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Sample records for volterra equations

  1. Optimal control of stochastic difference Volterra equations an introduction

    CERN Document Server

    Shaikhet, Leonid

    2015-01-01

    This book showcases a subclass of hereditary systems, that is, systems with behaviour depending not only on their current state but also on their past history; it is an introduction to the mathematical theory of optimal control for stochastic difference Volterra equations of neutral type. As such, it will be of much interest to researchers interested in modelling processes in physics, mechanics, automatic regulation, economics and finance, biology, sociology and medicine for all of which such equations are very popular tools. The text deals with problems of optimal control such as meeting given performance criteria, and stabilization, extending them to neutral stochastic difference Volterra equations. In particular, it contrasts the difference analogues of solutions to optimal control and optimal estimation problems for stochastic integral Volterra equations with optimal solutions for corresponding problems in stochastic difference Volterra equations. Optimal Control of Stochastic Difference Volterra Equation...

  2. Hamiltonian structure of the Lotka-Volterra equations

    Science.gov (United States)

    Nutku, Y.

    1990-03-01

    The Lotka-Volterra equations governing predator-prey relations are shown to admit Hamiltonian structure with respect to a generalized Poisson bracket. These equations provide an example of a system for which the naive criterion for the existence of Hamiltonian structure fails. We show further that there is a three-component generalization of the Lotka-Volterra equations which is a bi-Hamiltonian system.

  3. Solvability of Urysohn and Urysohn-Volterra equations with hysteresis in weighted spaces

    International Nuclear Information System (INIS)

    Darwish Mohamed Abdalla

    2005-09-01

    The existence of solutions to nonlinear integral equations of the second kind with hysteresis, of Urysohn-Volterra and Urysohn types has been established. We develop the solvability theory of Urysohn-Volterra equation with hysteresis in weighted spaces proposed by the author [M.A. Darwish, On solvability of Urysohn-Volterra equations with hysteresis in weighted spaces, J. Integral Equations and Application, 14(2) (2002), 151-163]. (author)

  4. Singularly perturbed volterra integro-differential equations | Bijura ...

    African Journals Online (AJOL)

    Several investigations have been made on singularly perturbed integral equations. This paper aims at presenting an algorithm for the construction of asymptotic solutions and then provide a proof asymptotic correctness to singularly perturbed systems of Volterra integro-differential equations. Mathematics Subject

  5. On a Volterra Stieltjes integral equation

    Directory of Open Access Journals (Sweden)

    P. T. Vaz

    1990-01-01

    Full Text Available The paper deals with a study of linear Volterra integral equations involving Lebesgue-Stieltjes integrals in two independent variables. The authors prove an existence theorem using the Banach fixed-point principle. An explicit example is also considered.

  6. On solutions of neutral stochastic delay Volterra equations with singular kernels

    Directory of Open Access Journals (Sweden)

    Xiaotai Wu

    2012-08-01

    Full Text Available In this paper, existence, uniqueness and continuity of the adapted solutions for neutral stochastic delay Volterra equations with singular kernels are discussed. In addition, continuous dependence on the initial date is also investigated. Finally, stochastic Volterra equation with the kernel of fractional Brownian motion is studied to illustrate the effectiveness of our results.

  7. Calculation of Volterra kernels for solutions of nonlinear differential equations

    NARCIS (Netherlands)

    van Hemmen, JL; Kistler, WM; Thomas, EGF

    2000-01-01

    We consider vector-valued autonomous differential equations of the form x' = f(x) + phi with analytic f and investigate the nonanticipative solution operator phi bar right arrow A(phi) in terms of its Volterra series. We show that Volterra kernels of order > 1 occurring in the series expansion of

  8. Any order approximate analytical solution of the nonlinear Volterra's integral equation for accelerator dynamic systems

    International Nuclear Information System (INIS)

    Liu Chunliang; Xie Xi; Chen Yinbao

    1991-01-01

    The universal nonlinear dynamic system equation is equivalent to its nonlinear Volterra's integral equation, and any order approximate analytical solution of the nonlinear Volterra's integral equation is obtained by exact analytical method, thus giving another derivation procedure as well as another computation algorithm for the solution of the universal nonlinear dynamic system equation

  9. Invariants for the generalized Lotka-Volterra equations

    Science.gov (United States)

    Cairó, Laurent; Feix, Marc R.; Goedert, Joao

    A generalisation of Lotka-Volterra System is given when self limiting terms are introduced in the model. We use a modification of the Carleman embedding method to find invariants for this system of equations. The position and stability of the equilibrium point and the regression of system under invariant conditions are studied.

  10. Numerical Study of Two-Dimensional Volterra Integral Equations by RDTM and Comparison with DTM

    Directory of Open Access Journals (Sweden)

    Reza Abazari

    2013-01-01

    Full Text Available The two-dimensional Volterra integral equations are solved using more recent semianalytic method, the reduced differential transform method (the so-called RDTM, and compared with the differential transform method (DTM. The concepts of DTM and RDTM are briefly explained, and their application to the two-dimensional Volterra integral equations is studied. The results obtained by DTM and RDTM together are compared with exact solution. As an important result, it is depicted that the RDTM results are more accurate in comparison with those obtained by DTM applied to the same Volterra integral equations. The numerical results reveal that the RDTM is very effective, convenient, and quite accurate compared to the other kind of nonlinear integral equations. It is predicted that the RDTM can be found widely applicable in engineering sciences.

  11. Aitken extrapolation and epsilon algorithm for an accelerated solution of weakly singular nonlinear Volterra integral equations

    International Nuclear Information System (INIS)

    Mesgarani, H; Parmour, P; Aghazadeh, N

    2010-01-01

    In this paper, we apply Aitken extrapolation and epsilon algorithm as acceleration technique for the solution of a weakly singular nonlinear Volterra integral equation of the second kind. In this paper, based on Tao and Yong (2006 J. Math. Anal. Appl. 324 225-37.) the integral equation is solved by Navot's quadrature formula. Also, Tao and Yong (2006) for the first time applied Richardson extrapolation to accelerating convergence for the weakly singular nonlinear Volterra integral equations of the second kind. To our knowledge, this paper may be the first attempt to apply Aitken extrapolation and epsilon algorithm for the weakly singular nonlinear Volterra integral equations of the second kind.

  12. Initial layer theory and model equations of Volterra type

    International Nuclear Information System (INIS)

    Bijura, Angelina M.

    2003-10-01

    It is demonstrated here that there exist initial layers to singularly perturbed Volterra equations whose thicknesses are not of order of magnitude of 0(ε), ε → 0. It is also shown that the initial layer theory is extremely useful because it allows one to construct the approximate solution to an equation, which is almost identical to the exact solution. (author)

  13. Asymptotic Behavior of Solutions for Nonlinear Volterra Discrete Equations

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    E. Messina

    2008-01-01

    Full Text Available We consider nonlinear difference equations of unbounded order of the form xi=bi−∑j=0iai,jfi−j(xj,  i=0,1,2,…, where fj(x  (j=0,…,i are suitable functions. We establish sufficient conditions for the boundedness and the convergence of xi as i→+∞. Some of these conditions are interesting mainly for studying stability of numerical methods for Volterra integral equations.

  14. An integrable symmetric (2+1)-dimensional Lotka-Volterra equation and a family of its solutions

    International Nuclear Information System (INIS)

    Hu Xingbiao; Li Chunxia; Nimmo, Jonathan J C; Yu Guofu

    2005-01-01

    A symmetric (2+1)-dimensional Lotka-Volterra equation is proposed. By means of a dependent variable transformation, the equation is firstly transformed into multilinear form and further decoupled into bilinear form by introducing auxiliary independent variables. A bilinear Baecklund transformation is found and then the corresponding Lax pair is derived. Explicit solutions expressed in terms of pfaffian solutions of the bilinear form of the symmetric (2+1)-dimensional Lotka-Volterra equation are given. As a special case of the pfaffian solutions, we obtain soliton solutions and dromions

  15. On Regularly Varying and History-Dependent Convergence Rates of Solutions of a Volterra Equation with Infinite Memory

    Directory of Open Access Journals (Sweden)

    Appleby JohnAD

    2010-01-01

    Full Text Available We consider the rate of convergence to equilibrium of Volterra integrodifferential equations with infinite memory. We show that if the kernel of Volterra operator is regularly varying at infinity, and the initial history is regularly varying at minus infinity, then the rate of convergence to the equilibrium is regularly varying at infinity, and the exact pointwise rate of convergence can be determined in terms of the rate of decay of the kernel and the rate of growth of the initial history. The result is considered both for a linear Volterra integrodifferential equation as well as for the delay logistic equation from population biology.

  16. The Volterra's integral equation theory for accelerator single-freedom nonlinear components

    International Nuclear Information System (INIS)

    Wang Sheng; Xie Xi

    1996-01-01

    The Volterra's integral equation equivalent to the dynamic equation of accelerator single-freedom nonlinear components is given, starting from which the transport operator of accelerator single-freedom nonlinear components and its inverse transport operator are obtained. Therefore, another algorithm for the expert system of the beam transport operator of accelerator single-freedom nonlinear components is developed

  17. Characterisation of Exponential Convergence to Nonequilibrium Limits for Stochastic Volterra Equations

    Directory of Open Access Journals (Sweden)

    John A. D. Appleby

    2008-01-01

    Full Text Available This paper considers necessary and sufficient conditions for the solution of a stochastically and deterministically perturbed Volterra equation to converge exponentially to a nonequilibrium and nontrivial limit. Convergence in an almost sure and pth mean sense is obtained.

  18. Nonlinear Delay Discrete Inequalities and Their Applications to Volterra Type Difference Equations

    Directory of Open Access Journals (Sweden)

    Yu Wu

    2010-01-01

    Full Text Available Delay discrete inequalities with more than one nonlinear term are discussed, which generalize some known results and can be used in the analysis of various problems in the theory of certain classes of discrete equations. Application examples to show boundedness and uniqueness of solutions of a Volterra type difference equation are also given.

  19. Biorthogonal Systems Approximating the Solution of the Nonlinear Volterra Integro-Differential Equation

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    Berenguer MI

    2010-01-01

    Full Text Available This paper deals with obtaining a numerical method in order to approximate the solution of the nonlinear Volterra integro-differential equation. We define, following a fixed-point approach, a sequence of functions which approximate the solution of this type of equation, due to some properties of certain biorthogonal systems for the Banach spaces and .

  20. Global existence for Volterra-Fredholm type neutral impulsive functional integrodifferential equations

    Directory of Open Access Journals (Sweden)

    V. Vijayakumar

    2012-09-01

    Full Text Available n this paper, we study the global existence of solutions for the initial value problems for Volterra-Fredholm type neutral impulsive functional integrodifferential equations. Using the Leray-Schauder's Alternative theorem, we derive conditions under which a solution exists globally. An application is provided to illustrate the theory.

  1. Stability analysis of solutions to nonlinear stiff Volterra functional differential equations in Banach spaces

    Institute of Scientific and Technical Information of China (English)

    LI Shoufu

    2005-01-01

    A series of stability, contractivity and asymptotic stability results of the solutions to nonlinear stiff Volterra functional differential equations (VFDEs) in Banach spaces is obtained, which provides the unified theoretical foundation for the stability analysis of solutions to nonlinear stiff problems in ordinary differential equations(ODEs), delay differential equations(DDEs), integro-differential equations(IDEs) and VFDEs of other type which appear in practice.

  2. Numerical Solution of Nonlinear Volterra Integral Equations System Using Simpson’s 3/8 Rule

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    Adem Kılıçman

    2012-01-01

    Full Text Available The Simpson’s 3/8 rule is used to solve the nonlinear Volterra integral equations system. Using this rule the system is converted to a nonlinear block system and then by solving this nonlinear system we find approximate solution of nonlinear Volterra integral equations system. One of the advantages of the proposed method is its simplicity in application. Further, we investigate the convergence of the proposed method and it is shown that its convergence is of order O(h4. Numerical examples are given to show abilities of the proposed method for solving linear as well as nonlinear systems. Our results show that the proposed method is simple and effective.

  3. Continuous Multistep Methods for Volterra Integro-Differential

    African Journals Online (AJOL)

    Kamoh et al.

    DIFFERENTIAL EQUATIONS OF THE SECOND ORDER. 1Kamoh N.M. ... methods, Volterra integro-differential equation, Convergent, ...... Research of a Multistep Method Applied to Numerical Solution of. Volterra ... Congress on Engineering.

  4. New stability and boundedness results to Volterra integro-differential equations with delay

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    Cemil Tunç

    2016-04-01

    Full Text Available In this paper, we consider a certain non-linear Volterra integro-differential equations with delay. We study stability and boundedness of solutions. The technique of proof involves defining suitable Lyapunov functionals. Our results improve and extend the results obtained in literature.

  5. A remark on the stability and boundedness criteria in retarded Volterra integro-differential equations

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    Cemil Tunç

    2017-10-01

    Full Text Available In this article, the authors obtain some clear assumptions for the asymptotic stability (AS and boundedness (B of solutions of non-linear retarded Volterra integro-differential equations (VIDEs of first order by constructing a new Lyapunov functional (LF. The results obtained are new and differ from those found in the literature, and they also contain and improve a result found in the literature under more less restrictive conditions. We establish an example and give a discussion to indicate the applicability of the weaker conditions obtained. We also employ MATLAB-Simulink to display the behaviors of the orbits of the (VIDEs considered. Keywords: Nonlinear, Volterra integro-differential equations, First order, Asymptotic stability, Boundedness, Lyapunov functional, MSC: 34D05, 34K20, 45J05

  6. A Two-Species Cooperative Lotka-Volterra System of Degenerate Parabolic Equations

    OpenAIRE

    Sun, Jiebao; Zhang, Dazhi; Wu, Boying

    2011-01-01

    We consider a cooperating two-species Lotka-Volterra model of degenerate parabolic equations. We are interested in the coexistence of the species in a bounded domain. We establish the existence of global generalized solutions of the initial boundary value problem by means of parabolic regularization and also consider the existence of the nontrivial time-periodic solution for this system.

  7. A predictor-corrector scheme for solving the Volterra integral equation

    KAUST Repository

    Al Jarro, Ahmed

    2011-08-01

    The occurrence of late time instabilities is a common problem of almost all time marching methods developed for solving time domain integral equations. Implicit marching algorithms are now considered stable with various efforts that have been developed for removing low and high frequency instabilities. On the other hand, literature on stabilizing explicit schemes, which might be considered more efficient since they do not require a matrix inversion at each time step, is practically non-existent. In this work, a stable but still explicit predictor-corrector scheme is proposed for solving the Volterra integral equation and its efficacy is verified numerically. © 2011 IEEE.

  8. The conditions of existence of first integrals and Hamiltonian structures of Lotka-Volterra and Volterra systems

    International Nuclear Information System (INIS)

    Dubovik, V.M.; Galperin, A.G.; Richvitsky, V.S.; Slepnyov, S.K.

    2000-01-01

    A study of a certain subset of Volterra equations has revealed that some statements about time-independent constants of motion, Hamiltonian functions, and Poisson structure matrices appearing in the Lotka-Volterra equations, either regarded as proven or of the sort that could be proven, are not valid, in fact. Particular cases are given as examples to explain the reasons for the occurring phenomena

  9. Integrable deformations of Lotka-Volterra systems

    International Nuclear Information System (INIS)

    Ballesteros, Angel; Blasco, Alfonso; Musso, Fabio

    2011-01-01

    The Hamiltonian structure of a class of three-dimensional (3D) Lotka-Volterra (LV) equations is revisited from a novel point of view by showing that the quadratic Poisson structure underlying its integrability structure is just a real three-dimensional Poisson-Lie group. As a consequence, the Poisson coalgebra map Δ (2) that is given by the group multiplication provides the keystone for the explicit construction of a new family of 3N-dimensional integrable systems that, under certain constraints, contain N sets of deformed versions of the 3D LV equations. Moreover, by considering the most generic Poisson-Lie structure on this group, a new two-parametric integrable perturbation of the 3D LV system through polynomial and rational perturbation terms is explicitly found. -- Highlights: → A new Poisson-Lie approach to the integrability of Lotka-Volterra system is given. → New integrable deformations of the 3D Lotka-Volterra system are obtained. → Integrable Lotka-Volterra-type equations in 3N dimensions are deduced.

  10. On filtering over Îto-Volterra observations

    Directory of Open Access Journals (Sweden)

    Michael V. Basin

    2000-01-01

    Full Text Available In this paper, the Kalman-Bucy filter is designed for an Îto-Volterra process over Ito-Volterra observations that cannot be reduced to the case of a differential observation equation. The Kalman-Bucy filter is then designed for an Ito-Volterra process over discontinuous Ito-Volterra observations. Based on the obtained results, the filtering problem over discrete observations with delays is solved. Proofs of the theorems substantiating the filtering algorithms are given.

  11. On Regularly Varying and History-Dependent Convergence Rates of Solutions of a Volterra Equation with Infinite Memory

    OpenAIRE

    John A. D. Appleby

    2010-01-01

    We consider the rate of convergence to equilibrium of Volterra integrodifferential equations with infinite memory. We show that if the kernel of Volterra operator is regularly varying at infinity, and the initial history is regularly varying at minus infinity, then the rate of convergence to the equilibrium is regularly varying at infinity, and the exact pointwise rate of convergence can be determined in terms of the rate of decay of the kernel and the rate of growth of the initial history. ...

  12. Composite spectral functions for solving Volterra's population model

    International Nuclear Information System (INIS)

    Ramezani, M.; Razzaghi, M.; Dehghan, M.

    2007-01-01

    An approximate method for solving Volterra's population model for population growth of a species in a closed system is proposed. Volterra's model is a nonlinear integro-differential equation, where the integral term represents the effect of toxin. The approach is based upon composite spectral functions approximations. The properties of composite spectral functions consisting of few terms of orthogonal functions are presented and are utilized to reduce the solution of the Volterra's model to the solution of a system of algebraic equations. The method is easy to implement and yields very accurate result

  13. Representation of neural networks as Lotka-Volterra systems

    International Nuclear Information System (INIS)

    Moreau, Yves; Vandewalle, Joos; Louies, Stephane; Brenig, Leon

    1999-01-01

    We study changes of coordinates that allow the representation of the ordinary differential equations describing continuous-time recurrent neural networks into differential equations describing predator-prey models--also called Lotka-Volterra systems. We transform the equations for the neural network first into quasi-monomial form, where we express the vector field of the dynamical system as a linear combination of products of powers of the variables. In practice, this transformation is possible only if the activation function is the hyperbolic tangent or the logistic sigmoied. From this quasi-monomial form, we can directly transform the system further into Lotka-Volterra equations. The resulting Lotka-Volterra system is of higher dimension than the original system, but the behavior of its first variables is equivalent to the behavior of the original neural network

  14. Explicit solution of the Volterra integral equation for transient fields on inhomogeneous arbitrarily shaped dielectric bodies

    KAUST Repository

    Al Jarro, Ahmed

    2011-09-01

    A new predictor-corrector scheme for solving the Volterra integral equation to analyze transient electromagnetic wave interactions with arbitrarily shaped inhomogeneous dielectric bodies is considered. Numerical results demonstrating stability and accuracy of the proposed method are presented. © 2011 IEEE.

  15. Formal Derivation of Lotka-Volterra-Haken Amplitude Equations of Task-Related Brain Activity in Multiple, Consecutively Performed Tasks

    Science.gov (United States)

    Frank, T. D.

    The Lotka-Volterra-Haken equations have been frequently used in ecology and pattern formation. Recently, the equations have been proposed by several research groups as amplitude equations for task-related patterns of brain activity. In this theoretical study, the focus is on the circular causality aspect of pattern formation systems as formulated within the framework of synergetics. Accordingly, the stable modes of a pattern formation system inhibit the unstable modes, whereas the unstable modes excite the stable modes. Using this circular causality principle it is shown that under certain conditions the Lotka-Volterra-Haken amplitude equations can be derived from a general model of brain activity akin to the Wilson-Cowan model. The model captures the amplitude dynamics for brain activity patterns in experiments involving several consecutively performed multiple-choice tasks. This is explicitly demonstrated for two-choice tasks involving grasping and walking. A comment on the relevance of the theoretical framework for clinical psychology and schizophrenia is given as well.

  16. Multi-Hamiltonian structure of Lotka-Volterra and quantum Volterra models

    International Nuclear Information System (INIS)

    Cronstroem, C.; Noga, M.

    1995-01-01

    We consider evolution equations of the Lotka-Volterra type, and elucidate especially their formulation as canonical Hamiltonian systems. The general conditions under which these equations admit several conserved quantities (multi-Hamiltonians) are analysed. A special case, which is related to the Liouville model on a lattice, is considered in detail, both as a classical and as a quantum system. (orig.)

  17. He's homotopy perturbation method for solving systems of Volterra integral equations of the second kind

    International Nuclear Information System (INIS)

    Biazar, J.; Ghazvini, H.

    2009-01-01

    In this paper, the He's homotopy perturbation method is applied to solve systems of Volterra integral equations of the second kind. Some examples are presented to illustrate the ability of the method for linear and non-linear such systems. The results reveal that the method is very effective and simple.

  18. Hybrid MPI/OpenMP parallelization of the explicit Volterra integral equation solver for multi-core computer architectures

    KAUST Repository

    Al Jarro, Ahmed; Bagci, Hakan

    2011-01-01

    A hybrid MPI/OpenMP scheme for efficiently parallelizing the explicit marching-on-in-time (MOT)-based solution of the time-domain volume (Volterra) integral equation (TD-VIE) is presented. The proposed scheme equally distributes tested field values

  19. The Convergence Study of the Homotopy Analysis Method for Solving Nonlinear Volterra-Fredholm Integrodifferential Equations

    Directory of Open Access Journals (Sweden)

    Behzad Ghanbari

    2014-01-01

    Full Text Available We aim to study the convergence of the homotopy analysis method (HAM in short for solving special nonlinear Volterra-Fredholm integrodifferential equations. The sufficient condition for the convergence of the method is briefly addressed. Some illustrative examples are also presented to demonstrate the validity and applicability of the technique. Comparison of the obtained results HAM with exact solution shows that the method is reliable and capable of providing analytic treatment for solving such equations.

