es; Pascual, Carolina [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)
2007-11-19
The first-order harmonic balance method via the first Fourier coefficient is used to construct two approximate frequency-amplitude relations for the relativistic oscillator for which the nonlinearity (anharmonicity) is a relativistic effect due to the time line dilation along the world line. Making a change of variable, a new nonlinear differential equation is obtained and two procedures are used to approximately solve this differential equation. In the first the differential equation is rewritten in a form that does not contain a square-root expression, while in the second the differential equation is solved directly. The approximate frequency obtained using the second procedure is more accurate than the frequency obtained with the first due to the fact that, in the second procedure, application of the harmonic balance method produces an infinite set of harmonics, while in the first procedure only two harmonics are produced. Both approximate frequencies are valid for the complete range of oscillation amplitudes, and excellent agreement of the approximate frequencies with the exact one are demonstrated and discussed. The discrepancy between the first-order approximate frequency obtained by means of the second procedure and the exact frequency never exceeds 1.6%. We also obtained the approximate frequency by applying the second-order harmonic balance method and in this case the relative error is as low 0.31% for all the range of values of amplitude of oscillation A.
She, Qianhong; Jin, Xue; Li, Qinghua; Tang, Chuyang Y
2012-05-01
Osmotically driven membrane processes, such as forward osmosis (FO) and pressure retarded osmosis (PRO), are attracting increasing interest in research and applications in environment and energy related fields. In this study, we systematically investigated the alginate fouling on an osmotic membrane during FO operation using four types of draw solutions (NaCl, MgCl(2), CaCl(2) and Ca(NO(3))(2)) to elucidate the relationships between reverse (from draw solution to feed solution) and forward (from feed solution to draw solution) solute diffusion, and membrane fouling. At the same water flux level (achieved by adjusting the draw solution concentration), the greatest reverse solute diffusion rate was observed for NaCl draw solution, followed by Ca(NO(3))(2) draw solution, and then CaCl(2) draw solution and MgCl(2) draw solution, the order of which was consistent with that of their solute permeability coefficients. Moreover, the reverse solute diffusion of draw solute (especially divalent cation) can change the feed solution chemistry and thus enhance membrane fouling by alginate, the extent of which is related to the rate of the reverse draw solute diffusion and its ability to interact with the foulant. The extent of fouling for the four types of draw solution followed an order of Ca(NO(3))(2) > CaCl(2) > MgCl(2) > NaCl. On the other hand, the rate of forward diffusion of feed solute (e.g., Na(+)) was in turn promoted under severe membrane fouling in active layer facing draw solution orientation, which may be attributed to the fouling enhanced concentration polarization (pore clogging enhanced ICP and cake enhanced concentration polarization). The enhanced concentration polarization can lead to additional water flux reduction and is an important mechanism governing the water flux behavior during FO membrane fouling. Findings have significant implications for the draw solution selection and membrane fouling control in osmotically driven membrane processes.
PHAT XIII: The Cepheid Period-Luminosity Relation in M31 Based on the PHAT Survey
Wagner-Kaiser, R; Dalcanton, J J; Williams, B F; Dolphin, A
2015-01-01
Using Hubble Space Telescope Advanced Camera for Surveys (HST/ACS) and Wide Field Camera 3 (WFC3) observations from the Panchromatic Hubble Andromeda Treasury (PHAT), we present new period-luminosity relations for Cepheid variables in M31. Cepheid from several ground-based studies are identified in the PHAT pho- tometry to derive new Period-Luminosity and Wesenheit Period-Luminosity relations in the NIR and visual filters. We derive a distance modulus to M31 of 24.51+/-0.08 in the IR bands and 24.32+/-0.09 in the visual bands, including the first PL relations in the F475W and F814W filters for M31. Our derived visual and IR distance moduli dis- agree at slightly more than a 1-{\\sigma} level. Differences in the Period-Luminosity relations between ground-based and HST observations are investigated for a subset of Cepheids. We find a significant discrepancy between ground-based and HST Period-Luminosity relations with the same Cepheids, suggesting adverse effects from photometric contam- ination in ground-based ...