  20. A Fibonacci collocation method for solving a class of Fredholm–Volterra integral equations in two-dimensional spaces

    Directory of Open Access Journals (Sweden)

    Farshid Mirzaee

    2014-06-01

    Full Text Available In this paper, we present a numerical method for solving two-dimensional Fredholm–Volterra integral equations (F-VIE. The method reduces the solution of these integral equations to the solution of a linear system of algebraic equations. The existence and uniqueness of the solution and error analysis of proposed method are discussed. The method is computationally very simple and attractive. Finally, numerical examples illustrate the efficiency and accuracy of the method.

  1. Application of homotopy perturbation method for systems of Volterra integral equations of the first kind

    International Nuclear Information System (INIS)

    Biazar, J.; Eslami, M.; Aminikhah, H.

    2009-01-01

    In this article, an application of He's homotopy perturbation method is applied to solve systems of Volterra integral equations of the first kind. Some non-linear examples are prepared to illustrate the efficiency and simplicity of the method. Applying the method for linear systems is so easily that it does not worth to have any example.

  2. Automatic Control Systems Modeling by Volterra Polynomials

    Directory of Open Access Journals (Sweden)

    S. V. Solodusha

    2012-01-01

    Full Text Available The problem of the existence of the solutions of polynomial Volterra integral equations of the first kind of the second degree is considered. An algorithm of the numerical solution of one class of Volterra nonlinear systems of the first kind is developed. Numerical results for test examples are presented.

  3. On the Volterra integral equation relating creep and relaxation

    International Nuclear Information System (INIS)

    Anderssen, R S; De Hoog, F R; Davies, A R

    2008-01-01

    The evolving stress–strain response of a material to an applied deformation is causal. If the current response depends on the earlier history of the stress–strain dynamics of the material (i.e. the material has memory), then Volterra integral equations become the natural framework within which to model the response. For viscoelastic materials, when the response is linear, the dual linear Boltzmann causal integral equations are the appropriate model. The choice of one rather than the other depends on whether the applied deformation is a stress or a strain, and the associated response is, respectively, a creep or a relaxation. The duality between creep and relaxation is known explicitly and is referred to as the 'interconversion equation'. Rheologically, its importance relates to the fact that it allows the creep to be determined from knowledge of the relaxation and vice versa. Computationally, it has been known for some time that the recovery of the relaxation from the creep is more problematic than the creep from the relaxation. Recent research, using discrete models for the creep and relaxation, has confirmed that this is an essential feature of interconversion. In this paper, the corresponding result is generalized for continuous models of the creep and relaxation

  4. Variational Iteration Method for Volterra Functional Integrodifferential Equations with Vanishing Linear Delays

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    Ali Konuralp

    2014-01-01

    Full Text Available Application process of variational iteration method is presented in order to solve the Volterra functional integrodifferential equations which have multi terms and vanishing delays where the delay function θ(t vanishes inside the integral limits such that θ(t=qt for 0

  5. On various integrable discretizations of a general two-component Volterra system

    International Nuclear Information System (INIS)

    Babalic, Corina N; Carstea, A S

    2013-01-01

    We present two integrable discretizations of a general differential–difference bicomponent Volterra system. The results are obtained by discretizing directly the corresponding Hirota bilinear equations in two different ways. Multisoliton solutions are presented together with a new discrete form of Lotka–Volterra equation obtained by an alternative bilinearization. (paper)

  6. Comparative analysis of the influence of creep of concrete composite beams of steel - concrete model based on Volterra integral equation

    Directory of Open Access Journals (Sweden)

    Partov Doncho

    2017-01-01

    Full Text Available The paper presents analysis of the stress-strain behaviour and deflection changes due to creep in statically determinate composite steel-concrete beam according to EUROCODE 2, ACI209R-92 and Gardner&Lockman models. The mathematical model involves the equation of equilibrium, compatibility and constitutive relationship, i.e. an elastic law for the steel part and an integral-type creep law of Boltzmann - Volterra for the concrete part considering the above mentioned models. On the basis of the theory of viscoelastic body of Maslov-Arutyunian-Trost-Zerna-Bažant for determining the redistribution of stresses in beam section between concrete plate and steel beam with respect to time 't', two independent Volterra integral equations of the second kind have been derived. Numerical method based on linear approximation of the singular kernel function in the integral equation is presented. Example with the model proposed is investigated.

  7. Solutions of First-Order Volterra Type Linear Integrodifferential Equations by Collocation Method

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    Olumuyiwa A. Agbolade

    2017-01-01

    Full Text Available The numerical solutions of linear integrodifferential equations of Volterra type have been considered. Power series is used as the basis polynomial to approximate the solution of the problem. Furthermore, standard and Chebyshev-Gauss-Lobatto collocation points were, respectively, chosen to collocate the approximate solution. Numerical experiments are performed on some sample problems already solved by homotopy analysis method and finite difference methods. Comparison of the absolute error is obtained from the present method and those from aforementioned methods. It is also observed that the absolute errors obtained are very low establishing convergence and computational efficiency.

  8. [Generalization of the Lotka-Volterra equation].

    Science.gov (United States)

    Nazarenko, V G

    1976-01-01

    A complete qualitative study of Lotka--Volterra model with cooperative interactions in the system predator-prey is carried out. The model is as follows: (see abstract). The character of all possible stationary states is investigated in the first quadrant of the phase plane of the model variables depending on the system parameters. It is shown that for the generalized model considered unstable and stable limit cycles only of the infinite amplitude are possible in the first quadrant.

  9. Convergence Analysis of Generalized Jacobi-Galerkin Methods for Second Kind Volterra Integral Equations with Weakly Singular Kernels

    Directory of Open Access Journals (Sweden)

    Haotao Cai

    2017-01-01

    Full Text Available We develop a generalized Jacobi-Galerkin method for second kind Volterra integral equations with weakly singular kernels. In this method, we first introduce some known singular nonpolynomial functions in the approximation space of the conventional Jacobi-Galerkin method. Secondly, we use the Gauss-Jacobi quadrature rules to approximate the integral term in the resulting equation so as to obtain high-order accuracy for the approximation. Then, we establish that the approximate equation has a unique solution and the approximate solution arrives at an optimal convergence order. One numerical example is presented to demonstrate the effectiveness of the proposed method.

  10. Quasipolynomial generalization of Lotka-Volterra mappings

    Science.gov (United States)

    Hernández-Bermejo, Benito; Brenig, Léon

    2002-07-01

    In recent years, it has been shown that Lotka-Volterra mappings constitute a valuable tool from both the theoretical and the applied points of view, with developments in very diverse fields such as physics, population dynamics, chemistry and economy. The purpose of this work is to demonstrate that many of the most important ideas and algebraic methods that constitute the basis of the quasipolynomial formalism (originally conceived for the analysis of ordinary differential equations) can be extended into the mapping domain. The extension of the formalism into the discrete-time context is remarkable as far as the quasipolynomial methodology had never been shown to be applicable beyond the differential case. It will be demonstrated that Lotka-Volterra mappings play a central role in the quasipolynomial formalism for the discrete-time case. Moreover, the extension of the formalism into the discrete-time domain allows a significant generalization of Lotka-Volterra mappings as well as a whole transfer of algebraic methods into the discrete-time context. The result is a novel and more general conceptual framework for the understanding of Lotka-Volterra mappings as well as a new range of possibilities that become open not only for the theoretical analysis of Lotka-Volterra mappings and their generalizations, but also for the development of new applications.

  11. Quasipolynomial generalization of Lotka-Volterra mappings

    International Nuclear Information System (INIS)

    Hernandez-Bermejo, Benito; Brenig, Leon

    2002-01-01

    In recent years, it has been shown that Lotka-Volterra mappings constitute a valuable tool from both the theoretical and the applied points of view, with developments in very diverse fields such as physics, population dynamics, chemistry and economy. The purpose of this work is to demonstrate that many of the most important ideas and algebraic methods that constitute the basis of the quasipolynomial formalism (originally conceived for the analysis of ordinary differential equations) can be extended into the mapping domain. The extension of the formalism into the discrete-time context is remarkable as far as the quasipolynomial methodology had never been shown to be applicable beyond the differential case. It will be demonstrated that Lotka-Volterra mappings play a central role in the quasipolynomial formalism for the discrete-time case. Moreover, the extension of the formalism into the discrete-time domain allows a significant generalization of Lotka-Volterra mappings as well as a whole transfer of algebraic methods into the discrete-time context. The result is a novel and more general conceptual framework for the understanding of Lotka-Volterra mappings as well as a new range of possibilities that become open not only for the theoretical analysis of Lotka-Volterra mappings and their generalizations, but also for the development of new applications. (author)

  12. Fibonacci collocation method with a residual error Function to solve linear Volterra integro differential equations

    Directory of Open Access Journals (Sweden)

    Salih Yalcinbas

    2016-01-01

    Full Text Available In this paper, a new collocation method based on the Fibonacci polynomials is introduced to solve the high-order linear Volterra integro-differential equations under the conditions. Numerical examples are included to demonstrate the applicability and validity of the proposed method and comparisons are made with the existing results. In addition, an error estimation based on the residual functions is presented for this method. The approximate solutions are improved by using this error estimation.

  13. Application of Reproducing Kernel Method for Solving Nonlinear Fredholm-Volterra Integrodifferential Equations

    Directory of Open Access Journals (Sweden)

    Omar Abu Arqub

    2012-01-01

    Full Text Available This paper investigates the numerical solution of nonlinear Fredholm-Volterra integro-differential equations using reproducing kernel Hilbert space method. The solution ( is represented in the form of series in the reproducing kernel space. In the mean time, the n-term approximate solution ( is obtained and it is proved to converge to the exact solution (. Furthermore, the proposed method has an advantage that it is possible to pick any point in the interval of integration and as well the approximate solution and its derivative will be applicable. Numerical examples are included to demonstrate the accuracy and applicability of the presented technique. The results reveal that the method is very effective and simple.

  14. The solution of linear and nonlinear systems of Volterra functional equations using Adomian-Pade technique

    International Nuclear Information System (INIS)

    Dehghan, Mehdi; Shakourifar, Mohammad; Hamidi, Asgar

    2009-01-01

    The purpose of this study is to implement Adomian-Pade (Modified Adomian-Pade) technique, which is a combination of Adomian decomposition method (Modified Adomian decomposition method) and Pade approximation, for solving linear and nonlinear systems of Volterra functional equations. The results obtained by using Adomian-Pade (Modified Adomian-Pade) technique, are compared to those obtained by using Adomian decomposition method (Modified Adomian decomposition method) alone. The numerical results, demonstrate that ADM-PADE (MADM-PADE) technique, gives the approximate solution with faster convergence rate and higher accuracy than using the standard ADM (MADM).

  15. Global attractivity of positive periodic solution to periodic Lotka-Volterra competition systems with pure delay

    Science.gov (United States)

    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].

  16. Prediction of rotor blade-vortex interaction using Volterra integrals

    Energy Technology Data Exchange (ETDEWEB)

    Wong, A.; Nitzsche, F. [Carleton Univ., Dept. of Mechanical and Aerospace Engineering, Ottawa, Ontario (Canada)]. E-mail: Fred_Nitzsche@carleton.ca; Khalid, M. [National Research Council Canada, Inst. for Aerospace Research, Ottawa, Ontario (Canada)

    2004-07-01

    The theory of Volterra integral equations for nonlinear system is applied to the prediction of the nonlinear aerodynamic response of an NACA 0012 airfoil experiencing blade-vortex interaction. The phenomenon is first modeled in two-dimensions using an Euler/Navier-Stoke code, and the resulting unsteady aerodynamic flow field sequences are appropriately combined to form a training dataset. The Volterra kernels are identified in the time-domain characteristics of the selected data, which is in turn used to predict the nonlinear aerodynamic response of the airfoil. The Volterra kernel based data is then compared against a standard airfoil response. The predicted lift time histories of the airfoil are shown to be in good agreement with the aerodynamic data. (author)

  17. Prediction of rotor blade-vortex interaction using Volterra integrals

    International Nuclear Information System (INIS)

    Wong, A.; Nitzsche, F.; Khalid, M.

    2004-01-01

    The theory of Volterra integral equations for nonlinear system is applied to the prediction of the nonlinear aerodynamic response of an NACA 0012 airfoil experiencing blade-vortex interaction. The phenomenon is first modeled in two-dimensions using an Euler/Navier-Stoke code, and the resulting unsteady aerodynamic flow field sequences are appropriately combined to form a training dataset. The Volterra kernels are identified in the time-domain characteristics of the selected data, which is in turn used to predict the nonlinear aerodynamic response of the airfoil. The Volterra kernel based data is then compared against a standard airfoil response. The predicted lift time histories of the airfoil are shown to be in good agreement with the aerodynamic data. (author)

  18. Stochastic Lotka-Volterra equations: A model of lagged diffusion of technology in an interconnected world

    Science.gov (United States)

    Chakrabarti, Anindya S.

    2016-01-01

    We present a model of technological evolution due to interaction between multiple countries and the resultant effects on the corresponding macro variables. The world consists of a set of economies where some countries are leaders and some are followers in the technology ladder. All of them potentially gain from technological breakthroughs. Applying Lotka-Volterra (LV) equations to model evolution of the technology frontier, we show that the way technology diffuses creates repercussions in the partner economies. This process captures the spill-over effects on major macro variables seen in the current highly globalized world due to trickle-down effects of technology.

  19. Lotka-Volterra representation of general nonlinear systems.

    Science.gov (United States)

    Hernández-Bermejo, B; Fairén, V

    1997-02-01

    In this article we elaborate on the structure of the generalized Lotka-Volterra (GLV) form for nonlinear differential equations. We discuss here the algebraic properties of the GLV family, such as the invariance under quasimonomial transformations and the underlying structure of classes of equivalence. Each class possesses a unique representative under the classical quadratic Lotka-Volterra form. We show how other standard modeling forms of biological interest, such as S-systems or mass-action systems, are naturally embedded into the GLV form, which thus provides a formal framework for their comparison and for the establishment of transformation rules. We also focus on the issue of recasting of general nonlinear systems into the GLV format. We present a procedure for doing so and point at possible sources of ambiguity that could make the resulting Lotka-Volterra system dependent on the path followed. We then provide some general theorems that define the operational and algorithmic framework in which this is not the case.

  20. Transcendental smallness in singularly perturbed equations of volterra type

    International Nuclear Information System (INIS)

    Bijura, Angelina M.

    2003-11-01

    The application of different limit processes to a physical problem is an important tool in layer type techniques. Hence the study of initial layer correction functions is of central importance for understanding layer-type problems. It is shown that for singularly perturbed problems of Volterra type, the concept of transcendental smallness is an asymptotic one. Transcendentally small terms may be numerically important. (author)

  1. On vector analogs of the modified Volterra lattice

    Energy Technology Data Exchange (ETDEWEB)

    Adler, V E; Postnikov, V V [L D Landau Institute for Theoretical Physics, 1a Semenov pr, 142432 Chernogolovka (Russian Federation); Sochi Branch of Peoples' Friendship University of Russia, 32 Kuibyshev str, 354000 Sochi (Russian Federation)], E-mail: adler@itp.ac.ru, E-mail: postnikovvv@rambler.ru

    2008-11-14

    The zero curvature representations, Baecklund transformations, nonlinear superposition principle and the simplest explicit solutions of soliton and breather type are presented for two vector generalizations of modified Volterra lattice. The relations with some other integrable equations are established.

  2. Continuous multistep methods for volterra integro-differential ...

    African Journals Online (AJOL)

    A new class of numerical methods for Volterra integro-differential equations of the second order is developed. The methods are based on interpolation and collocation of the shifted Legendre polynomial as basis function with Trapezoidal quadrature rules. The convergence analysis revealed that the methods are consistent ...

  3. Food Web Assembly Rules for Generalized Lotka-Volterra Equations.

    Directory of Open Access Journals (Sweden)

    Jan O Haerter

    2016-02-01

    Full Text Available In food webs, many interacting species coexist despite the restrictions imposed by the competitive exclusion principle and apparent competition. For the generalized Lotka-Volterra equations, sustainable coexistence necessitates nonzero determinant of the interaction matrix. Here we show that this requirement is equivalent to demanding that each species be part of a non-overlapping pairing, which substantially constrains the food web structure. We demonstrate that a stable food web can always be obtained if a non-overlapping pairing exists. If it does not, the matrix rank can be used to quantify the lack of niches, corresponding to unpaired species. For the species richness at each trophic level, we derive the food web assembly rules, which specify sustainable combinations. In neighboring levels, these rules allow the higher level to avert competitive exclusion at the lower, thereby incorporating apparent competition. In agreement with data, the assembly rules predict high species numbers at intermediate levels and thinning at the top and bottom. Using comprehensive food web data, we demonstrate how omnivores or parasites with hosts at multiple trophic levels can loosen the constraints and help obtain coexistence in food webs. Hence, omnivory may be the glue that keeps communities intact even under extinction or ecological release of species.

  4. Food Web Assembly Rules for Generalized Lotka-Volterra Equations.

    Science.gov (United States)

    Haerter, Jan O; Mitarai, Namiko; Sneppen, Kim

    2016-02-01

    In food webs, many interacting species coexist despite the restrictions imposed by the competitive exclusion principle and apparent competition. For the generalized Lotka-Volterra equations, sustainable coexistence necessitates nonzero determinant of the interaction matrix. Here we show that this requirement is equivalent to demanding that each species be part of a non-overlapping pairing, which substantially constrains the food web structure. We demonstrate that a stable food web can always be obtained if a non-overlapping pairing exists. If it does not, the matrix rank can be used to quantify the lack of niches, corresponding to unpaired species. For the species richness at each trophic level, we derive the food web assembly rules, which specify sustainable combinations. In neighboring levels, these rules allow the higher level to avert competitive exclusion at the lower, thereby incorporating apparent competition. In agreement with data, the assembly rules predict high species numbers at intermediate levels and thinning at the top and bottom. Using comprehensive food web data, we demonstrate how omnivores or parasites with hosts at multiple trophic levels can loosen the constraints and help obtain coexistence in food webs. Hence, omnivory may be the glue that keeps communities intact even under extinction or ecological release of species.

  5. A phenomenological Hamiltonian for the Lotka-Volterra problem

    International Nuclear Information System (INIS)

    Georgian, T.; Findley, G.L.

    1996-01-01

    We have presented a Hamiltonian theory of phenomenological chemical kinetics. In the present paper, we extend this treatment to the Lotka-Volterra model of sustained oscillations. Our approach begins with the usual definition of an intrinsic reaction coordinate space (x 1 ,x 2 ) for the Lotka-Volterra problem, which leads to the rate equations x 1 =ax 1 -bx 1 x 2 , x 2 =-cx 2 +bx 1 x 2 , with a,b and c being real constants. We thereafter present a Hamiltonian function H(x,y)[y 1 = x 1 and y 2 = x 2 ] and an associated holonomic constraint, which give rise to the above rates as half of Hamilton's equations. We provide trajectories by numerical integration (4th order Runge-Kutta) and show that H(x,y) is a constant of the motion. Finally, issues involved in developing an analytic solution to this problem are discussed

  6. Numerical solutions of stochastic Lotka-Volterra equations via operational matrices

    Directory of Open Access Journals (Sweden)

    F. Hosseini Shekarabi

    2016-03-01

    Full Text Available In this paper, an efficient and convenient method for numerical solutions of stochastic Lotka-Volterra dynamical system is proposed. Here, we consider block pulse functions and their operational matrices of integration. Illustrative example is included to demonstrate the procedure and accuracy of the operational matrices based on block pulse functions.

  7. Lie Symmetry of the Diffusive Lotka–Volterra System with Time-Dependent Coefficients

    Directory of Open Access Journals (Sweden)

    Vasyl’ Davydovych

    2018-02-01

    Full Text Available Lie symmetry classification of the diffusive Lotka–Volterra system with time-dependent coefficients in the case of a single space variable is studied. A set of such symmetries in an explicit form is constructed. A nontrivial ansatz reducing the Lotka–Volterra system with correctly-specified coefficients to the system of ordinary differential equations (ODEs and an example of the exact solution with a biological interpretation are found.

  8. Some new retarded nonlinear Volterra-Fredholm type integral inequalities with maxima in two variables and their applications.

    Science.gov (United States)

    Xu, Run; Ma, Xiangting

    2017-01-01

    In this paper, we establish some new retarded nonlinear Volterra-Fredholm type integral inequalities with maxima in two independent variables, and we present the applications to research the boundedness of solutions to retarded nonlinear Volterra-Fredholm type integral equations.

  9. Hamiltonian structure and Darboux theorem for families of generalized Lotka-Volterra systems

    Science.gov (United States)

    Hernández-Bermejo, Benito; Fairén, Víctor

    1998-11-01

    This work is devoted to the establishment of a Poisson structure for a format of equations known as generalized Lotka-Volterra systems. These equations, which include the classical Lotka-Volterra systems as a particular case, have been deeply studied in the literature. They have been shown to constitute a whole hierarchy of systems, the characterization of which is made in the context of simple algebra. Our main result is to show that this algebraic structure is completely translatable into the Poisson domain. Important Poisson structures features, such as the symplectic foliation and the Darboux canonical representation, rise as a result of rather simple matrix manipulations.

  10. Algebraic features of some generalizations of the Lotka-Volterra system

    Science.gov (United States)

    Bibik, Yu. V.; Sarancha, D. A.

    2010-10-01

    For generalizations of the Lotka-Volterra system, an integration method is proposed based on the nontrivial algebraic structure of these generalizations. The method makes use of an auxiliary first-order differential equation derived from the phase curve equation with the help of this algebraic structure. Based on this equation, a Hamiltonian approach can be developed and canonical variables (moreover, action-angle variables) can be constructed.

  11. Functional equations with causal operators

    CERN Document Server

    Corduneanu, C

    2003-01-01

    Functional equations encompass most of the equations used in applied science and engineering: ordinary differential equations, integral equations of the Volterra type, equations with delayed argument, and integro-differential equations of the Volterra type. The basic theory of functional equations includes functional differential equations with causal operators. Functional Equations with Causal Operators explains the connection between equations with causal operators and the classical types of functional equations encountered by mathematicians and engineers. It details the fundamentals of linear equations and stability theory and provides several applications and examples.

  12. Hybrid MPI/OpenMP parallelization of the explicit Volterra integral equation solver for multi-core computer architectures

    KAUST Repository

    Al Jarro, Ahmed

    2011-08-01

    A hybrid MPI/OpenMP scheme for efficiently parallelizing the explicit marching-on-in-time (MOT)-based solution of the time-domain volume (Volterra) integral equation (TD-VIE) is presented. The proposed scheme equally distributes tested field values and operations pertinent to the computation of tested fields among the nodes using the MPI standard; while the source field values are stored in all nodes. Within each node, OpenMP standard is used to further accelerate the computation of the tested fields. Numerical results demonstrate that the proposed parallelization scheme scales well for problems involving three million or more spatial discretization elements. © 2011 IEEE.

  13. Integrability of some generalized Lotka - Volterra systems

    Energy Technology Data Exchange (ETDEWEB)

    Bountis, T.C.; Bier, M.; Hijmans, J.

    1983-08-08

    Several integrable systems of nonlinear ordinary differential equations of the Lotka-Volterra type are identified by the Painleve property and completely integrated. One such integrable case of N first order ode's is found, with N - 2 free parameters and N arbitrary. The concept of integrability of a general dynamical system, not necessarily derived from a hamiltonian, is also discussed.

  14. Handbook of integral equations

    CERN Document Server

    Polyanin, Andrei D

    2008-01-01

    This handbook contains over 2,500 integral equations with solutions as well as analytical and numerical methods for solving linear and nonlinear equations. It explores Volterra, Fredholm, WienerHopf, Hammerstein, Uryson, and other equations that arise in mathematics, physics, engineering, the sciences, and economics. This second edition includes new chapters on mixed multidimensional equations and methods of integral equations for ODEs and PDEs, along with over 400 new equations with exact solutions. With many examples added for illustrative purposes, it presents new material on Volterra, Fredholm, singular, hypersingular, dual, and nonlinear integral equations, integral transforms, and special functions.

  15. A direct method for numerical solution of a class of nonlinear Volterra integro-differential equations and its application to the nonlinear fission and fusion reactor kinetics

    International Nuclear Information System (INIS)

    Nakahara, Yasuaki; Ise, Takeharu; Kobayashi, Kensuke; Itoh, Yasuyuki

    1975-12-01

    A new method has been developed for numerical solution of a class of nonlinear Volterra integro-differential equations with quadratic nonlinearity. After dividing the domain of the variable into subintervals, piecewise approximations are applied in the subintervals. The equation is first integrated over a subinterval to obtain the piecewise equation, to which six approximate treatments are applied, i.e. fully explicit, fully implicit, Crank-Nicolson, linear interpolation, quadratic and cubic spline. The numerical solution at each time step is obtained directly as a positive root of the resulting algebraic quadratic equation. The point reactor kinetics with a ramp reactivity insertion, linear temperature feedback and delayed neutrons can be described by one of this type of nonlinear Volterra integro-differential equations. The algorithm is applied to the Argonne benchmark problem and a model problem for a fast reactor without delayed neutrons. The fully implicit method has been found to be unconditionally stable in the sense that it always gives the positive real roots. The cubic spline method is divergent, and the other four methods are intermediate in between. From the estimation of the stability, convergency, accuracy and CPU time, it is concluded that the Crank-Nicolson method is best, then the linear interpolation method comes closely next to it. Discussions are also made on the possibility of applying the algorithm to the fusion reactor kinetics in the form of a nonlinear partial differential equation. (auth.)

  16. A unified construction for the algebro-geometric quasiperiodic solutions of the Lotka-Volterra and relativistic Lotka-Volterra hierarchy

    Science.gov (United States)

    Zhao, Peng; Fan, Engui

    2015-04-01

    In this paper, a new type of integrable differential-difference hierarchy, namely, the generalized relativistic Lotka-Volterra (GRLV) hierarchy, is introduced. This hierarchy is closely related to Lotka-Volterra lattice and relativistic Lotka-Volterra lattice, which allows us to provide a unified and effective way to obtain some exact solutions for both the Lotka-Volterra hierarchy and the relativistic Lotka-Volterra hierarchy. In particular, we shall construct algebro-geometric quasiperiodic solutions for the LV hierarchy and the RLV hierarchy in a unified manner on the basis of the finite gap integration theory.

  17. Classification of integrable Volterra-type lattices on the sphere: isotropic case

    International Nuclear Information System (INIS)

    Adler, V E

    2008-01-01

    The symmetry approach is used for classification of integrable isotropic vector Volterra lattices on the sphere. The list of integrable lattices consists mainly of new equations. Their symplectic structure and associated PDE of vector NLS type are discussed

  18. Volterra model and quark hadronization into multicomponent hadron system

    International Nuclear Information System (INIS)

    Darbaidze, Ya.Z.; Rostovtsev, V.A.

    1989-01-01

    The examples of the multiparticle process characteristic dependence on the number of a low correlated components are considered. The possibility for reducing the differential equation system, which was obtained earlier, to a dissipative type Volterra model of competing biological species for the same food is discussed. An algorithm for the analytical computation of the high order differential equation as a resultant of the of the arising system is given. The examples of linearization and solution of these equations describing the associated multiplicities of charge particles are represented. 25 refs.; 1 tab

  19. The Jungle Universe: coupled cosmological models in a Lotka-Volterra framework

    Science.gov (United States)

    Perez, Jérôme; Füzfa, André; Carletti, Timoteo; Mélot, Laurence; Guedezounme, Lazare

    2014-06-01

    In this paper, we exploit the fact that the dynamics of homogeneous and isotropic Friedmann-Lemaître universes is a special case of generalized Lotka-Volterra system where the competitive species are the barotropic fluids filling the Universe. Without coupling between those fluids, Lotka-Volterra formulation offers a pedagogical and simple way to interpret usual Friedmann-Lemaître cosmological dynamics. A natural and physical coupling between cosmological fluids is proposed which preserves the structure of the dynamical equations. Using the standard tools of Lotka-Volterra dynamics, we obtain the general Lyapunov function of the system when one of the fluids is coupled to dark energy. This provides in a rigorous form a generic asymptotic behavior for cosmic expansion in presence of coupled species, beyond the standard de Sitter, Einstein-de Sitter and Milne cosmologies. Finally, we conjecture that chaos can appear for at least four interacting fluids.

  20. Predicting the effects of ionising radiation on ecosystems by a generic model based on the Lotka-Volterra equations

    International Nuclear Information System (INIS)

    Monte, Luigi

    2009-01-01

    The present work describes a model for predicting the population dynamics of the main components (resources and consumers) of terrestrial ecosystems exposed to ionising radiation. The ecosystem is modelled by the Lotka-Volterra equations with consumer competition. Linear dose-response relationships without threshold are assumed to relate the values of the model parameters to the dose rates. The model accounts for the migration of consumers from areas characterised by different levels of radionuclide contamination. The criteria to select the model parameter values are motivated by accounting for the results of the empirical studies of past decades. Examples of predictions for long-term chronic exposure are reported and discussed.

  1. Aeroelastic System Development Using Proper Orthogonal Decomposition and Volterra Theory

    Science.gov (United States)

    Lucia, David J.; Beran, Philip S.; Silva, Walter A.

    2003-01-01

    This research combines Volterra theory and proper orthogonal decomposition (POD) into a hybrid methodology for reduced-order modeling of aeroelastic systems. The out-come of the method is a set of linear ordinary differential equations (ODEs) describing the modal amplitudes associated with both the structural modes and the POD basis functions for the uid. For this research, the structural modes are sine waves of varying frequency, and the Volterra-POD approach is applied to the fluid dynamics equations. The structural modes are treated as forcing terms which are impulsed as part of the uid model realization. Using this approach, structural and uid operators are coupled into a single aeroelastic operator. This coupling converts a free boundary uid problem into an initial value problem, while preserving the parameter (or parameters) of interest for sensitivity analysis. The approach is applied to an elastic panel in supersonic cross ow. The hybrid Volterra-POD approach provides a low-order uid model in state-space form. The linear uid model is tightly coupled with a nonlinear panel model using an implicit integration scheme. The resulting aeroelastic model provides correct limit-cycle oscillation prediction over a wide range of panel dynamic pressure values. Time integration of the reduced-order aeroelastic model is four orders of magnitude faster than the high-order solution procedure developed for this research using traditional uid and structural solvers.

  2. Nonlinear Stability and Convergence of Two-Step Runge-Kutta Methods for Volterra Delay Integro-Differential Equations

    Directory of Open Access Journals (Sweden)

    Haiyan Yuan

    2013-01-01

    Full Text Available This paper introduces the stability and convergence of two-step Runge-Kutta methods with compound quadrature formula for solving nonlinear Volterra delay integro-differential equations. First, the definitions of (k,l-algebraically stable and asymptotically stable are introduced; then the asymptotical stability of a (k,l-algebraically stable two-step Runge-Kutta method with 0

  3. On the integrability of some generalized Lotka-Volterra systems

    Science.gov (United States)

    Bier, M.; Hijmans, J.; Bountis, T. C.

    1983-08-01

    Several integrable systems of nonlinear ordinary differential equations of the Lotka-Volterra type are identified by the Painleveproperty and completely integrated. One such integrable case of N first order ode's is found, with N-2 free parameters and N arbitrary. The concept of integrability of a general dynamical system, not necessarily derived from a Hamiltonian, is also discussed.

  4. Evolution of Black-Box Models Based on Volterra Series

    Directory of Open Access Journals (Sweden)

    Daniel D. Silveira

    2015-01-01

    Full Text Available This paper presents a historical review of the many behavioral models actually used to model radio frequency power amplifiers and a new classification of these behavioral models. It also discusses the evolution of these models, from a single polynomial to multirate Volterra models, presenting equations and estimation methods. New trends in RF power amplifier behavioral modeling are suggested.

  5. The period function of the generalized Lotka-Volterra centers

    Science.gov (United States)

    Villadelprat, J.

    2008-05-01

    The present paper deals with the period function of the quadratic centers. In the literature different terminologies are used to classify these centers, but essentially there are four families: Hamiltonian, reversible , codimension four Q4 and generalized Lotka-Volterra systems . Chicone [C. Chicone, Review in MathSciNet, Ref. 94h:58072] conjectured that the reversible centers have at most two critical periods, and that the centers of the three other families have a monotonic period function. With regard to the second part of this conjecture, only the monotonicity of the Hamiltonian and Q4 families [W.A. Coppel, L. Gavrilov, The period function of a Hamiltonian quadratic system, Differential Integral Equations 6 (1993) 1357-1365; Y. Zhao, The monotonicity of period function for codimension four quadratic system Q4, J. Differential Equations 185 (2002) 370-387] has been proved. Concerning the family, no substantial progress has been made since the middle 80s, when several authors showed independently the monotonicity of the classical Lotka-Volterra centers [F. Rothe, The periods of the Volterra-Lokta system, J. Reine Angew. Math. 355 (1985) 129-138; R. Schaaf, Global behaviour of solution branches for some Neumann problems depending on one or several parameters, J. Reine Angew. Math. 346 (1984) 1-31; J. Waldvogel, The period in the Lotka-Volterra system is monotonic, J. Math. Anal. Appl. 114 (1986) 178-184]. By means of the first period constant one can easily conclude that the period function of the centers in the family is monotone increasing near the inner boundary of its period annulus (i.e., the center itself). Thus, according to Chicone's conjecture, it should be also monotone increasing near the outer boundary, which in the Poincaré disc is a polycycle. In this paper we show that this is true. In addition we prove that, except for a zero measure subset of the parameter plane, there is no bifurcation of critical periods from the outer boundary. Finally we

  6. Asymptotic Behaviour and Extinction of Delay Lotka-Volterra Model with Jump-Diffusion

    OpenAIRE

    Dan Li; Jing’an Cui; Guohua Song

    2014-01-01

    This paper studies the effect of jump-diffusion random environmental perturbations on the asymptotic behaviour and extinction of Lotka-Volterra population dynamics with delays. The contributions of this paper lie in the following: (a) to consider delay stochastic differential equation with jumps, we introduce a proper initial data space, in which the initial data may be discontinuous function with downward jumps; (b) we show that the delay stochastic differential equation with jumps associate...

  7. Cross-diffusional effect in a telegraph reaction diffusion Lotka-Volterra two competitive system

    International Nuclear Information System (INIS)

    Abdusalam, H.A; Fahmy, E.S.

    2003-01-01

    It is known now that, telegraph equation is more suitable than ordinary diffusion equation in modelling reaction diffusion in several branches of sciences. Telegraph reaction diffusion Lotka-Volterra two competitive system is considered. We observed that this system can give rise to diffusive instability only in the presence of cross-diffusion. Local and global stability analysis in the cross-diffusional effect are studied by considering suitable Lyapunov functional

  8. A Historical Gem from Vito Volterra.

    Science.gov (United States)

    Dunham, William

    1990-01-01

    Presented is the theorem proposed by Volterra based on the idea that there is no function continuous at each rational point and discontinuous at each irrational point. Discussed are the two conclusions that were drawn by Volterra based on his solution to this problem. (KR)

  9. On the fractional Eulerian numbers and equivalence of maps with long term power-law memory (integral Volterra equations of the second kind) to Grünvald-Letnikov fractional difference (differential) equations.

    Science.gov (United States)

    Edelman, Mark

    2015-07-01

    In this paper, we consider a simple general form of a deterministic system with power-law memory whose state can be described by one variable and evolution by a generating function. A new value of the system's variable is a total (a convolution) of the generating functions of all previous values of the variable with weights, which are powers of the time passed. In discrete cases, these systems can be described by difference equations in which a fractional difference on the left hand side is equal to a total (also a convolution) of the generating functions of all previous values of the system's variable with the fractional Eulerian number weights on the right hand side. In the continuous limit, the considered systems can be described by the Grünvald-Letnikov fractional differential equations, which are equivalent to the Volterra integral equations of the second kind. New properties of the fractional Eulerian numbers and possible applications of the results are discussed.

  10. Lattice defects as Lotka-Volterra societies

    Energy Technology Data Exchange (ETDEWEB)

    Yost, F.G.

    1995-07-01

    Since the early part of this century the Lotka-Volterra or predator-prey equations have been known to simulate the stability, instability, and persistent oscillations observed in many biological and ecological societies. These equations have been modified in many ways and have been used to model phenomena as varied as childhood epidemics, enzyme reactions, and conventional warfare. In the work to be described, similarities are drawn between various lattice defects and Lotka-Volterra (LV) societies. Indeed, grain boundaries are known to ``consume`` dislocations, inclusions ``infect`` grain boundaries, and dislocations ``annihilate`` dislocations. Several specific cases of lattice defect interaction kinetics models are drawn from the materials science literature to make these comparisons. Each model will be interpreted as if it were a description of a biological system. Various approaches to the modification of this class of interaction kinetics will be presented and discussed. The earliest example is the Damask-Dienes treatment of vacancy-divacancy annealing kinetics. This historical model will be modified to include the effects of an intermediate species and the results will be compared with the original model. The second example to be examined is the Clark-Alden model for deformation-enhanced grain growth. Dislocation kinetics will be added to this model and results will be discussed considering the original model. The third example to be presented is the Ananthakrishna-Sahoo model of the Portevin-Le Chatelier effect that was offered in 1985 as an extension of the classical Cottrell atmosphere explanation. Their treatment will be modified by inclusion of random interference from a pesky but peripheral species and by allowing a rate constant to be a function of time.

  11. On generalized Volterra systems

    Science.gov (United States)

    Charalambides, S. A.; Damianou, P. A.; Evripidou, C. A.

    2015-01-01

    We construct a large family of evidently integrable Hamiltonian systems which are generalizations of the KM system. The algorithm uses the root system of a complex simple Lie algebra. The Hamiltonian vector field is homogeneous cubic but in a number of cases a simple change of variables transforms such a system to a quadratic Lotka-Volterra system. We present in detail all such systems in the cases of A3, A4 and we also give some examples from higher dimensions. We classify all possible Lotka-Volterra systems that arise via this algorithm in the An case.

  12. Nonpolynomial vector fields under the Lotka-Volterra normal form

    Science.gov (United States)

    Hernández-Bermejo, Benito; Fairén, Víctor

    1995-02-01

    We carry out the generalization of the Lotka-Volterra embedding to flows not explicitly recognizable under the generalized Lotka-Volterra format. The procedure introduces appropriate auxiliary variables, and it is shown how, to a great extent, the final Lotka-Volterra system is independent of their specific definition. Conservation of the topological equivalence during the process is also demonstrated.

  13. Volterra Filtering for ADC Error Correction

    Directory of Open Access Journals (Sweden)

    J. Saliga

    2001-09-01

    Full Text Available Dynamic non-linearity of analog-to-digital converters (ADCcontributes significantly to the distortion of digitized signals. Thispaper introduces a new effective method for compensation such adistortion based on application of Volterra filtering. Considering ana-priori error model of ADC allows finding an efficient inverseVolterra model for error correction. Efficiency of proposed method isdemonstrated on experimental results.

  14. Stationary Response of Lotka—Volterra System with Real Noises

    International Nuclear Information System (INIS)

    Qi Lu-Yuan; Xu Wei; Gao Wei-Ting

    2013-01-01

    A stochastic version of Lotka—Volterra model subjected to real noises is proposed and investigated. The approximate stationary probability densities for both predator and prey are obtained analytically. The original system is firstly transformed to a pair of Itô stochastic differential equations. The Itô formula is then carried out to obtain the Itô stochastic differential equation for the period orbit function. The orbit function is considered as slowly varying process under reasonable assumptions. By applying the stochastic averaging method to the orbit function in one period, the averaged Itô stochastic differential equation of the motion orbit and the corresponding Fokker—Planck equation are derived. The probability density functions of the two species are thus formulated. Finally, a classical real noise model is given as an example to show the proposed approximate method. The accuracy of the proposed procedure is verified by Monte Carlo simulation. (interdisciplinary physics and related areas of science and technology)

  15. Volterra Series Based Distortion Effect

    DEFF Research Database (Denmark)

    Agerkvist, Finn T.

    2010-01-01

    A large part of the characteristic sound of the electric guitar comes from nonlinearities in the signal path. Such nonlinearities may come from the input- or output-stage of the amplier, which is often equipped with vacuum tubes or a dedicated distortion pedal. In this paper the Volterra series...... expansion for non linear systems is investigated with respect to generating good distortion. The Volterra series allows for unlimited adjustment of the level and frequency dependency of each distortion component. Subjectively relevant ways of linking the dierent orders are discussed....

  16. Volterra, Fascism, and France.

    Science.gov (United States)

    Capristo, Annalisa

    2015-12-01

    My contribution focuses on two aspects strictly related each other. On one hand, the progressive marginalization of Volterra from Italian scientific and political life after the rise of Fascism - because of his public anti-Fascist stance, both as a senator and as a professor - until his definitive exclusion on racial grounds in 1938. On the other hand, the reactions of his French colleagues and friends to this ostracism, and the support he received from them. As it emerges from several sources (Volterra's correspondence, institutional documentation, conference proceedings, etc.), it was mainly thanks to their support that he was able to escape the complete isolation and the "civil death" to which the regime condemned many of its adversaries.

  17. Dynamics of a Lotka-Volterra type model with applications to marine phage population dynamics

    International Nuclear Information System (INIS)

    Gavin, C; Pokrovskii, A; Prentice, M; Sobolev, V

    2006-01-01

    The famous Lotka-Volterra equations play a fundamental role in the mathematical modeling of various ecological and chemical systems. A new modification of these equations has been recently suggested to model the structure of marine phage populations, which are the most abundant biological entities in the biosphere. The purpose of the paper is: (i) to make some methodical remarks concerning this modification; (ii) to discuss new types of canards which arise naturally in this context; (iii) to present results of some numerical experiments

  18. Ecological communities with Lotka-Volterra dynamics

    Science.gov (United States)

    Bunin, Guy

    2017-04-01

    Ecological communities in heterogeneous environments assemble through the combined effect of species interaction and migration. Understanding the effect of these processes on the community properties is central to ecology. Here we study these processes for a single community subject to migration from a pool of species, with population dynamics described by the generalized Lotka-Volterra equations. We derive exact results for the phase diagram describing the dynamical behaviors, and for the diversity and species abundance distributions. A phase transition is found from a phase where a unique globally attractive fixed point exists to a phase where multiple dynamical attractors exist, leading to history-dependent community properties. The model is shown to possess a symmetry that also establishes a connection with other well-known models.

  19. The diffusive Lotka-Volterra predator-prey system with delay.

    Science.gov (United States)

    Al Noufaey, K S; Marchant, T R; Edwards, M P

    2015-12-01

    Semi-analytical solutions for the diffusive Lotka-Volterra predator-prey system with delay are considered in one and two-dimensional domains. The Galerkin method is applied, which approximates the spatial structure of both the predator and prey populations. This approach is used to obtain a lower-order, ordinary differential delay equation model for the system of governing delay partial differential equations. Steady-state and transient solutions and the region of parameter space, in which Hopf bifurcations occur, are all found. In some cases simple linear expressions are found as approximations, to describe steady-state solutions and the Hopf parameter regions. An asymptotic analysis for the periodic solution near the Hopf bifurcation point is performed for the one-dimensional domain. An excellent agreement is shown in comparisons between semi-analytical and numerical solutions of the governing equations. Copyright © 2015 Elsevier Inc. All rights reserved.

  20. On chaos in Lotka–Volterra systems: an analytical approach

    International Nuclear Information System (INIS)

    Kozlov, Vladimir; Vakulenko, Sergey

    2013-01-01

    In this paper, we study Lotka–Volterra systems with N species and n resources. We show that the long time dynamics of these systems may be complicated. Depending on parameter choice, they can generate all types of hyperbolic dynamics, in particular, chaotic ones. Moreover, Lotka–Volterra systems can generate Lorenz dynamics. We state the conditions on the strong persistence of Lotka–Volterra systems when the number of resources is less than the number of species. (paper)

  1. Gelfand-Dikii Hamiltonian operator and co-ad joint representation of the Volterra group

    International Nuclear Information System (INIS)

    Lebedev, D.R.; Manin, Yu.I.

    1978-01-01

    It is shown that the Gelfand-Dikii Hamiltonian structure is an analogue of a very special class of finite-dimensional symplectic structures, namely, the Kirillow structures on the orbits of the co-adjoint representation of the Lie groups. The Lie group is represented by the Volterra operators. The main interest lies in the possibility of application of the ideology of ''geometric quantization'' to the Lax equations

  2. Reduced Complexity Volterra Models for Nonlinear System Identification

    Directory of Open Access Journals (Sweden)

    Hacıoğlu Rıfat

    2001-01-01

    Full Text Available A broad class of nonlinear systems and filters can be modeled by the Volterra series representation. However, its practical use in nonlinear system identification is sometimes limited due to the large number of parameters associated with the Volterra filter′s structure. The parametric complexity also complicates design procedures based upon such a model. This limitation for system identification is addressed in this paper using a Fixed Pole Expansion Technique (FPET within the Volterra model structure. The FPET approach employs orthonormal basis functions derived from fixed (real or complex pole locations to expand the Volterra kernels and reduce the number of estimated parameters. That the performance of FPET can considerably reduce the number of estimated parameters is demonstrated by a digital satellite channel example in which we use the proposed method to identify the channel dynamics. Furthermore, a gradient-descent procedure that adaptively selects the pole locations in the FPET structure is developed in the paper.

  3. Efficient multidimensional regularization for Volterra series estimation

    Science.gov (United States)

    Birpoutsoukis, Georgios; Csurcsia, Péter Zoltán; Schoukens, Johan

    2018-05-01

    This paper presents an efficient nonparametric time domain nonlinear system identification method. It is shown how truncated Volterra series models can be efficiently estimated without the need of long, transient-free measurements. The method is a novel extension of the regularization methods that have been developed for impulse response estimates of linear time invariant systems. To avoid the excessive memory needs in case of long measurements or large number of estimated parameters, a practical gradient-based estimation method is also provided, leading to the same numerical results as the proposed Volterra estimation method. Moreover, the transient effects in the simulated output are removed by a special regularization method based on the novel ideas of transient removal for Linear Time-Varying (LTV) systems. Combining the proposed methodologies, the nonparametric Volterra models of the cascaded water tanks benchmark are presented in this paper. The results for different scenarios varying from a simple Finite Impulse Response (FIR) model to a 3rd degree Volterra series with and without transient removal are compared and studied. It is clear that the obtained models capture the system dynamics when tested on a validation dataset, and their performance is comparable with the white-box (physical) models.

  4. Convergence analysis of the alternating RGLS algorithm for the identification of the reduced complexity Volterra model.

    Science.gov (United States)

    Laamiri, Imen; Khouaja, Anis; Messaoud, Hassani

    2015-03-01

    In this paper we provide a convergence analysis of the alternating RGLS (Recursive Generalized Least Square) algorithm used for the identification of the reduced complexity Volterra model describing stochastic non-linear systems. The reduced Volterra model used is the 3rd order SVD-PARAFC-Volterra model provided using the Singular Value Decomposition (SVD) and the Parallel Factor (PARAFAC) tensor decomposition of the quadratic and the cubic kernels respectively of the classical Volterra model. The Alternating RGLS (ARGLS) algorithm consists on the execution of the classical RGLS algorithm in alternating way. The ARGLS convergence was proved using the Ordinary Differential Equation (ODE) method. It is noted that the algorithm convergence canno׳t be ensured when the disturbance acting on the system to be identified has specific features. The ARGLS algorithm is tested in simulations on a numerical example by satisfying the determined convergence conditions. To raise the elegies of the proposed algorithm, we proceed to its comparison with the classical Alternating Recursive Least Squares (ARLS) presented in the literature. The comparison has been built on a non-linear satellite channel and a benchmark system CSTR (Continuous Stirred Tank Reactor). Moreover the efficiency of the proposed identification approach is proved on an experimental Communicating Two Tank system (CTTS). Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

  5. Exponential Convergence for Numerical Solution of Integral Equations Using Radial Basis Functions

    Directory of Open Access Journals (Sweden)

    Zakieh Avazzadeh

    2014-01-01

    Full Text Available We solve some different type of Urysohn integral equations by using the radial basis functions. These types include the linear and nonlinear Fredholm, Volterra, and mixed Volterra-Fredholm integral equations. Our main aim is to investigate the rate of convergence to solve these equations using the radial basis functions which have normic structure that utilize approximation in higher dimensions. Of course, the use of this method often leads to ill-posed systems. Thus we propose an algorithm to improve the results. Numerical results show that this method leads to the exponential convergence for solving integral equations as it was already confirmed for partial and ordinary differential equations.

  6. Some stability and boundedness criteria for a class of Volterra integro-differential systems

    Directory of Open Access Journals (Sweden)

    Jito Vanualailai

    2002-01-01

    Full Text Available Using Lyapunov and Lyapunov-like functionals, we study the stability and boundedness of the solutions of a system of Volterra integrodifferential equations. Our results, also extending some of the more well-known criteria, give new sufficient conditions for stability of the zero solution of the nonperturbed system, and prove that the same conditions for the perturbed system yield boundedness when the perturbation is $L^2$.

  7. Matrix form of Legendre polynomials for solving linear integro-differential equations of high order

    Science.gov (United States)

    Kammuji, M.; Eshkuvatov, Z. K.; Yunus, Arif A. M.

    2017-04-01

    This paper presents an effective approximate solution of high order of Fredholm-Volterra integro-differential equations (FVIDEs) with boundary condition. Legendre truncated series is used as a basis functions to estimate the unknown function. Matrix operation of Legendre polynomials is used to transform FVIDEs with boundary conditions into matrix equation of Fredholm-Volterra type. Gauss Legendre quadrature formula and collocation method are applied to transfer the matrix equation into system of linear algebraic equations. The latter equation is solved by Gauss elimination method. The accuracy and validity of this method are discussed by solving two numerical examples and comparisons with wavelet and methods.

  8. An equivalent condition for stability properties of Lotka-Volterra systems

    International Nuclear Information System (INIS)

    Chu Tianguang

    2007-01-01

    We give a solvable Lie algebraic condition for the equivalence of four typical stability notions (asymptotic stability, D-stability, total stability, and Volterra-Lyapunov stability) concerning Lotka-Volterra systems. Our approach makes use of the decomposition of the interaction matrix into symmetric and skew-symmetric parts, which may be related to the cooperative and competitive interaction pattern of a Lotka-Volterra system. The present result covers a known condition and can yield a larger set of interaction matrices for equivalence of the stability properties

  9. Nonmonotonic Behavior of Supermultiplet Pattern Formation in a Noisy Lotka-Volterra System

    International Nuclear Information System (INIS)

    Fiasconaro, A.; Valenti, D.; Spagnolo, B.

    2004-01-01

    The noise-induced pattern formation in a population dynamical model of three interacting species in the coexistence regime is investigated. A coupled map lattice of Lotka-Volterra equations in the presence of multiplicative noise is used to analyze the spatiotemporal evolution. The spatial correlation of the species concentration as a function of time and of the noise intensity is investigated. A nonmonotonic behavior of the area of the patterns as a function of both noise intensity and evolution time is found. (author)

  10. A differential-difference hierarchy associated with relativistic Toda and Volterra hierarchies

    International Nuclear Information System (INIS)

    Fan Engui; Dai Huihui

    2008-01-01

    By embedding a free function into a compatible zero curvature equation, we enlarge the original differential-difference hierarchy into a new hierarchy with the free function which still admits zero curvature representation. The new hierarchy not only includes the original hierarchy, but also the well-known relativistic Toda hierarchy and the Volterra hierarchy as special reductions by properly choosing the free function. Infinitely many conservation laws and Darboux transformation for a representative differential-difference system are constructed based on its Lax representation. The exact solutions follow by applying the Darboux transformation

  11. SOLVING FRACTIONAL-ORDER COMPETITIVE LOTKA-VOLTERRA MODEL BY NSFD SCHEMES

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    S.ZIBAEI

    2016-12-01

    Full Text Available In this paper, we introduce fractional-order into a model competitive Lotka- Volterra prey-predator system. We will discuss the stability analysis of this fractional system. The non-standard nite difference (NSFD scheme is implemented to study the dynamic behaviors in the fractional-order Lotka-Volterra system. Proposed non-standard numerical scheme is compared with the forward Euler and fourth order Runge-Kutta methods. Numerical results show that the NSFD approach is easy and accurate for implementing when applied to fractional-order Lotka-Volterra model.

  12. On the long time behavior of non-autonomous Lotka-Volterra models with diffusion via the sub-supertrajectory method

    Science.gov (United States)

    Langa, José A.; Rodríguez-Bernal, Aníbal; Suárez, Antonio

    In this paper we study in detail the geometrical structure of global pullback and forwards attractors associated to non-autonomous Lotka-Volterra systems in all the three cases of competition, symbiosis or prey-predator. In particular, under some conditions on the parameters, we prove the existence of a unique nondegenerate global solution for these models, which attracts any other complete bounded trajectory. Thus, we generalize the existence of a unique strictly positive stable (stationary) solution from the autonomous case and we extend to Lotka-Volterra systems the result for scalar logistic equations. To this end we present the sub-supertrajectory tool as a generalization of the now classical sub-supersolution method. In particular, we also conclude pullback and forwards permanence for the above models.

  13. Lie Point Symmetries and Exact Solutions of the Coupled Volterra System

    International Nuclear Information System (INIS)

    Ping, Liu; Sen-Yue, Lou

    2010-01-01

    The coupled Volterra system, an integrable discrete form of a coupled Korteweg–de Vries (KdV) system applied widely in fluids, Bose–Einstein condensation and atmospheric dynamics, is studied with the help of the Lie point symmetries. Two types of delayed differential reduction systems are derived from the coupled Volterra system by means of the symmetry reduction approach and symbolic computation. Cnoidal wave and solitary wave solutions for a delayed differential reduction system and the coupled Volterra system are proposed, respectively. (general)

  14. Generalized symmetries and conserved quantities of the Lotka-Volterra model

    Science.gov (United States)

    Baumann, G.; Freyberger, M.

    1991-07-01

    We examine the generalized symmetries of the Lotka-Volterra model to find the parameter values at which one time-dependent integral of motion exists. In this case the integral can be read off from the symmetries themselves. We also demonstrate the connection to a Hamiltonian structure of the Lotka-Volterra model.

  15. Lotka-Volterra system in a random environment

    Science.gov (United States)

    Dimentberg, Mikhail F.

    2002-03-01

    Classical Lotka-Volterra (LV) model for oscillatory behavior of population sizes of two interacting species (predator-prey or parasite-host pairs) is conservative. This may imply unrealistically high sensitivity of the system's behavior to environmental variations. Thus, a generalized LV model is considered with the equation for preys' reproduction containing the following additional terms: quadratic ``damping'' term that accounts for interspecies competition, and term with white-noise random variations of the preys' reproduction factor that simulates the environmental variations. An exact solution is obtained for the corresponding Fokker-Planck-Kolmogorov equation for stationary probability densities (PDF's) of the population sizes. It shows that both population sizes are independent γ-distributed stationary random processes. Increasing level of the environmental variations does not lead to extinction of the populations. However it may lead to an intermittent behavior, whereby one or both population sizes experience very rare and violent short pulses or outbreaks while remaining on a very low level most of the time. This intermittency is described analytically by direct use of the solutions for the PDF's as well as by applying theory of excursions of random functions and by predicting PDF of peaks in the predators' population size.

  16. Qualitative properties of functional differential equation

    Directory of Open Access Journals (Sweden)

    Diana Otrocol

    2014-10-01

    Full Text Available The aim of this paper is to discuss some basic problems (existence and uniqueness, data dependence of the fixed point theory for a functional differential equation with an abstract Volterra operator. In the end an application is given.

  17. Generalized ordinary differential equations not absolutely continuous solutions

    CERN Document Server

    Kurzweil, Jaroslav

    2012-01-01

    This book provides a systematic treatment of the Volterra integral equation by means of a modern integration theory which extends considerably the field of differential equations. It contains many new concepts and results in the framework of a unifying theory. In particular, this new approach is suitable in situations where fast oscillations occur.

  18. Volterra equalization of complex modulation utilizing frequency chirp in directly modulated lasers

    Science.gov (United States)

    Hu, Shaohua; Yi, Xingwen; Zhang, Jing; Song, Yang; Zhu, Mingyue; Qiu, Kun

    2018-02-01

    We apply Volterra-based equalization for complex modulated optical signals utilizing the frequency chirp in DMLs. We experimentally demonstrate that the higher order Volterra filter is necessary in the higher speed transmissions. For further study, we isolate the adiabatic chirp by injection locking and realize the optical PM transmission. We make a comparison among IM, FM and PM with Volterra equalization, finding that PM and FM are more power insensitive and suitable for high speed, power limited fiber transmission. The performance can be further improved by exploiting the diversity gain.

  19. The matrix realization of affine Jacobi varieties and the extended Lotka-Volterra lattice

    International Nuclear Information System (INIS)

    Inoue, Rei

    2004-01-01

    We study completely integrable Hamiltonian systems whose monodromy matrices are related to the representatives for the set of gauge equivalence classes M F of polynomial matrices. Let X be the algebraic curve given by the common characteristic equation for M F . We construct the isomorphism from the set of representatives to an affine part of the Jacobi variety of X. This variety corresponds to the invariant manifold of the system, where the Hamiltonian flow is linearized. As an application, we discuss the algebraic complete integrability of the extended Lotka-Volterra lattice with a periodic boundary condition

  20. The inverse problem of determining several coefficients in a nonlinear Lotka–Volterra system

    International Nuclear Information System (INIS)

    Roques, Lionel; Cristofol, Michel

    2012-01-01

    In this paper, we prove a uniqueness result in the inverse problem of determining several non-constant coefficients of a system of two parabolic equations, which corresponds to a Lotka–Volterra competition model. Our result gives a sufficient condition for the uniqueness of the determination of four coefficients of the system. This sufficient condition only involves pointwise measurements of the solution (u, v) of the system and of the spatial derivative ∂u/∂x or ∂v/∂x of one component at a single point x 0 , during a time interval (0, ε). Our results are illustrated by numerical computations. (paper)

  1. Approximate solution of integro-differential equation of fractional (arbitrary order

    Directory of Open Access Journals (Sweden)

    Asma A. Elbeleze

    2016-01-01

    Full Text Available In the present paper, we study the integro-differential equations which are combination of differential and Fredholm–Volterra equations that have the fractional order with constant coefficients by the homotopy perturbation and the variational iteration. The fractional derivatives are described in Caputo sense. Some illustrative examples are presented.

  2. Asymptotic Behaviour and Extinction of Delay Lotka-Volterra Model with Jump-Diffusion

    Directory of Open Access Journals (Sweden)

    Dan Li

    2014-01-01

    Full Text Available This paper studies the effect of jump-diffusion random environmental perturbations on the asymptotic behaviour and extinction of Lotka-Volterra population dynamics with delays. The contributions of this paper lie in the following: (a to consider delay stochastic differential equation with jumps, we introduce a proper initial data space, in which the initial data may be discontinuous function with downward jumps; (b we show that the delay stochastic differential equation with jumps associated with our model has a unique global positive solution and give sufficient conditions that ensure stochastically ultimate boundedness, moment average boundedness in time, and asymptotic polynomial growth of our model; (c the sufficient conditions for the extinction of the system are obtained, which generalized the former results and showed that the sufficiently large random jump magnitudes and intensity (average rate of jump events arrival may lead to extinction of the population.

  3. Method for solving the periodic problem for integro-differential equations

    Directory of Open Access Journals (Sweden)

    Snezhana G. Hristova

    1989-05-01

    Full Text Available In the paper a monotone-iterative method for approximate finding a couple of minimal and maximal quasisolutions of the periodic problem for a system of integro-differential equations of Volterra type is justified.

  4. Comparative nonlinear modeling of renal autoregulation in rats: Volterra approach versus artificial neural networks

    DEFF Research Database (Denmark)

    Chon, K H; Holstein-Rathlou, N H; Marsh, D J

    1998-01-01

    kernel estimation method based on Laguerre expansions. The results for the two types of artificial neural networks and the Volterra models are comparable in terms of normalized mean square error (NMSE) of the respective output prediction for independent testing data. However, the Volterra models obtained...

  5. Integral equation for Coulomb problem

    International Nuclear Information System (INIS)

    Sasakawa, T.

    1986-01-01

    For short range potentials an inhomogeneous (homogeneous) Lippmann-Schwinger integral equation of the Fredholm type yields the wave function of scattering (bound) state. For the Coulomb potential, this statement is no more valid. It has been felt difficult to express the Coulomb wave function in a form of an integral equation with the Coulomb potential as the perturbation. In the present paper, the author shows that an inhomogeneous integral equation of a Volterra type with the Coulomb potential as the perturbation can be constructed both for the scattering and the bound states. The equation yielding the binding energy is given in an integral form. The present treatment is easily extended to the coupled Coulomb problems

  6. Hartman-Wintner growth results for sublinear functional differential equations

    Directory of Open Access Journals (Sweden)

    John A. D. Appleby

    2017-01-01

    Full Text Available This article determines the rate of growth to infinity of scalar autonomous nonlinear functional and Volterra differential equations. In these equations, the right-hand side is a positive continuous linear functional of f(x. We assume f grows sublinearly, leading to subexponential growth in the solutions. The main results show that the solution of the functional differential equations are asymptotic to that of an auxiliary autonomous ordinary differential equation with right-hand side proportional to f. This happens provided f grows more slowly than l(x=x/log(x. The linear-logarithmic growth rate is also shown to be critical: if f grows more rapidly than l, the ODE dominates the FDE; if f is asymptotic to a constant multiple of l, the FDE and ODE grow at the same rate, modulo a constant non-unit factor; if f grows more slowly than l, the ODE and FDE grow at exactly the same rate. A partial converse of the last result is also proven. In the case when the growth rate is slower than that of the ODE, sharp bounds on the growth rate are determined. The Volterra and finite memory equations can have differing asymptotic behaviour and we explore the source of these differences.

  7. A modified Lotka-Volterra model for the evolution of coordinate symbiosis in energy enterprise

    Science.gov (United States)

    Zhou, Li; Wang, Teng; Lyu, Xiaohuan; Yu, Jing

    2018-02-01

    Recent developments in energy markets make the operating industries more dynamic and complex, and energy enterprises cooperate more closely in the industrial chain and symbiosis. In order to further discuss the evolution of coordinate symbiosis in energy enterprises, a modified Lotka-Volterra equation is introduced to develop a symbiosis analysis model of energy groups. According to the equilibrium and stability analysis, a conclusion is obtained that if the upstream energy group and the downstream energy group are in symbiotic state, the growth of their utility will be greater than their independent value. Energy enterprises can get mutual benefits and positive promotions in industrial chain by their cooperation.

  8. Volterra-series-based nonlinear system modeling and its engineering applications: A state-of-the-art review

    Science.gov (United States)

    Cheng, C. M.; Peng, Z. K.; Zhang, W. M.; Meng, G.

    2017-03-01

    Nonlinear problems have drawn great interest and extensive attention from engineers, physicists and mathematicians and many other scientists because most real systems are inherently nonlinear in nature. To model and analyze nonlinear systems, many mathematical theories and methods have been developed, including Volterra series. In this paper, the basic definition of the Volterra series is recapitulated, together with some frequency domain concepts which are derived from the Volterra series, including the general frequency response function (GFRF), the nonlinear output frequency response function (NOFRF), output frequency response function (OFRF) and associated frequency response function (AFRF). The relationship between the Volterra series and other nonlinear system models and nonlinear problem solving methods are discussed, including the Taylor series, Wiener series, NARMAX model, Hammerstein model, Wiener model, Wiener-Hammerstein model, harmonic balance method, perturbation method and Adomian decomposition. The challenging problems and their state of arts in the series convergence study and the kernel identification study are comprehensively introduced. In addition, a detailed review is then given on the applications of Volterra series in mechanical engineering, aeroelasticity problem, control engineering, electronic and electrical engineering.

  9. Security analysis of chaotic communication systems based on Volterra-Wiener-Korenberg model

    International Nuclear Information System (INIS)

    Lei Min; Meng Guang; Feng Zhengjin

    2006-01-01

    Pseudo-randomicity is an important cryptological characteristic for proof of encryption algorithms. This paper proposes a nonlinear detecting method based on Volterra-Wiener-Korenberg model and suggests an autocorrelation function to analyze the pseudo-randomicity of chaotic secure systems under different sampling interval. The results show that: (1) the increase of the order of the chaotic transmitter will not necessarily result in a high degree of security; (2) chaotic secure systems have higher and stronger pseudo-randomicity at sparse sampling interval due to the similarity of chaotic time series to the noise; (3) Volterra-Wiener-Korenberg method can also give a further appropriate sparse sampling interval for improving the security of chaotic secure communication systems. For unmasking chaotic communication systems, the Volterra-Wiener-Korenberg technique can be applied to analyze the chaotic time series with surrogate data

  10. Bifurcation analysis in the diffusive Lotka-Volterra system: An application to market economy

    International Nuclear Information System (INIS)

    Wijeratne, A.W.; Yi Fengqi; Wei Junjie

    2009-01-01

    A diffusive Lotka-Volterra system is formulated in this paper that represents the dynamics of market share at duopoly. A case in Sri Lankan mobile telecom market was considered that conceptualized the model in interest. Detailed Hopf bifurcation, transcritical and pitchfork bifurcation analysis were performed. The distribution of roots of the characteristic equation suggests that a stable coexistence equilibrium can be achieved by increasing the innovation while minimizing competition by each competitor while regulating existing policies and introducing new ones for product differentiation and value addition. The avenue is open for future research that may use real time information in order to formulate mathematically sound tools for decision making in competitive business environments.

  11. Bifurcation analysis in the diffusive Lotka-Volterra system: An application to market economy

    Energy Technology Data Exchange (ETDEWEB)

    Wijeratne, A.W. [Department of Mathematics, Harbin Institute of Technology, Harbin 150001 (China); Department of Agri-Business Management, Sabaragamuwa University of Sri Lanka, Belihuloya 70140 (Sri Lanka); Yi Fengqi [Department of Mathematics, Harbin Institute of Technology, Harbin 150001 (China); Wei Junjie [Department of Mathematics, Harbin Institute of Technology, Harbin 150001 (China)], E-mail: weijj@hit.edu.cn

    2009-04-30

    A diffusive Lotka-Volterra system is formulated in this paper that represents the dynamics of market share at duopoly. A case in Sri Lankan mobile telecom market was considered that conceptualized the model in interest. Detailed Hopf bifurcation, transcritical and pitchfork bifurcation analysis were performed. The distribution of roots of the characteristic equation suggests that a stable coexistence equilibrium can be achieved by increasing the innovation while minimizing competition by each competitor while regulating existing policies and introducing new ones for product differentiation and value addition. The avenue is open for future research that may use real time information in order to formulate mathematically sound tools for decision making in competitive business environments.

  12. elative controllability of nonlinear neutral Volterra Integrodiferential ...

    African Journals Online (AJOL)

    In this paper we established sufficient conditions for the relative controllability of the nonlinear neutral volterra integro-differential systems with distributed delays in the control. The results were established using the Schauder's fixed point theorem which is an extension of known results. Journal of the Nigerian Association of ...

  13. Existence of smooth solutions of multi-term Caputo-type fractional differential equations

    OpenAIRE

    Sin, Chung-Sik; Cheng, Shusen; Ri, Gang-Il; Kim, Mun-Chol

    2017-01-01

    This paper deals with the initial value problem for the multi-term fractional differential equation. The fractional derivative is defined in the Caputo sense. Firstly the initial value problem is transformed into a equivalent Volterra-type integral equation under appropriate assumptions. Then new existence results for smooth solutions are established by using the Schauder fixed point theorem.

  14. Nonlinear System Identification via Basis Functions Based Time Domain Volterra Model

    Directory of Open Access Journals (Sweden)

    Yazid Edwar

    2014-07-01

    Full Text Available This paper proposes basis functions based time domain Volterra model for nonlinear system identification. The Volterra kernels are expanded by using complex exponential basis functions and estimated via genetic algorithm (GA. The accuracy and practicability of the proposed method are then assessed experimentally from a scaled 1:100 model of a prototype truss spar platform. Identification results in time and frequency domain are presented and coherent functions are performed to check the quality of the identification results. It is shown that results between experimental data and proposed method are in good agreement.

  15. Complete factorisation and analytic solutions of generalized Lotka-Volterra equations

    Science.gov (United States)

    Brenig, L.

    1988-11-01

    It is shown that many systems of nonlinear differential equations of interest in various fields are naturally imbedded in a new family of differential equations. This family is invariant under nonlinear transformations based on the concept of matrix power of a vector. Each equation belonging to that family can be brought into a factorized canonical form for which integrable cases can be easily identified and solutions can be found by quadratures.

  16. A new approach to stochastic transport via the functional Volterra expansion

    International Nuclear Information System (INIS)

    Ziya Akcasu, A.; Corngold, N.

    2005-01-01

    In this paper we present a new algorithm (FDA) for the calculation of the mean and the variance of the flux in stochastic transport when the transport equation contains a spatially random parameter θ(r), such as the density of the medium. The approach is based on the renormalized functional Volterra expansion of the flux around its mean. The attractive feature of the approach is that it explicitly displays the functional dependence of the flux on the products of θ(r i ), and hence enables one to take ensemble averages directly to calculate the moments of the flux in terms of the correlation functions of the underlying random process. The renormalized deterministic transport equation for the mean flux has been obtained to the second order in θ(r), and a functional relationship between the variance and the mean flux has been derived to calculate the variance to this order. The feasibility and accuracy of FDA has been demonstrated in the case of stochastic diffusion, using the diffusion equation with a spatially random diffusion coefficient. The connection of FDA with the well-established approximation schemes in the field of stochastic linear differential equations, such as the Bourret approximation, developed by Van Kampen using cumulant expansion, and by Terwiel using projection operator formalism, which has recently been extended to stochastic transport by Corngold. We hope that FDA's potential will be explored numerically in more realistic applications of the stochastic transport. (authors)

  17. Dynamic behaviors of the periodic Lotka-Volterra competing system with impulsive perturbations

    International Nuclear Information System (INIS)

    Liu Bing; Teng Zhidong; Liu Wanbo

    2007-01-01

    In this paper, we investigate a classical periodic Lotka-Volterra competing system with impulsive perturbations. The conditions for the linear stability of trivial periodic solution and semi-trivial periodic solutions are given by applying Floquet theory of linear periodic impulsive equation, and we also give the conditions for the global stability of these solutions as a consequence of some abstract monotone iterative schemes introduced in this paper, which will be also used to get some sufficient conditions for persistence. By using the method of coincidence degree, the conditions for the existence of at least one strictly positive (componentwise) periodic solution are derived. The theoretical results are confirmed by a specific example and numerical simulations. It shows that the dynamic behaviors of the system we consider are quite different from the corresponding system without pulses

  18. On the Restriction of the Location of Stable Points for Generalized Lotka-Volterra

    OpenAIRE

    Livesay, Michael Richard

    2017-01-01

    We develop tools to determine which fixed points in a generalized Lotka-Volterra system are stable, under certain non-degeneracy conditions. We characterize which faces of the boundary of the domain of the Lotka-Volterra system could contain a stable fixed point. Under various relaxed conditions, we show that whenever a face of the boundary contains a stable point there are no other stable points in any strictly larger face of the boundary.

  19. Three-dimensional discrete-time Lotka-Volterra models with an application to industrial clusters

    Science.gov (United States)

    Bischi, G. I.; Tramontana, F.

    2010-10-01

    We consider a three-dimensional discrete dynamical system that describes an application to economics of a generalization of the Lotka-Volterra prey-predator model. The dynamic model proposed is used to describe the interactions among industrial clusters (or districts), following a suggestion given by [23]. After studying some local and global properties and bifurcations in bidimensional Lotka-Volterra maps, by numerical explorations we show how some of them can be extended to their three-dimensional counterparts, even if their analytic and geometric characterization becomes much more difficult and challenging. We also show a global bifurcation of the three-dimensional system that has no two-dimensional analogue. Besides the particular economic application considered, the study of the discrete version of Lotka-Volterra dynamical systems turns out to be a quite rich and interesting topic by itself, i.e. from a purely mathematical point of view.

  20. Numerical approximations of difference functional equations and applications

    Directory of Open Access Journals (Sweden)

    Zdzisław Kamont

    2005-01-01

    Full Text Available We give a theorem on the error estimate of approximate solutions for difference functional equations of the Volterra type. We apply this general result in the investigation of the stability of difference schemes generated by nonlinear first order partial differential functional equations and by parabolic problems. We show that all known results on difference methods for initial or initial boundary value problems can be obtained as particular cases of this general and simple result. We assume that the right hand sides of equations satisfy nonlinear estimates of the Perron type with respect to functional variables.

  1. Geometry of carrying simplices of 3-species competitive Lotka–Volterra systems

    International Nuclear Information System (INIS)

    Baigent, Stephen

    2013-01-01

    We investigate the existence, uniqueness and Gaussian curvature of the invariant carrying simplices of 3 species autonomous totally competitive Lotka–Volterra systems. Explicit examples are given where the carrying simplex is convex or concave, but also where the curvature is not single-signed. Our method monitors the curvature of an evolving surface that converges uniformly to the carrying simplex, and generally relies on establishing that the Gaussian image of the evolving surface is confined to an invariant cone. We also discuss the relationship between the curvature of the carrying simplex near an interior fixed point and its Split Lyapunov stability. Finally we comment on extensions to general Lotka–Volterra systems that are not competitive. (paper)

  2. Equation-free modeling unravels the behavior of complex ecological systems

    Science.gov (United States)

    DeAngelis, Donald L.; Yurek, Simeon

    2015-01-01

    Ye et al. (1) address a critical problem confronting the management of natural ecosystems: How can we make forecasts of possible future changes in populations to help guide management actions? This problem is especially acute for marine and anadromous fisheries, where the large interannual fluctuations of populations, arising from complex nonlinear interactions among species and with varying environmental factors, have defied prediction over even short time scales. The empirical dynamic modeling (EDM) described in Ye et al.’s report, the latest in a series of papers by Sugihara and his colleagues, offers a promising quantitative approach to building models using time series to successfully project dynamics into the future. With the term “equation-free” in the article title, Ye et al. (1) are suggesting broader implications of their approach, considering the centrality of equations in modern science. From the 1700s on, nature has been increasingly described by mathematical equations, with differential or difference equations forming the basic framework for describing dynamics. The use of mathematical equations for ecological systems came much later, pioneered by Lotka and Volterra, who showed that population cycles might be described in terms of simple coupled nonlinear differential equations. It took decades for Lotka–Volterra-type models to become established, but the development of appropriate differential equations is now routine in modeling ecological dynamics. There is no question that the injection of mathematical equations, by forcing “clarity and precision into conjecture” (2), has led to increased understanding of population and community dynamics. As in science in general, in ecology equations are a key method of communication and of framing hypotheses. These equations serve as compact representations of an enormous amount of empirical data and can be analyzed by the powerful methods of mathematics.

  3. Lp-valued stochastic convolution integral driven by Volterra noise

    Czech Academy of Sciences Publication Activity Database

    Čoupek, P.; Maslowski, B.; Ondreját, Martin

    2018-01-01

    Roč. 18, č. 6 (2018), č. článku 1850048. ISSN 0219-4937 R&D Projects: GA ČR(CZ) GA15-08819S Institutional support: RVO:67985556 Keywords : Volterra process * Rosenblatt process * hypercontractivity Subject RIV: BA - General Mathematics Impact factor: 0.820, year: 2016

  4. Periodic dynamics of delayed Lotka–Volterra competition systems with discontinuous harvesting policies via differential inclusions

    International Nuclear Information System (INIS)

    Cai, Zuowei; Huang, Lihong

    2013-01-01

    Highlights: • A more practical form of harvesting management policy (DHP) has been proposed. • We analyze the periodic dynamics of a class of discontinuous and delayed Lotka–Volterra competition systems. • We present a new method to obtain the existence of positive periodic solutions via differential inclusions. • The global convergence in measure of harvesting solution is discussed. -- Abstract: This paper considers a general class of delayed Lotka–Volterra competition systems where the harvesting policies are modeled by discontinuous functions or by non-Lipschitz functions. By means of differential inclusions theory, cone expansion and compression fixed point theorem of multi-valued maps and nonsmooth analysis theory with generalized Lyapunov approach, a series of useful criteria on existence, uniqueness and global asymptotic stability of the positive periodic solution is established for the delayed Lotka–Volterra competition systems with discontinuous right-hand sides. Moreover, the global convergence in measure of harvesting solution is discussed. Our results improve and extend previous works on periodic dynamics of delayed Lotka–Volterra competition systems with not only continuous or even Lipschitz continuous but also discontinuous harvesting functions. Finally, we give some corollaries and numerical examples to show the applicability and effectiveness of the proposed criteria

  5. Constructing New Discrete Integrable Coupling System for Soliton Equation by Kronecker Product

    International Nuclear Information System (INIS)

    Yu Fajun; Zhang Hongqing

    2008-01-01

    It is shown that the Kronecker product can be applied to constructing new discrete integrable coupling system of soliton equation hierarchy in this paper. A direct application to the fractional cubic Volterra lattice spectral problem leads to a novel integrable coupling system of soliton equation hierarchy. It is also indicated that the study of discrete integrable couplings by using the Kronecker product is an efficient and straightforward method. This method can be used generally

  6. Existence of solutions for nonlinear mixed type integrodifferential equation of second order

    Directory of Open Access Journals (Sweden)

    Haribhau Laxman Tidke

    2010-04-01

    Full Text Available In this paper, we investigate the existence of solutions for nonlinear mixed Volterra-Fredholm integrodifferential equation of second order with nonlocal conditions in Banach spaces. Our analysis is based on Leray-Schauder alternative, rely on a priori bounds of solutions and the inequality established by B. G. Pachpatte.

  7. A Lotka-Volterra competition model with seasonal succession.

    Science.gov (United States)

    Hsu, Sze-Bi; Zhao, Xiao-Qiang

    2012-01-01

    A complete classification for the global dynamics of a Lotka-Volterra two species competition model with seasonal succession is obtained via the stability analysis of equilibria and the theory of monotone dynamical systems. The effects of two death rates in the bad season and the proportion of the good season on the competition outcomes are also discussed. © Springer-Verlag 2011

  8. A simple spatiotemporal chaotic Lotka-Volterra model

    International Nuclear Information System (INIS)

    Sprott, J.C.; Wildenberg, J.C.; Azizi, Yousef

    2005-01-01

    A mathematically simple example of a high-dimensional (many-species) Lotka-Volterra model that exhibits spatiotemporal chaos in one spatial dimension is described. The model consists of a closed ring of identical agents, each competing for fixed finite resources with two of its four nearest neighbors. The model is prototypical of more complicated models in its quasiperiodic route to chaos (including attracting 3-tori), bifurcations, spontaneous symmetry breaking, and spatial pattern formation

  9. A systematic method for constructing time discretizations of integrable lattice systems: local equations of motion

    International Nuclear Information System (INIS)

    Tsuchida, Takayuki

    2010-01-01

    We propose a new method for discretizing the time variable in integrable lattice systems while maintaining the locality of the equations of motion. The method is based on the zero-curvature (Lax pair) representation and the lowest-order 'conservation laws'. In contrast to the pioneering work of Ablowitz and Ladik, our method allows the auxiliary dependent variables appearing in the stage of time discretization to be expressed locally in terms of the original dependent variables. The time-discretized lattice systems have the same set of conserved quantities and the same structures of the solutions as the continuous-time lattice systems; only the time evolution of the parameters in the solutions that correspond to the angle variables is discretized. The effectiveness of our method is illustrated using examples such as the Toda lattice, the Volterra lattice, the modified Volterra lattice, the Ablowitz-Ladik lattice (an integrable semi-discrete nonlinear Schroedinger system) and the lattice Heisenberg ferromagnet model. For the modified Volterra lattice, we also present its ultradiscrete analogue.

  10. Sharp conditions for global stability of Lotka-Volterra systems with distributed delays

    Science.gov (United States)

    Faria, Teresa

    We give a criterion for the global attractivity of a positive equilibrium of n-dimensional non-autonomous Lotka-Volterra systems with distributed delays. For a class of autonomous Lotka-Volterra systems, we show that such a criterion is sharp, in the sense that it provides necessary and sufficient conditions for the global asymptotic stability independently of the choice of the delay functions. The global attractivity of positive equilibria is established by imposing a diagonal dominance of the instantaneous negative feedback terms, and relies on auxiliary results showing the boundedness of all positive solutions. The paper improves and generalizes known results in the literature, namely by considering systems with distributed delays rather than discrete delays.

  11. Blind I/Q imbalance and nonlinear ISI mitigation in Nyquist-SCM direct detection system with cascaded widely linear and Volterra equalizer

    Science.gov (United States)

    Liu, Na; Ju, Cheng

    2018-02-01

    Nyquist-SCM signal after fiber transmission, direct detection (DD), and analog down-conversion suffers from linear ISI, nonlinear ISI, and I/Q imbalance, simultaneously. Theoretical analysis based on widely linear (WL) and Volterra series is given to explain the relationship and interaction of these three interferences. A blind equalization algorithm, cascaded WL and Volterra equalizer, is designed to mitigate these three interferences. Furthermore, the feasibility of the proposed cascaded algorithm is experimentally demonstrated based on a 40-Gbps data rate 16-quadrature amplitude modulation (QAM) virtual single sideband (VSSB) Nyquist-SCM DD system over 100-km standard single mode fiber (SSMF) transmission. In addition, the performances of conventional strictly linear equalizer, WL equalizer, Volterra equalizer, and cascaded WL and Volterra equalizer are experimentally evaluated, respectively.

  12. Verhulst-Lotka-Volterra (VLV) model of ideological struggle

    Science.gov (United States)

    Vitanov, Nikolay K.; Dimitrova, Zlatinka I.; Ausloos, Marcel

    2010-11-01

    A model for ideological struggles is formulated. The underlying set is a closed one, like a country but in which the population size is variable in time. The dynamics of the struggle is described by model equations of Verhulst-Lotka-Volterra kind. Several “ideologies” compete to increase their number of adepts. Such followers can be either converted from one ideology to another or become followers of an ideology though being previously ideologically-free. A reverse process is also allowed. Two kinds of conversions are considered: unitary conversion, e.g. by means of mass communication tools, or binary conversion, e.g. by means of interactions between people. It is found that the steady state, when it exists, depends on the number of ideologies. Moreover when the number of ideologies increases some tension arises between them. This tension can change in the course of time. We propose to measure the ideology tensions through an appropriately defined scale index. Finally it is shown that a slight change in the conditions of the environment can prevent the extinction of some ideology; after almost collapsing the ideology can spread again and can affect a significant part of the country’s population. Two kinds of such resurrection effects are described as phoenix effects.

  13. Long-Term Dynamics of Autonomous Fractional Differential Equations

    Science.gov (United States)

    Liu, Tao; Xu, Wei; Xu, Yong; Han, Qun

    This paper aims to investigate long-term dynamic behaviors of autonomous fractional differential equations with effective numerical method. The long-term dynamic behaviors predict where systems are heading after long-term evolution. We make some modification and transplant cell mapping methods to autonomous fractional differential equations. The mapping time duration of cell mapping is enlarged to deal with the long memory effect. Three illustrative examples, i.e. fractional Lotka-Volterra equation, fractional van der Pol oscillator and fractional Duffing equation, are studied with our revised generalized cell mapping method. We obtain long-term dynamics, such as attractors, basins of attraction, and saddles. Compared with some existing stability and numerical results, the validity of our method is verified. Furthermore, we find that the fractional order has its effect on the long-term dynamics of autonomous fractional differential equations.

  14. Global asymptotic stability for a nonautonomous Lotka-Volterra competition system

    OpenAIRE

    TANIGUCHI, Kunihiko

    2014-01-01

    We consider nonautonomous N-dimensional generalized Lotka-Volterra competition systems. Under certain conditions we show that there exists a unique solution u* whose components are bounded above and below by positive constants on R, and u* attracts any solution. If such system is periodic, so is u*.

  15. Lie and conditional symmetries of the three-component diffusive Lotka–Volterra system

    International Nuclear Information System (INIS)

    Cherniha, Roman; Davydovych, Vasyl’

    2013-01-01

    Lie and Q-conditional symmetries of the classical three-component diffusive Lotka–Volterra system in the case of one space variable are studied. The group-classification problems for finding Lie symmetries and Q-conditional symmetries of the first type are completely solved. Notably, non-Lie symmetries (Q-conditional symmetry operators) for a multi-component nonlinear reaction–diffusion system are constructed for the first time. The results are compared with those derived for the two-component diffusive Lotka–Volterra system. The conditional symmetry obtained for the non-Lie reduction of the three-component system used for modeling competition between three species in population dynamics is applied and the relevant exact solutions are found. Particularly, the exact solution describing different scenarios of competition between three species is constructed. (paper)

  16. On Newton-Kantorovich Method for Solving the Nonlinear Operator Equation

    Directory of Open Access Journals (Sweden)

    Hameed Husam Hameed

    2015-01-01

    Full Text Available We develop the Newton-Kantorovich method to solve the system of 2×2 nonlinear Volterra integral equations where the unknown function is in logarithmic form. A new majorant function is introduced which leads to the increment of the convergence interval. The existence and uniqueness of approximate solution are proved and a numerical example is provided to show the validation of the method.

  17. The cyclicity of period annulus of a quadratic reversible Lotka–Volterra system

    International Nuclear Information System (INIS)

    Li, Chengzhi; Llibre, Jaume

    2009-01-01

    We prove that by perturbing the periodic annulus of the quadratic polynomial reversible Lotka–Volterra differential system, inside the class of all quadratic polynomial differential systems we can obtain at most two limit cycles

  18. Dynamical behaviors determined by the Lyapunov function in competitive Lotka-Volterra systems

    Science.gov (United States)

    Tang, Ying; Yuan, Ruoshi; Ma, Yian

    2013-01-01

    Dynamical behaviors of the competitive Lotka-Volterra system even for 3 species are not fully understood. In this paper, we study this problem from the perspective of the Lyapunov function. We construct explicitly the Lyapunov function using three examples of the competitive Lotka-Volterra system for the whole state space: (1) the general 2-species case, (2) a 3-species model, and (3) the model of May-Leonard. The basins of attraction for these examples are demonstrated, including cases with bistability and cyclical behavior. The first two examples are the generalized gradient system, where the energy dissipation may not follow the gradient of the Lyapunov function. In addition, under a new type of stochastic interpretation, the Lyapunov function also leads to the Boltzmann-Gibbs distribution on the final steady state when multiplicative noise is added.

  19. A textbook on ordinary differential equations

    CERN Document Server

    Ahmad, Shair

    2015-01-01

    This book offers readers a primer on the theory and applications of Ordinary Differential Equations. The style used is simple, yet thorough and rigorous. Each chapter ends with a broad set of exercises that range from the routine to the more challenging and thought-provoking. Solutions to selected exercises can be found at the end of the book. The book contains many interesting examples on topics such as electric circuits, the pendulum equation, the logistic equation, the Lotka-Volterra system, the Laplace Transform, etc., which introduce students to a number of interesting aspects of the theory and applications. The work is mainly intended for students of Mathematics, Physics, Engineering, Computer Science and other areas of the natural and social sciences that use ordinary differential equations, and who have a firm grasp of Calculus and a minimal understanding of the basic concepts used in Linear Algebra. It also studies a few more advanced topics, such as Stability Theory and Boundary Value Problems, whic...

  20. A textbook on ordinary differential equations

    CERN Document Server

    Ahmad, Shair

    2014-01-01

    The book is a primer of the theory of Ordinary Differential Equations. Each chapter is completed by a broad set of exercises; the reader will also find a set of solutions of selected exercises. The book contains many interesting examples as well (like the equations for the electric circuits, the pendium equation, the logistic equation, the Lotka-Volterra system, and many other) which introduce the reader to some interesting aspects of the theory and its applications. The work is mainly addressed to students of Mathematics, Physics, Engineering, Statistics, Computer Sciences, with  knowledge of Calculus and Linear Algebra, and contains more advanced topics for further developments, such as Laplace transform; Stability theory and existence of solutions to Boundary Value problems. The authors are preparing a complete solutions manual, containing solutions to all the exercises published in the book. The manual will be available Summer 2014. Instructors who wish to adopt the book may request the manual by writing...

  1. A novel nonlinear adaptive filter using a pipelined second-order Volterra recurrent neural network.

    Science.gov (United States)

    Zhao, Haiquan; Zhang, Jiashu

    2009-12-01

    To enhance the performance and overcome the heavy computational complexity of recurrent neural networks (RNN), a novel nonlinear adaptive filter based on a pipelined second-order Volterra recurrent neural network (PSOVRNN) is proposed in this paper. A modified real-time recurrent learning (RTRL) algorithm of the proposed filter is derived in much more detail. The PSOVRNN comprises of a number of simple small-scale second-order Volterra recurrent neural network (SOVRNN) modules. In contrast to the standard RNN, these modules of a PSOVRNN can be performed simultaneously in a pipelined parallelism fashion, which can lead to a significant improvement in its total computational efficiency. Moreover, since each module of the PSOVRNN is a SOVRNN in which nonlinearity is introduced by the recursive second-order Volterra (RSOV) expansion, its performance can be further improved. Computer simulations have demonstrated that the PSOVRNN performs better than the pipelined recurrent neural network (PRNN) and RNN for nonlinear colored signals prediction and nonlinear channel equalization. However, the superiority of the PSOVRNN over the PRNN is at the cost of increasing computational complexity due to the introduced nonlinear expansion of each module.

  2. Hamiltonian structures and integrability for a discrete coupled KdV-type equation hierarchy

    International Nuclear Information System (INIS)

    Zhao Haiqiong; Zhu Zuonong; Zhang Jingli

    2011-01-01

    Coupled Korteweg-de Vries (KdV) systems have many important physical applications. By considering a 4 × 4 spectral problem, we derive a discrete coupled KdV-type equation hierarchy. Our hierarchy includes the coupled Volterra system proposed by Lou et al. (e-print arXiv: 0711.0420) as the first member which is a discrete version of the coupled KdV equation. We also investigate the integrability in the Liouville sense and the multi-Hamiltonian structures for the obtained hierarchy. (authors)

  3. The discrete hungry Lotka Volterra system and a new algorithm for computing matrix eigenvalues

    Science.gov (United States)

    Fukuda, Akiko; Ishiwata, Emiko; Iwasaki, Masashi; Nakamura, Yoshimasa

    2009-01-01

    The discrete hungry Lotka-Volterra (dhLV) system is a generalization of the discrete Lotka-Volterra (dLV) system which stands for a prey-predator model in mathematical biology. In this paper, we show that (1) some invariants exist which are expressed by dhLV variables and are independent from the discrete time and (2) a dhLV variable converges to some positive constant or zero as the discrete time becomes sufficiently large. Some characteristic polynomial is then factorized with the help of the dhLV system. The asymptotic behaviour of the dhLV system enables us to design an algorithm for computing complex eigenvalues of a certain band matrix.

  4. The discrete hungry Lotka–Volterra system and a new algorithm for computing matrix eigenvalues

    International Nuclear Information System (INIS)

    Fukuda, Akiko; Ishiwata, Emiko; Iwasaki, Masashi; Nakamura, Yoshimasa

    2009-01-01

    The discrete hungry Lotka–Volterra (dhLV) system is a generalization of the discrete Lotka–Volterra (dLV) system which stands for a prey–predator model in mathematical biology. In this paper, we show that (1) some invariants exist which are expressed by dhLV variables and are independent from the discrete time and (2) a dhLV variable converges to some positive constant or zero as the discrete time becomes sufficiently large. Some characteristic polynomial is then factorized with the help of the dhLV system. The asymptotic behaviour of the dhLV system enables us to design an algorithm for computing complex eigenvalues of a certain band matrix

  5. A predictor-corrector scheme for solving the Volterra integral equation

    KAUST Repository

    Al Jarro, Ahmed; Bagci, Hakan

    2011-01-01

    The occurrence of late time instabilities is a common problem of almost all time marching methods developed for solving time domain integral equations. Implicit marching algorithms are now considered stable with various efforts that have been

  6. Lotka-Volterra competition models for sessile organisms.

    Science.gov (United States)

    Spencer, Matthew; Tanner, Jason E

    2008-04-01

    Markov models are widely used to describe the dynamics of communities of sessile organisms, because they are easily fitted to field data and provide a rich set of analytical tools. In typical ecological applications, at any point in time, each point in space is in one of a finite set of states (e.g., species, empty space). The models aim to describe the probabilities of transitions between states. In most Markov models for communities, these transition probabilities are assumed to be independent of state abundances. This assumption is often suspected to be false and is rarely justified explicitly. Here, we start with simple assumptions about the interactions among sessile organisms and derive a model in which transition probabilities depend on the abundance of destination states. This model is formulated in continuous time and is equivalent to a Lotka-Volterra competition model. We fit this model and a variety of alternatives in which transition probabilities do not depend on state abundances to a long-term coral reef data set. The Lotka-Volterra model describes the data much better than all models we consider other than a saturated model (a model with a separate parameter for each transition at each time interval, which by definition fits the data perfectly). Our approach provides a basis for further development of stochastic models of sessile communities, and many of the methods we use are relevant to other types of community. We discuss possible extensions to spatially explicit models.

  7. A Volterra series approach to the approximation of stochastic nonlinear dynamics

    NARCIS (Netherlands)

    Wouw, van de N.; Nijmeijer, H.; Campen, van D.H.

    2002-01-01

    A response approximation method for stochastically excited, nonlinear, dynamic systems is presented. Herein, the output of the nonlinear system isapproximated by a finite-order Volterra series. The original nonlinear system is replaced by a bilinear system in order to determine the kernels of this

  8. Effective methods of solving of model equations of certain class of thermal systems

    International Nuclear Information System (INIS)

    Lach, J.

    1985-01-01

    A number of topics connected with solving of model equations of certain class of thermal systems by the method of successive approximations is touched. A system of partial differential equations of the first degree, appearing most frequently in practical applications of heat and mass transfer theory is reduced to an equivalent system of Volterra integral equations of the second kind. Among a few sample applications the thermal processes appearing in the fuel channel of nuclear reactor are solved. The theoretical analysis is illustrated by the results of numerical calculations given in tables and diagrams. 111 refs., 17 figs., 16 tabs. (author)

  9. q-fractional calculus and equations

    CERN Document Server

    Annaby, Mahmoud H

    2012-01-01

    This nine-chapter monograph introduces a rigorous investigation of q-difference operators in standard and fractional settings. It starts with elementary calculus of q-differences and integration of Jackson’s type before turning to q-difference equations. The existence and uniqueness theorems are derived using successive approximations, leading to systems of equations with retarded arguments. Regular  q-Sturm–Liouville theory is also introduced; Green’s function is constructed and the eigenfunction expansion theorem is given. The monograph also discusses some integral equations of Volterra and Abel type, as introductory material for the study of fractional q-calculi. Hence fractional q-calculi of the types Riemann–Liouville; Grünwald–Letnikov;  Caputo;  Erdélyi–Kober and Weyl are defined analytically. Fractional q-Leibniz rules with applications  in q-series are  also obtained with rigorous proofs of the formal  results of  Al-Salam-Verma, which remained unproved for decades. In working ...

  10. Turing patterns in a modified Lotka-Volterra model

    International Nuclear Information System (INIS)

    McGehee, Edward A.; Peacock-Lopez, Enrique

    2005-01-01

    In this Letter we consider a modified Lotka-Volterra model widely known as the Bazykin model, which is the MacArthur-Rosenzweig (MR) model that includes a prey-dependent response function and is modified with the inclusion of intraspecies interactions. We show that a quadratic intra-prey interaction term, which is the most realistic nonlinearity, yields sufficient conditions for Turing patterns. For the Bazykin model we find the Turing region in parameter space and Turing patterns in one dimension

  11. Singular boundary value problem for the integrodifferential equation in an insurance model with stochastic premiums: Analysis and numerical solution

    Science.gov (United States)

    Belkina, T. A.; Konyukhova, N. B.; Kurochkin, S. V.

    2012-10-01

    A singular boundary value problem for a second-order linear integrodifferential equation with Volterra and non-Volterra integral operators is formulated and analyzed. The equation is defined on ℝ+, has a weak singularity at zero and a strong singularity at infinity, and depends on several positive parameters. Under natural constraints on the coefficients of the equation, existence and uniqueness theorems for this problem with given limit boundary conditions at singular points are proved, asymptotic representations of the solution are given, and an algorithm for its numerical determination is described. Numerical computations are performed and their interpretation is given. The problem arises in the study of the survival probability of an insurance company over infinite time (as a function of its initial surplus) in a dynamic insurance model that is a modification of the classical Cramer-Lundberg model with a stochastic process rate of premium under a certain investment strategy in the financial market. A comparative analysis of the results with those produced by the model with deterministic premiums is given.

  12. Corrigendum to ;Lotka-Volterra systems satisfying a strong Painlevé property; [Phys. Lett. A 380 (47) (2016) 3977-3982

    Science.gov (United States)

    Bountis, Tassos; Vanhaecke, Pol

    2017-12-01

    The comment made after the proof of Proposition 3.3, in our paper [T. Bountis, P. Vanhaecke, Lotka-Volterra systems satisfying a strong Pailevé property, Phys. Lett. A 380 (47) (2016) 3977-3982], saying that the proposition can be generalized when linear terms are added to the Lotka-Volterra systems considered in the paper, is wrong. In general such deformed systems are not even Hamiltonian.

  13. Dirac Mass Dynamics in Multidimensional Nonlocal Parabolic Equations

    KAUST Repository

    Lorz, Alexander

    2011-01-17

    Nonlocal Lotka-Volterra models have the property that solutions concentrate as Dirac masses in the limit of small diffusion. Is it possible to describe the dynamics of the limiting concentration points and of the weights of the Dirac masses? What is the long time asymptotics of these Dirac masses? Can several Dirac masses coexist? We will explain how these questions relate to the so-called "constrained Hamilton-Jacobi equation" and how a form of canonical equation can be established. This equation has been established assuming smoothness. Here we build a framework where smooth solutions exist and thus the full theory can be developed rigorously. We also show that our form of canonical equation comes with a kind of Lyapunov functional. Numerical simulations show that the trajectories can exhibit unexpected dynamics well explained by this equation. Our motivation comes from population adaptive evolution a branch of mathematical ecology which models Darwinian evolution. © Taylor & Francis Group, LLC.

  14. Positive periodic solutions of delayed periodic Lotka-Volterra systems

    International Nuclear Information System (INIS)

    Lin Wei; Chen Tianping

    2005-01-01

    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

  15. Numerical treatments for solving nonlinear mixed integral equation

    Directory of Open Access Journals (Sweden)

    M.A. Abdou

    2016-12-01

    Full Text Available We consider a mixed type of nonlinear integral equation (MNLIE of the second kind in the space C[0,T]×L2(Ω,T<1. The Volterra integral terms (VITs are considered in time with continuous kernels, while the Fredholm integral term (FIT is considered in position with singular general kernel. Using the quadratic method and separation of variables method, we obtain a nonlinear system of Fredholm integral equations (NLSFIEs with singular kernel. A Toeplitz matrix method, in each case, is then used to obtain a nonlinear algebraic system. Numerical results are calculated when the kernels take a logarithmic form or Carleman function. Moreover, the error estimates, in each case, are then computed.

  16. Instantaneous nonlinear assessment of complex cardiovascular dynamics by Laguerre-Volterra point process models.

    Science.gov (United States)

    Valenza, Gaetano; Citi, Luca; Barbieri, Riccardo

    2013-01-01

    We report an exemplary study of instantaneous assessment of cardiovascular dynamics performed using point-process nonlinear models based on Laguerre expansion of the linear and nonlinear Wiener-Volterra kernels. As quantifiers, instantaneous measures such as high order spectral features and Lyapunov exponents can be estimated from a quadratic and cubic autoregressive formulation of the model first order moment, respectively. Here, these measures are evaluated on heartbeat series coming from 16 healthy subjects and 14 patients with Congestive Hearth Failure (CHF). Data were gathered from the on-line repository PhysioBank, which has been taken as landmark for testing nonlinear indices. Results show that the proposed nonlinear Laguerre-Volterra point-process methods are able to track the nonlinear and complex cardiovascular dynamics, distinguishing significantly between CHF and healthy heartbeat series.

  17. Global stability and pattern formation in a nonlocal diffusive Lotka-Volterra competition model

    Science.gov (United States)

    Ni, Wenjie; Shi, Junping; Wang, Mingxin

    2018-06-01

    A diffusive Lotka-Volterra competition model with nonlocal intraspecific and interspecific competition between species is formulated and analyzed. The nonlocal competition strength is assumed to be determined by a diffusion kernel function to model the movement pattern of the biological species. It is shown that when there is no nonlocal intraspecific competition, the dynamics properties of nonlocal diffusive competition problem are similar to those of classical diffusive Lotka-Volterra competition model regardless of the strength of nonlocal interspecific competition. Global stability of nonnegative constant equilibria are proved using Lyapunov or upper-lower solution methods. On the other hand, strong nonlocal intraspecific competition increases the system spatiotemporal dynamic complexity. For the weak competition case, the nonlocal diffusive competition model may possess nonconstant positive equilibria for some suitably large nonlocal intraspecific competition coefficients.

  18. Nonlinear features identified by Volterra series for damage detection in a buckled beam

    Directory of Open Access Journals (Sweden)

    Shiki S. B.

    2014-01-01

    Full Text Available The present paper proposes a new index for damage detection based on nonlinear features extracted from prediction errors computed by multiple convolutions using the discrete-time Volterra series. A reference Volterra model is identified with data in the healthy condition and used for monitoring the system operating with linear or nonlinear behavior. When the system has some structural change, possibly associated with damage, the index metrics computed could give an alert to separate the linear and nonlinear contributions, besides provide a diagnostic about the structural state. To show the applicability of the method, an experimental test is performed using nonlinear vibration signals measured in a clamped buckled beam subject to different levels of force applied and with simulated damages through discontinuities inserted in the beam surface.

  19. Joint and collaborative representation with local Volterra kernels convolution feature for face recognition

    Science.gov (United States)

    Feng, Guang; Li, Hengjian; Dong, Jiwen; Chen, Xi; Yang, Huiru

    2018-04-01

    In this paper, we proposed a joint and collaborative representation with Volterra kernel convolution feature (JCRVK) for face recognition. Firstly, the candidate face images are divided into sub-blocks in the equal size. The blocks are extracted feature using the two-dimensional Voltera kernels discriminant analysis, which can better capture the discrimination information from the different faces. Next, the proposed joint and collaborative representation is employed to optimize and classify the local Volterra kernels features (JCR-VK) individually. JCR-VK is very efficiently for its implementation only depending on matrix multiplication. Finally, recognition is completed by using the majority voting principle. Extensive experiments on the Extended Yale B and AR face databases are conducted, and the results show that the proposed approach can outperform other recently presented similar dictionary algorithms on recognition accuracy.

  20. Existence and global attractivity of positive periodic solutions of periodic n-species Lotka-Volterra competition systems with several deviating arguments.

    Science.gov (United States)

    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.

  1. Qualitative aspects of Volterra integro-dynamic system on time scales

    Directory of Open Access Journals (Sweden)

    Vasile Lupulescu

    2013-01-01

    Full Text Available This paper deals with the resolvent, asymptotic stability and boundedness of the solution of time-varying Volterra integro-dynamic system on time scales in which the coefficient matrix is not necessarily stable. We generalize at time scale some known properties about asymptotic behavior and boundedness from the continuous case. Some new results for discrete case are obtained.

  2. Accurate and efficient quadrature for volterra integral equations

    International Nuclear Information System (INIS)

    Knirk, D.L.

    1976-01-01

    Four quadrature schemes were tested and compared in considerable detail to determine their usefulness in the noniterative integral equation method for single-channel quantum-mechanical calculations. They are two forms of linear approximation (trapezoidal rule) and two forms of quadratic approximation (Simpson's rule). Their implementation in this method is shown, a formal discussion of error propagation is given, and tests are performed to determine actual operating characteristics on various bound and scattering problems in different potentials. The quadratic schemes are generally superior to the linear ones in terms of accuracy and efficiency. The previous implementation of Simpson's rule is shown to possess an inherent instability which requires testing on each problem for which it is used to assure its reliability. The alternative quadratic approximation does not suffer this deficiency, but still enjoys the advantages of higher order. In addition, the new scheme obeys very well an h 4 Richardson extrapolation, whereas the old one does so rather poorly. 6 figures, 11 tables

  3. Block-pulse functions approach to numerical solution of Abel’s integral equation

    Directory of Open Access Journals (Sweden)

    Monireh Nosrati Sahlan

    2015-12-01

    Full Text Available This study aims to present a computational method for solving Abel’s integral equation of the second kind. The introduced method is based on the use of Block-pulse functions (BPFs via collocation method. Abel’s integral equations as singular Volterra integral equations are hard and heavy in computation, but because of the properties of BPFs, as is reported in examples, this method is more efficient and more accurate than some other methods for solving this class of integral equations. On the other hand, the benefit of this method is low cost of computing operations. The applied method transforms the singular integral equation into triangular linear algebraic system that can be solved easily. An error analysis is worked out and applications are demonstrated through illustrative examples.

  4. Coexistence and Survival in Conservative Lotka-Volterra Networks

    Science.gov (United States)

    Knebel, Johannes; Krüger, Torben; Weber, Markus F.; Frey, Erwin

    2013-04-01

    Analyzing coexistence and survival scenarios of Lotka-Volterra (LV) networks in which the total biomass is conserved is of vital importance for the characterization of long-term dynamics of ecological communities. Here, we introduce a classification scheme for coexistence scenarios in these conservative LV models and quantify the extinction process by employing the Pfaffian of the network’s interaction matrix. We illustrate our findings on global stability properties for general systems of four and five species and find a generalized scaling law for the extinction time.

  5. The persistence in a Lotka-Volterra competition systems with impulsive

    International Nuclear Information System (INIS)

    Zhen Jin; Han Maoan; Li Guihua

    2005-01-01

    In this paper, a nonautonomous two-dimensional competitive Lotka-Volterra system with impulsive is considered. we study the persistence and extinction, giving two inequalities involving averages of the growth rates and impulsive value, which guarantees persistence of the system. An extension of the principle of competition exclusion is obtained in this paper. Moreover, several examples are also worked out, they show that the impulsive can change the persistence of the system

  6. Asymptotic Comparison of the Solutions of Linear Time-Delay Systems with Point and Distributed Lags with Those of Their Limiting Equations

    Directory of Open Access Journals (Sweden)

    M. De la Sen

    2009-01-01

    Full Text Available This paper investigates the relations between the particular eigensolutions of a limiting functional differential equation of any order, which is the nominal (unperturbed linear autonomous differential equations, and the associate ones of the corresponding perturbed functional differential equation. Both differential equations involve point and distributed delayed dynamics including Volterra class dynamics. The proofs are based on a Perron-type theorem for functional equations so that the comparison is governed by the real part of a dominant zero of the characteristic equation of the nominal differential equation. The obtained results are also applied to investigate the global stability of the perturbed equation based on that of its corresponding limiting equation.

  7. A combinatorial method for the vanishing of the Poisson brackets of an integrable Lotka-Volterra system

    International Nuclear Information System (INIS)

    Itoh, Yoshiaki

    2009-01-01

    The combinatorial method is useful to obtain conserved quantities for some nonlinear integrable systems, as an alternative to the Lax representation method. Here we extend the combinatorial method and introduce an elementary geometry to show the vanishing of the Poisson brackets of the Hamiltonian structure for a Lotka-Volterra system of competing species. We associate a set of points on a circle with a set of species of the Lotka-Volterra system, where the dominance relations between points are given by the dominance relations between the species. We associate each term of the conserved quantities with a subset of points on the circle, which simplifies to show the vanishing of the Poisson brackets

  8. On stochastic integration for volatility modulated Brownian-driven Volterra processes via white noise analysis

    DEFF Research Database (Denmark)

    E. Barndorff-Nielsen, Ole; Benth, Fred Espen; Szozda, Benedykt

    This paper generalizes the integration theory for volatility modulated Brownian-driven Volterra processes onto the space G* of Potthoff-Timpel distributions. Sufficient conditions for integrability of generalized processes are given, regularity results and properties of the integral are discussed...

  9. On stochastic integration for volatility modulated Brownian-driven Volterra processes via white noise analysis

    DEFF Research Database (Denmark)

    Barndorff-Nielsen, Ole E.; Benth, Fred Espen; Szozda, Benedykt

    This paper generalizes the integration theory for volatility modulated Brownian-driven Volterra processes onto the space G∗ of Potthoff--Timpel distributions. Sufficient conditions for integrability of generalized processes are given, regularity results and properties of the integral are discusse...

  10. Nonlinear degradation of a visible-light communication link: A Volterra-series approach

    Science.gov (United States)

    Kamalakis, Thomas; Dede, Georgia

    2018-06-01

    Visible light communications can be used to provide illumination and data communication at the same time. In this paper, a reverse-engineering approach is presented for assessing the impact of nonlinear signal distortion in visible light communication links. The approach is based on the Volterra series expansion and has the advantage of accurately accounting for memory effects in contrast to the static nonlinear models that are popular in the literature. Volterra kernels describe the end-to-end system response and can be inferred from measurements. Consequently, this approach does not rely on any particular physical models and assumptions regarding the individual link components. We provide the necessary framework for estimating the nonlinear distortion on the symbol estimates of a discrete multitone modulated link. Various design aspects such as waveform clipping and predistortion are also incorporated in the analysis. Using this framework, the nonlinear signal-to-interference is calculated for the system at hand. It is shown that at high signal amplitudes, the nonlinear signal-to-interference can be less than 25 dB.

  11. Filtered-X Affine Projection Algorithms for Active Noise Control Using Volterra Filters

    Directory of Open Access Journals (Sweden)

    Sicuranza Giovanni L

    2004-01-01

    Full Text Available We consider the use of adaptive Volterra filters, implemented in the form of multichannel filter banks, as nonlinear active noise controllers. In particular, we discuss the derivation of filtered-X affine projection algorithms for homogeneous quadratic filters. According to the multichannel approach, it is then easy to pass from these algorithms to those of a generic Volterra filter. It is shown in the paper that the AP technique offers better convergence and tracking capabilities than the classical LMS and NLMS algorithms usually applied in nonlinear active noise controllers, with a limited complexity increase. This paper extends in two ways the content of a previous contribution published in Proc. IEEE-EURASIP Workshop on Nonlinear Signal and Image Processing (NSIP '03, Grado, Italy, June 2003. First of all, a general adaptation algorithm valid for any order of affine projections is presented. Secondly, a more complete set of experiments is reported. In particular, the effects of using multichannel filter banks with a reduced number of channels are investigated and relevant results are shown.

  12. A Two-Species Cooperative Lotka-Volterra System of Degenerate Parabolic Equations

    Directory of Open Access Journals (Sweden)

    Jiebao Sun

    2011-01-01

    parabolic equations. We are interested in the coexistence of the species in a bounded domain. We establish the existence of global generalized solutions of the initial boundary value problem by means of parabolic regularization and also consider the existence of the nontrivial time-periodic solution for this system.

  13. Bifurcation structure of positive stationary solutions for a Lotka-Volterra competition model with diffusion I

    Science.gov (United States)

    Kan-On, Yukio

    2007-04-01

    This paper is concerned with the bifurcation structure of positive stationary solutions for a generalized Lotka-Volterra competition model with diffusion. To establish the structure, the bifurcation theory and the interval arithmetic are employed.

  14. The determination of an unknown boundary condition in a fractional diffusion equation

    KAUST Repository

    Rundell, William

    2013-07-01

    In this article we consider an inverse boundary problem, in which the unknown boundary function ∂u/∂v = f(u) is to be determined from overposed data in a time-fractional diffusion equation. Based upon the free space fundamental solution, we derive a representation for the solution f as a nonlinear Volterra integral equation of second kind with a weakly singular kernel. Uniqueness and reconstructibility by iteration is an immediate result of a priori assumption on f and applying the fixed point theorem. Numerical examples are presented to illustrate the validity and effectiveness of the proposed method. © 2013 Copyright Taylor and Francis Group, LLC.

  15. Embedding recurrent neural networks into predator-prey models.

    Science.gov (United States)

    Moreau, Yves; Louiès, Stephane; Vandewalle, Joos; Brenig, Leon

    1999-03-01

    We study changes of coordinates that allow the embedding of ordinary differential equations describing continuous-time recurrent neural networks into differential equations describing predator-prey models-also called Lotka-Volterra systems. We transform the equations for the neural network first into quasi-monomial form (Brenig, L. (1988). Complete factorization and analytic solutions of generalized Lotka-Volterra equations. Physics Letters A, 133(7-8), 378-382), where we express the vector field of the dynamical system as a linear combination of products of powers of the variables. In practice, this transformation is possible only if the activation function is the hyperbolic tangent or the logistic sigmoid. From this quasi-monomial form, we can directly transform the system further into Lotka-Volterra equations. The resulting Lotka-Volterra system is of higher dimension than the original system, but the behavior of its first variables is equivalent to the behavior of the original neural network. We expect that this transformation will permit the application of existing techniques for the analysis of Lotka-Volterra systems to recurrent neural networks. Furthermore, our results show that Lotka-Volterra systems are universal approximators of dynamical systems, just as are continuous-time neural networks.

  16. Effective quadrature formula in solving linear integro-differential equations of order two

    Science.gov (United States)

    Eshkuvatov, Z. K.; Kammuji, M.; Long, N. M. A. Nik; Yunus, Arif A. M.

    2017-08-01

    In this note, we solve general form of Fredholm-Volterra integro-differential equations (IDEs) of order 2 with boundary condition approximately and show that proposed method is effective and reliable. Initially, IDEs is reduced into integral equation of the third kind by using standard integration techniques and identity between multiple and single integrals then truncated Legendre series are used to estimate the unknown function. For the kernel integrals, we have applied Gauss-Legendre quadrature formula and collocation points are chosen as the roots of the Legendre polynomials. Finally, reduce the integral equations of the third kind into the system of algebraic equations and Gaussian elimination method is applied to get approximate solutions. Numerical examples and comparisons with other methods reveal that the proposed method is very effective and dominated others in many cases. General theory of existence of the solution is also discussed.

  17. String networks in ZN Lotka–Volterra competition models

    International Nuclear Information System (INIS)

    Avelino, P.P.; Bazeia, D.; Menezes, J.; Oliveira, B.F. de

    2014-01-01

    In this Letter we give specific examples of Z N Lotka–Volterra competition models leading to the formation of string networks. We show that, in order to promote coexistence, the species may arrange themselves around regions with a high number density of empty sites generated by predator–prey interactions between competing species. These configurations extend into the third dimension giving rise to string networks. We investigate the corresponding dynamics using both stochastic and mean field theory simulations, showing that the coarsening of these string networks follows a scaling law which is analogous to that found in other physical systems in condensed matter and cosmology

  18. Stability and Hopf bifurcations in a competitive Lotka-Volterra system with two delays

    International Nuclear Information System (INIS)

    Song Yongli; Han Maoan; Peng Yahong

    2004-01-01

    We consider a Lotka-Volterra competition system with two delays. We first investigate the stability of the positive equilibrium and the existence of Hopf bifurcations, and then using the normal form theory and center manifold argument, derive the explicit formulas which determine the stability, direction and other properties of bifurcating periodic solutions

  19. On positive periodic solution of periodic competition Lotka-Volterra system with time delay and diffusion

    International Nuclear Information System (INIS)

    Sun Wen; Chen Shihua; Hong Zhiming; Wang Changping

    2007-01-01

    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

  20. Delay-Induced Oscillations in a Competitor-Competitor-Mutualist Lotka-Volterra Model

    Directory of Open Access Journals (Sweden)

    Changjin Xu

    2017-01-01

    Full Text Available This paper deals with a competitor-competitor-mutualist Lotka-Volterra model. A series of sufficient criteria guaranteeing the stability and the occurrence of Hopf bifurcation for the model are obtained. Several concrete formulae determine the properties of bifurcating periodic solutions by applying the normal form theory and the center manifold principle. Computer simulations are given to support the theoretical predictions. At last, biological meaning and a conclusion are presented.

  1. Generalized Lotka—Volterra systems connected with simple Lie algebras

    International Nuclear Information System (INIS)

    Charalambides, Stelios A; Damianou, Pantelis A; Evripidou, Charalambos A

    2015-01-01

    We devise a new method for producing Hamiltonian systems by constructing the corresponding Lax pairs. This is achieved by considering a larger subset of the positive roots than the simple roots of the root system of a simple Lie algebra. We classify all subsets of the positive roots of the root system of type A n for which the corresponding Hamiltonian systems are transformed, via a simple change of variables, to Lotka-Volterra systems. For some special cases of subsets of the positive roots of the root system of type A n , we produce new integrable Hamiltonian systems. (paper)

  2. Generalized Lotka—Volterra systems connected with simple Lie algebras

    Science.gov (United States)

    Charalambides, Stelios A.; Damianou, Pantelis A.; Evripidou, Charalambos A.

    2015-06-01

    We devise a new method for producing Hamiltonian systems by constructing the corresponding Lax pairs. This is achieved by considering a larger subset of the positive roots than the simple roots of the root system of a simple Lie algebra. We classify all subsets of the positive roots of the root system of type An for which the corresponding Hamiltonian systems are transformed, via a simple change of variables, to Lotka-Volterra systems. For some special cases of subsets of the positive roots of the root system of type An, we produce new integrable Hamiltonian systems.

  3. Theoretical analysis and simulations of the generalized Lotka-Volterra model

    Science.gov (United States)

    Malcai, Ofer; Biham, Ofer; Richmond, Peter; Solomon, Sorin

    2002-09-01

    The dynamics of generalized Lotka-Volterra systems is studied by theoretical techniques and computer simulations. These systems describe the time evolution of the wealth distribution of individuals in a society, as well as of the market values of firms in the stock market. The individual wealths or market values are given by a set of time dependent variables wi, i=1,...,N. The equations include a stochastic autocatalytic term (representing investments), a drift term (representing social security payments), and a time dependent saturation term (due to the finite size of the economy). The wi's turn out to exhibit a power-law distribution of the form P(w)~w-1-α. It is shown analytically that the exponent α can be expressed as a function of one parameter, which is the ratio between the constant drift component (social security) and the fluctuating component (investments). This result provides a link between the lower and upper cutoffs of this distribution, namely, between the resources available to the poorest and those available to the richest in a given society. The value of α is found to be insensitive to variations in the saturation term, which represent the expansion or contraction of the economy. The results are of much relevance to empirical studies that show that the distribution of the individual wealth in different countries during different periods in the 20th century has followed a power-law distribution with 1<α<2.

  4. On the general solution for the modified Emden-type equation x-doubledot + αxx-dot + βx3 = 0

    International Nuclear Information System (INIS)

    Chandrasekar, V K; Senthilvelan, M; Lakshmanan, M

    2007-01-01

    In this paper, we demonstrate that the modified equation of Emden type (MEE), x-doubledot + αxx-dot + βx 3 = 0, is integrable either explicitly or by quadrature for any value of α and β. We also prove that the MEE possesses appropriate time-independent Hamiltonian functions for the full range of parameters α and β. In addition we show that the MEE is intimately connected with two well-known nonlinear models, namely the equation of force-free Duffing-type oscillator and the two-dimensional Lotka-Volterra equation, and thus the complete integrability of the latter two models can also be understood in terms of the MEE

  5. Turing pattern dynamics and adaptive discretization for a superdiffusive Lotka-Volterra system

    OpenAIRE

    Bendahmane , Mostafa; Ruiz-Baier , Ricardo; Tian , Canrong

    2016-01-01

    International audience; We focus our attention on the effects of introducing the fractional-in-space operator into a Lotka-Volterra competitive model describing population superdiffusion. First, we address the weak solvability of the coupled problem employing the Faedo-Galerkin method and compactness arguments. In addition, we are interested in how cross superdiffusion influences the formation of spatial patterns: a linear stability analysis has been carried out, showing that cross superdiffu...

  6. Stable power laws in variable economies; Lotka-Volterra implies Pareto-Zipf

    Science.gov (United States)

    Solomon, S.; Richmond, P.

    2002-05-01

    In recent years we have found that logistic systems of the Generalized Lotka-Volterra type (GLV) describing statistical systems of auto-catalytic elements posses power law distributions of the Pareto-Zipf type. In particular, when applied to economic systems, GLV leads to power laws in the relative individual wealth distribution and in market returns. These power laws and their exponent α are invariant to arbitrary variations in the total wealth of the system and to other endogenously and exogenously induced variations.

  7. Analysis of potential urban unstable areas and landslide-induced damages on Volterra historical site through a remote sensing approach

    Science.gov (United States)

    Del Soldato, Matteo; Bianchini, Silvia; Nolesini, Teresa; Frodella, William; Casagli, Nicola

    2017-04-01

    Multisystem remote sensing techniques were exploited to provide a comprehensive overview of Volterra (Italy) site stability with regards to its landscape, urban fabric and cultural heritage. Interferometric Synthetic Aperture Radar (InSAR) techniques allow precise measurements of Earth surface displacement, as well as the detection of building deformations on large urban areas. In the field of cultural heritage conservation Infrared thermography (IRT) provides surface temperature mapping and therefore detects various potential criticalities, such as moisture, seepage areas, cracks and structural anomalies. Between winter 2014 and spring 2015 the historical center and south-western sectors of Volterra (Tuscany region, central Italy) were affected by instability phenomena. The spatial distribution, typology and effect on the urban fabrics of the landslide phenomena were investigated by analyzing the geological and geomorphological settings, traditional geotechnical monitoring and advanced remote sensing data such as Persistent Scatterers Interferometry (PSI). The ground deformation rates and the maximum settlement values derived from SAR acquisitions of historical ENVISAT and recent COSMO-SkyMed sensors, in 2003-2009 and 2010-2015 respectively, were compared with background geological data, constructive features, in situ evidences and detailed field inspections in order to classify landslide-damaged buildings. In this way, the detected movements and their potential correspondences with recognized damages were investigated in order to perform an assessment of the built-up areas deformations and damages on Volterra. The IRT technique was applied in order to survey the surface temperature of the historical Volterra wall-enclosure, and allowed highlighting thermal anomalies on this cultural heritage element of the site. The obtained results permitted to better correlate the landslide effects of the recognized deformations in the urban fabric, in order to provide useful

  8. Four positive periodic solutions of a discrete time Lotka-Volterra competitive system with harvesting terms

    Directory of Open Access Journals (Sweden)

    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.

  9. The human body metabolism process mathematical simulation based on Lotka-Volterra model

    Science.gov (United States)

    Oliynyk, Andriy; Oliynyk, Eugene; Pyptiuk, Olexandr; DzierŻak, RóŻa; Szatkowska, Małgorzata; Uvaysova, Svetlana; Kozbekova, Ainur

    2017-08-01

    The mathematical model of metabolism process in human organism based on Lotka-Volterra model has beeng proposed, considering healing regime, nutrition system, features of insulin and sugar fragmentation process in the organism. The numerical algorithm of the model using IV-order Runge-Kutta method has been realized. After the result of calculations the conclusions have been made, recommendations about using the modeling results have been showed, the vectors of the following researches are defined.

  10. Use of artificial bee colonies algorithm as numerical approximation of differential equations solution

    Science.gov (United States)

    Fikri, Fariz Fahmi; Nuraini, Nuning

    2018-03-01

    The differential equation is one of the branches in mathematics which is closely related to human life problems. Some problems that occur in our life can be modeled into differential equations as well as systems of differential equations such as the Lotka-Volterra model and SIR model. Therefore, solving a problem of differential equations is very important. Some differential equations are difficult to solve, so numerical methods are needed to solve that problems. Some numerical methods for solving differential equations that have been widely used are Euler Method, Heun Method, Runge-Kutta and others. However, some of these methods still have some restrictions that cause the method cannot be used to solve more complex problems such as an evaluation interval that we cannot change freely. New methods are needed to improve that problems. One of the method that can be used is the artificial bees colony algorithm. This algorithm is one of metaheuristic algorithm method, which can come out from local search space and do exploration in solution search space so that will get better solution than other method.

  11. Neural network modeling of nonlinear systems based on Volterra series extension of a linear model

    Science.gov (United States)

    Soloway, Donald I.; Bialasiewicz, Jan T.

    1992-01-01

    A Volterra series approach was applied to the identification of nonlinear systems which are described by a neural network model. A procedure is outlined by which a mathematical model can be developed from experimental data obtained from the network structure. Applications of the results to the control of robotic systems are discussed.

  12. Global stability and quadratic Hamiltonian structure in Lotka-Volterra and quasi-polynomial systems

    Energy Technology Data Exchange (ETDEWEB)

    Szederkenyi, Gabor; Hangos, Katalin M

    2004-04-26

    We show that the global stability of quasi-polynomial (QP) and Lotka-Volterra (LV) systems with the well-known logarithmic Lyapunov function is equivalent to the existence of a local generalized dissipative Hamiltonian description of the LV system with a diagonal quadratic form as a Hamiltonian function. The Hamiltonian function can be calculated and the quadratic dissipativity neighborhood of the origin can be estimated by solving linear matrix inequalities.

  13. Global asymptotic behavior in a Lotka–Volterra competition system with spatio-temporal delays

    International Nuclear Information System (INIS)

    Zhang, Jia-Fang; Chen, Heshan

    2014-01-01

    This paper is concerned with a Lotka–Volterra competition system with spatio-temporal delays. By using the linearization method, we show the local asymptotic behavior of the nonnegative steady-state solutions. Especially, the global asymptotic stability of the positive steady-state solution is investigated by the method of upper and lower solutions. The result of global asymptotic stability implies that the system has no nonconstant positive steady-state solution

  14. Global stability and quadratic Hamiltonian structure in Lotka-Volterra and quasi-polynomial systems

    Science.gov (United States)

    Szederkényi, Gábor; Hangos, Katalin M.

    2004-04-01

    We show that the global stability of quasi-polynomial (QP) and Lotka-Volterra (LV) systems with the well-known logarithmic Lyapunov function is equivalent to the existence of a local generalized dissipative Hamiltonian description of the LV system with a diagonal quadratic form as a Hamiltonian function. The Hamiltonian function can be calculated and the quadratic dissipativity neighborhood of the origin can be estimated by solving linear matrix inequalities.

  15. Global stability and quadratic Hamiltonian structure in Lotka-Volterra and quasi-polynomial systems

    International Nuclear Information System (INIS)

    Szederkenyi, Gabor; Hangos, Katalin M.

    2004-01-01

    We show that the global stability of quasi-polynomial (QP) and Lotka-Volterra (LV) systems with the well-known logarithmic Lyapunov function is equivalent to the existence of a local generalized dissipative Hamiltonian description of the LV system with a diagonal quadratic form as a Hamiltonian function. The Hamiltonian function can be calculated and the quadratic dissipativity neighborhood of the origin can be estimated by solving linear matrix inequalities

  16. The existence of periodic solutions of the n-species Lotka-Volterra competition systems with impulsive

    Energy Technology Data Exchange (ETDEWEB)

    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.

  17. The existence of periodic solutions of the n-species Lotka-Volterra competition systems with impulsive

    International Nuclear Information System (INIS)

    Jin Zhen; Ma Zhien; Maoan Han

    2004-01-01

    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

  18. Fault Detection for Shipboard Monitoring – Volterra Kernel and Hammerstein Model Approaches

    DEFF Research Database (Denmark)

    Lajic, Zoran; Blanke, Mogens; Nielsen, Ulrik Dam

    2009-01-01

    In this paper nonlinear fault detection for in-service monitoring and decision support systems for ships will be presented. The ship is described as a nonlinear system, and the stochastic wave elevation and the associated ship responses are conveniently modelled in frequency domain. The transform....... The transformation from time domain to frequency domain has been conducted by use of Volterra theory. The paper takes as an example fault detection of a containership on which a decision support system has been installed....

  19. Entropy, free energy and phase transitions in the lattice Lotka-Volterra model

    International Nuclear Information System (INIS)

    Chichigina, O. A.; Tsekouras, G. A.; Provata, A.

    2006-01-01

    A thermodynamic approach is developed for reactive dynamic models restricted to substrates of arbitrary dimensions, including fractal substrates. The thermodynamic formalism is successfully applied to the lattice Lotka-Volterra (LLV) model of autocatalytic reactions on various lattice substrates. Different regimes of reactions described as phases, and phase transitions, are obtained using this approach. The predictions of thermodynamic theory confirm extensive numerical kinetic Monte Carlo simulations on square and fractal lattices. Extensions of the formalism to multispecies LLV models are also presented

  20. Simulating Chemical Kinetics Without Differential Equations: A Quantitative Theory Based on Chemical Pathways.

    Science.gov (United States)

    Bai, Shirong; Skodje, Rex T

    2017-08-17

    A new approach is presented for simulating the time-evolution of chemically reactive systems. This method provides an alternative to conventional modeling of mass-action kinetics that involves solving differential equations for the species concentrations. The method presented here avoids the need to solve the rate equations by switching to a representation based on chemical pathways. In the Sum Over Histories Representation (or SOHR) method, any time-dependent kinetic observable, such as concentration, is written as a linear combination of probabilities for chemical pathways leading to a desired outcome. In this work, an iterative method is introduced that allows the time-dependent pathway probabilities to be generated from a knowledge of the elementary rate coefficients, thus avoiding the pitfalls involved in solving the differential equations of kinetics. The method is successfully applied to the model Lotka-Volterra system and to a realistic H 2 combustion model.

  1. Existence of Generalized Homoclinic Solutions of Lotka-Volterra System under a Small Perturbation

    OpenAIRE

    Mi, Yuzhen

    2016-01-01

    This paper investigates Lotka-Volterra system under a small perturbation vxx=-μ(1-a2u-v)v+ϵf(ϵ,v,vx,u,ux), uxx=-(1-u-a1v)u+ϵg(ϵ,v,vx,u,ux). By the Fourier series expansion technique method, the fixed point theorem, the perturbation theorem, and the reversibility, we prove that near μ=0 the system has a generalized homoclinic solution exponentially approaching a periodic solution.

  2. Existence of Generalized Homoclinic Solutions of Lotka-Volterra System under a Small Perturbation

    Directory of Open Access Journals (Sweden)

    Yuzhen Mi

    2016-01-01

    Full Text Available This paper investigates Lotka-Volterra system under a small perturbation vxx=-μ(1-a2u-vv+ϵf(ϵ,v,vx,u,ux, uxx=-(1-u-a1vu+ϵg(ϵ,v,vx,u,ux. By the Fourier series expansion technique method, the fixed point theorem, the perturbation theorem, and the reversibility, we prove that near μ=0 the system has a generalized homoclinic solution exponentially approaching a periodic solution.

  3. String networks in Z{sub N} Lotka–Volterra competition models

    Energy Technology Data Exchange (ETDEWEB)

    Avelino, P.P., E-mail: Pedro.Avelino@astro.up.pt [Centro de Astrofísica da Universidade do Porto, Rua das Estrelas, 4150-762 Porto (Portugal); Departamento de Física e Astronomia, Faculdade de Ciências, Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto (Portugal); Bazeia, D. [Instituto de Física, Universidade de São Paulo, 05314-970 São Paulo, SP (Brazil); Departamento de Física, Universidade Federal da Paraíba, 58051-970 João Pessoa, PB (Brazil); Menezes, J. [Centro de Física do Porto, Rua do Campo Alegre 687, 4169-007 Porto (Portugal); Escola de Ciências e Tecnologia, Universidade Federal do Rio Grande do Norte, Caixa Postal 1524, 59072-970 Natal, RN (Brazil); Oliveira, B.F. de [Departamento de Física, Universidade Estadual de Maringá, Av. Colombo 5790, 87020-900 Maringá, PR (Brazil)

    2014-01-17

    In this Letter we give specific examples of Z{sub N} Lotka–Volterra competition models leading to the formation of string networks. We show that, in order to promote coexistence, the species may arrange themselves around regions with a high number density of empty sites generated by predator–prey interactions between competing species. These configurations extend into the third dimension giving rise to string networks. We investigate the corresponding dynamics using both stochastic and mean field theory simulations, showing that the coarsening of these string networks follows a scaling law which is analogous to that found in other physical systems in condensed matter and cosmology.

  4. Lagrangian structures, integrability and chaos for 3D dynamical equations

    International Nuclear Information System (INIS)

    Bustamante, Miguel D; Hojman, Sergio A

    2003-01-01

    In this paper, we consider the general setting for constructing action principles for three-dimensional first-order autonomous equations. We present the results for some integrable and non-integrable cases of the Lotka-Volterra equation, and show Lagrangian descriptions which are valid for systems satisfying Shil'nikov criteria on the existence of strange attractors, though chaotic behaviour has not been verified up to now. The Euler-Lagrange equations we get for these systems usually present 'time reparametrization' invariance, though other kinds of invariance may be found according to the kernel of the associated symplectic 2-form. The formulation of a Hamiltonian structure (Poisson brackets and Hamiltonians) for these systems from the Lagrangian viewpoint leads to a method of finding new constants of the motion starting from known ones, which is applied to some systems found in the literature known to possess a constant of the motion, to find the other and thus showing their integrability. In particular, we show that the so-called ABC system is completely integrable if it possesses one constant of the motion

  5. The Stationary Distribution and Extinction of Generalized Multispecies Stochastic Lotka-Volterra Predator-Prey System

    OpenAIRE

    Yin, Fancheng; Yu, Xiaoyan

    2015-01-01

    This paper is concerned with the existence of stationary distribution and extinction for multispecies stochastic Lotka-Volterra predator-prey system. The contributions of this paper are as follows. (a) By using Lyapunov methods, the sufficient conditions on existence of stationary distribution and extinction are established. (b) By using the space decomposition technique and the continuity of probability, weaker conditions on extinction of the system are obtained. Finally, a numer...

  6. Interaction of Acidithiobacillus ferrooxidans, Rhizobium phaseoli and Rhodotorula sp. in bioleaching process based on Lotka–Volterra model

    Directory of Open Access Journals (Sweden)

    Xuecheng Zheng

    2016-07-01

    Conclusion: The relationship among microorganisms during leaching could be described appropriately by Lotka–Volterra model between the initial and peak values. The relationship of A. ferrooxidans and R. phaseoli could be considered as mutualism, whereas, the relationship of A. ferrooxidans and R. phaseoli could be considered as commensalism.

  7. On the existence of solutions for Volterra integral inclusions in Banach spaces

    Directory of Open Access Journals (Sweden)

    Evgenios P. Avgerinos

    1993-01-01

    Full Text Available In this paper we examine a class of nonlinear integral inclusions defined in a separable Banach space. For this class of inclusions of Volterra type we establish two existence results, one for inclusions with a convex-valued orientor field and the other for inclusions with nonconvex-valued orientor field. We present conditions guaranteeing that the multivalued map that represents the right-hand side of the inclusion is α-condensing using for the proof of our results a known fixed point theorem for α-condensing maps.

  8. Identificación de sistemas no lineales usando series Volterra – Laguerre

    OpenAIRE

    Medina Ramos, Carlos Celestino; Medina Ramos, Carlos Celestino

    2011-01-01

    Este trabajo de Tesis está enfocado en la identificación de sistemas no lineales de modelo dinámico no conocido, adicionalmente y en base a los resultados obtenidos, se propone la aplicación del sistema de Control Predictivo no Lineal Basado en Modelos, NMPC, usando el algoritmo de la Matriz Dinámica de Control no Lineal, NDMC. El primer objetivo de este trabajo consiste en implementar una metodología para la identificación de sistemas no lineales usando series de Volterra truncadas; proye...

  9. Stabilization of Large Generalized Lotka-Volterra Foodwebs By Evolutionary Feedback

    Science.gov (United States)

    Ackland, G. J.; Gallagher, I. D.

    2004-10-01

    Conventional ecological models show that complexity destabilizes foodwebs, suggesting that foodwebs should have neither large numbers of species nor a large number of interactions. However, in nature the opposite appears to be the case. Here we show that if the interactions between species are allowed to evolve within a generalized Lotka-Volterra model such stabilizing feedbacks and weak interactions emerge automatically. Moreover, we show that trophic levels also emerge spontaneously from the evolutionary approach, and the efficiency of the unperturbed ecosystem increases with time. The key to stability in large foodwebs appears to arise not from complexity perse but from evolution at the level of the ecosystem which favors stabilizing (negative) feedbacks.

  10. Reproducing kernel method with Taylor expansion for linear Volterra integro-differential equations

    Directory of Open Access Journals (Sweden)

    Azizallah Alvandi

    2017-06-01

    Full Text Available This research aims of the present a new and single algorithm for linear integro-differential equations (LIDE. To apply the reproducing Hilbert kernel method, there is made an equivalent transformation by using Taylor series for solving LIDEs. Shown in series form is the analytical solution in the reproducing kernel space and the approximate solution $ u_{N} $ is constructed by truncating the series to $ N $ terms. It is easy to prove the convergence of $ u_{N} $ to the analytical solution. The numerical solutions from the proposed method indicate that this approach can be implemented easily which shows attractive features.

  11. Non-classical relaxation cycle of a three-dimensional system of Lotka-Volterra equations

    International Nuclear Information System (INIS)

    Kolesov, Yu S

    2000-01-01

    A mathematical model of the well-known Belousov's reaction is the object of study. It is reasonable to assume that one coefficient in the corresponding system of differential equations is large, while the other parameters are finite. Non-standard tools taking account of the peculiarities of the problem bring one to a theorem on the existence of a relaxation cycle, allowing at the same time to reveal its characteristic features

  12. Numerical approximations of nonlinear fractional differential difference equations by using modified He-Laplace method

    Directory of Open Access Journals (Sweden)

    J. Prakash

    2016-03-01

    Full Text Available In this paper, a numerical algorithm based on a modified He-Laplace method (MHLM is proposed to solve space and time nonlinear fractional differential-difference equations (NFDDEs arising in physical phenomena such as wave phenomena in fluids, coupled nonlinear optical waveguides and nanotechnology fields. The modified He-Laplace method is a combined form of the fractional homotopy perturbation method and Laplace transforms method. The nonlinear terms can be easily decomposed by the use of He’s polynomials. This algorithm has been tested against time-fractional differential-difference equations such as the modified Lotka Volterra and discrete (modified KdV equations. The proposed scheme grants the solution in the form of a rapidly convergent series. Three examples have been employed to illustrate the preciseness and effectiveness of the proposed method. The achieved results expose that the MHLM is very accurate, efficient, simple and can be applied to other nonlinear FDDEs.

  13. Entire solutions of a diffusive and competitive Lotka–Volterra type system with nonlocal delays

    International Nuclear Information System (INIS)

    Wang, Mingxin; Lv, Guangying

    2010-01-01

    This paper is concerned with the entire solution of a diffusive and competitive Lotka–Volterra type system with nonlocal delays. The existence of the entire solution is proved by transforming the system with nonlocal delays to a four-dimensional system without delay and using the comparing argument and the sub-super-solution method. Here an entire solution means a classical solution defined for all space and time variables, which behaves as two wave fronts coming from both sides of the x-axis

  14. The influence of noise on nonlinear time series detection based on Volterra-Wiener-Korenberg model

    Energy Technology Data Exchange (ETDEWEB)

    Lei Min [State Key Laboratory of Vibration, Shock and Noise, Shanghai Jiao Tong University, Shanghai 200030 (China)], E-mail: leimin@sjtu.edu.cn; Meng Guang [State Key Laboratory of Vibration, Shock and Noise, Shanghai Jiao Tong University, Shanghai 200030 (China)

    2008-04-15

    This paper studies the influence of noises on Volterra-Wiener-Korenberg (VWK) nonlinear test model. Our numerical results reveal that different types of noises lead to different behavior of VWK model detection. For dynamic noise, it is difficult to distinguish chaos from nonchaotic but nonlinear determinism. For time series, measure noise has no impact on chaos determinism detection. This paper also discusses various behavior of VWK model detection with surrogate data for different noises.

  15. A boundary value problem for a third order hyperbolic equation with degeneration of order inside the domain

    Directory of Open Access Journals (Sweden)

    Ruzanna Kh. Makaova

    2017-12-01

    Full Text Available In this paper we study the boundary value problem for a degenerating third order equation of hyperbolic type in a mixed domain. The equation under consideration in the positive part of the domain coincides with the Hallaire equation, which is a pseudoparabolic type equation. Moreover, in the negative part of the domain it coincides with a degenerating hyperbolic equation of the first kind, the particular case of the Bitsadze–Lykov equation. The existence and uniqueness theorem for the solution is proved. The uniqueness of the solution to the problem is proved with the Tricomi method. Using the functional relationships of the positive and negative parts of the domain on the degeneration line, we arrive at the convolution type Volterra integral equation of the 2nd kind with respect to the desired solution by a derivative trace. With the Laplace transform method, we obtain the solution of the integral equation in its explicit form. At last, the solution to the problem under study is written out explicitly as the solution of the second boundary-value problem in the positive part of the domain for the Hallaire equation and as the solution to the Cauchy problem in the negative part of the domain for a degenerate hyperbolic equation of the first kind.

  16. Phase portraits of cubic polynomial vector fields of Lotka-Volterra type having a rational first integral of degree 2

    International Nuclear Information System (INIS)

    Cairo, Laurent; Llibre, Jaume

    2007-01-01

    We classify all the global phase portraits of the cubic polynomial vector fields of Lotka-Volterra type having a rational first integral of degree 2. For such vector fields there are exactly 28 different global phase portraits in the Poincare disc up to a reversal of sense of all orbits

  17. Chaotic interactions of self-replicating RNA.

    Science.gov (United States)

    Forst, C V

    1996-03-01

    A general system of high-order differential equations describing complex dynamics of replicating biomolecules is given. Symmetry relations and coordinate transformations of general replication systems leading to topologically equivalent systems are derived. Three chaotic attractors observed in Lotka-Volterra equations of dimension n = 3 are shown to represent three cross-sections of one and the same chaotic regime. Also a fractal torus in a generalized three-dimensional Lotka-Volterra Model has been linked to one of the chaotic attractors. The strange attractors are studied in the equivalent four-dimensional catalytic replicator network. The fractal torus has been examined in adapted Lotka-Volterra equations. Analytic expressions are derived for the Lyapunov exponents of the flow in the replicator system. Lyapunov spectra for different pathways into chaos has been calculated. In the generalized Lotka-Volterra system a second inner rest point--coexisting with (quasi)-periodic orbits--can be observed; with an abundance of different bifurcations. Pathways from chaotic tori, via quasi-periodic tori, via limit cycles, via multi-periodic orbits--emerging out of periodic doubling bifurcations--to "simple" chaotic attractors can be found.

  18. Extinction in neutrally stable stochastic Lotka-Volterra models

    Science.gov (United States)

    Dobrinevski, Alexander; Frey, Erwin

    2012-05-01

    Populations of competing biological species exhibit a fascinating interplay between the nonlinear dynamics of evolutionary selection forces and random fluctuations arising from the stochastic nature of the interactions. The processes leading to extinction of species, whose understanding is a key component in the study of evolution and biodiversity, are influenced by both of these factors. Here, we investigate a class of stochastic population dynamics models based on generalized Lotka-Volterra systems. In the case of neutral stability of the underlying deterministic model, the impact of intrinsic noise on the survival of species is dramatic: It destroys coexistence of interacting species on a time scale proportional to the population size. We introduce a new method based on stochastic averaging which allows one to understand this extinction process quantitatively by reduction to a lower-dimensional effective dynamics. This is performed analytically for two highly symmetrical models and can be generalized numerically to more complex situations. The extinction probability distributions and other quantities of interest we obtain show excellent agreement with simulations.

  19. Volterra series based predistortion for broadband RF power amplifiers with memory effects

    Institute of Scientific and Technical Information of China (English)

    Jin Zhe; Song Zhihuan; He Jiaming

    2008-01-01

    RF power amplifiers(PAs)are usually considered as memoryless devices in most existing predistortion techniques.However,in broadband communication systems,such as WCDMA,the PA memory effects are significant,and memoryless predistortion cannot linearize the PAs effectively.After analyzing the PA memory effects,a novel predistortion method based on the simplified Volterra series is proposed to linearize broadband RF PAs with memory effects.The indirect learning architecture is adopted to design the predistortion scheme and the recursive least squares algorithm with forgetting factor is applied to identify the parameters of the predistorter.Simulation results show that the proposed predistortion method can compensate the nonlinear distortion and memory effects of broadband RF PAs effectively.

  20. Periodic solutions of Volterra integral equations

    Directory of Open Access Journals (Sweden)

    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.

  1. Local and global stability for Lotka-Volterra systems with distributed delays and instantaneous negative feedbacks

    Science.gov (United States)

    Faria, Teresa; Oliveira, José J.

    This paper addresses the local and global stability of n-dimensional Lotka-Volterra systems with distributed delays and instantaneous negative feedbacks. Necessary and sufficient conditions for local stability independent of the choice of the delay functions are given, by imposing a weak nondelayed diagonal dominance which cancels the delayed competition effect. The global asymptotic stability of positive equilibria is established under conditions slightly stronger than the ones required for the linear stability. For the case of monotone interactions, however, sharper conditions are presented. This paper generalizes known results for discrete delays to systems with distributed delays. Several applications illustrate the results.

  2. On Traveling Waves in Lattices: The Case of Riccati Lattices

    Science.gov (United States)

    Dimitrova, Zlatinka

    2012-09-01

    The method of simplest equation is applied for analysis of a class of lattices described by differential-difference equations that admit traveling-wave solutions constructed on the basis of the solution of the Riccati equation. We denote such lattices as Riccati lattices. We search for Riccati lattices within two classes of lattices: generalized Lotka-Volterra lattices and generalized Holling lattices. We show that from the class of generalized Lotka-Volterra lattices only the Wadati lattice belongs to the class of Riccati lattices. Opposite to this many lattices from the Holling class are Riccati lattices. We construct exact traveling wave solutions on the basis of the solution of Riccati equation for three members of the class of generalized Holling lattices.

  3. Elucidating the consumption and CO_2 emissions of fossil fuels and low-carbon energy in the United States using Lotka–Volterra models

    International Nuclear Information System (INIS)

    Tsai, Bi-Huei; Chang, Chih-Jen; Chang, Chun-Hsien

    2016-01-01

    By using the Lotka–Volterra model, this work examines for the first time the feasibility of using low-carbon energy to reduce fossil fuel consumption in the United States and, ultimately, to decrease CO_2 emissions. The research sample in this work consists of data on energy consumption and CO_2 emissions in the United States. Parameter estimation results reveal that although the consumption of low-carbon energy increases the consumption of fossil fuels, the latter does not affect the former. Low-carbon energy usage, including nuclear energy and solar photovoltaic power, increases fossil fuel consumption because the entire lifetime of a nuclear or solar energy facility, from the construction of electricity plants to decommissioning, consumes tremendous amounts of fossil fuels. This result verifies the infeasibility of low-carbon energy to replace fossil fuels under the current mining technology, electricity generation skills and governmental policy in the United States and explains why the United States refused to become a signatory of the Kyoto Protocol. Equilibrium analysis results indicate that the annual consumption of fossil fuels will ultimately exceed that of low-carbon energy by 461%. Since our proposed Lotka–Volterra model accurately predicts the consumption and CO_2 emission of different energy sources, this work contributes to the energy policies. - Highlights: • Our Lotka–Volterra model accurately predicts consumption of different energy sources. • We find the current infeasibility of using low-carbon energy to reduce fossil fuels. • The set-up of nuclear and solar plants increases fossil fuel usage in the U.S. • The consumption of fossil fuels will exceed that of low-carbon energy by 435%. • United States government prefers economic development over environmental protection.

  4. Detecting Slope and Urban Potential Unstable Areas by Means of Multi-Platform Remote Sensing Techniques: The Volterra (Italy Case Study

    Directory of Open Access Journals (Sweden)

    Teresa Nolesini

    2016-09-01

    Full Text Available Volterra (Central Italy is a town of great historical interest, due to its vast and well-preserved cultural heritage, including a 2.6 km long Etruscan-medieval wall enclosure representing one of the most important elements. Volterra is located on a clayey hilltop prone to landsliding, soil erosion, therefore the town is subject to structural deterioration. During 2014, two impressive collapses occurred on the wall enclosure in the southwestern urban sector. Following these events, a monitoring campaign was carried out by means of remote sensing techniques, such as space-borne (PS-InSAR and ground-based (GB-InSAR radar interferometry, in order to analyze the displacements occurring both in the urban area and the surrounding slopes, and therefore to detect possible critical sectors with respect to instability phenomena. Infrared thermography (IRT was also applied with the aim of detecting possible criticalities on the wall-enclosure, with special regards to moisture and seepage areas. PS-InSAR data allowed a stability back-monitoring on the area, revealing 19 active clusters displaying ground velocity higher than 10 mm/year in the period 2011–2015. The GB-InSAR system detected an acceleration up to 1.7 mm/h in near-real time as the March 2014 failure precursor. The IRT technique, employed on a double survey campaign, in both dry and rainy conditions, permitted to acquire 65 thermograms covering 23 sectors of the town wall, highlighting four thermal anomalies. The outcomes of this work demonstrate the usefulness of different remote sensing technologies for deriving information in risk prevention and management, and the importance of choosing the appropriate technology depending on the target, time sampling and investigation scale. In this paper, the use of a multi-platform remote sensing system permitted technical support of the local authorities and conservators, providing a comprehensive overview of the Volterra site, its cultural heritage and

  5. Conservation laws for two (2 + 1)-dimensional differential-difference systems

    International Nuclear Information System (INIS)

    Yu Guofu; Tam, H.-W.

    2006-01-01

    Two integrable differential-difference equations are considered. One is derived from the discrete BKP equation and the other is a symmetric (2 + 1)-dimensional Lotka-Volterra equation. An infinite number of conservation laws for the two differential-difference equations are deduced

  6. Stability in distribution of a stochastic hybrid competitive Lotka–Volterra model with Lévy jumps

    International Nuclear Information System (INIS)

    Zhao, Yu; Yuan, Sanling

    2016-01-01

    Stability in distribution, implying the existence of the invariant probability measure, is an important measure of stochastic hybrid system. However, the effect of Lévy jumps on the stability in distribution is still unclear. In this paper, we consider a n-species competitive Lotka–Volterra model with Lévy jumps under regime-switching. First, we prove the existence of the global positive solution, obtain the upper and lower boundedness. Then, asymptotic stability in distribution as the main result of our paper is derived under some sufficient conditions. Finally, numerical simulations are carried out to support our theoretical results and a brief discussion is given.

  7. Mapping of the stochastic Lotka-Volterra model to models of population genetics and game theory

    Science.gov (United States)

    Constable, George W. A.; McKane, Alan J.

    2017-08-01

    The relationship between the M -species stochastic Lotka-Volterra competition (SLVC) model and the M -allele Moran model of population genetics is explored via timescale separation arguments. When selection for species is weak and the population size is large but finite, precise conditions are determined for the stochastic dynamics of the SLVC model to be mappable to the neutral Moran model, the Moran model with frequency-independent selection, and the Moran model with frequency-dependent selection (equivalently a game-theoretic formulation of the Moran model). We demonstrate how these mappings can be used to calculate extinction probabilities and the times until a species' extinction in the SLVC model.

  8. Global analysis of an impulsive delayed Lotka-Volterra competition system

    Science.gov (United States)

    Xia, Yonghui

    2011-03-01

    In this paper, a retarded impulsive n-species Lotka-Volterra competition system with feedback controls is studied. Some sufficient conditions are obtained to guarantee the global exponential stability and global asymptotic stability of a unique equilibrium for such a high-dimensional biological system. The problem considered in this paper is in many aspects more general and incorporates as special cases various problems which have been extensively studied in the literature. Moreover, applying the obtained results to some special cases, I derive some new criteria which generalize and greatly improve some well known results. A method is proposed to investigate biological systems subjected to the effect of both impulses and delays. The method is based on Banach fixed point theory and matrix's spectral theory as well as Lyapunov function. Moreover, some novel analytic techniques are employed to study GAS and GES. It is believed that the method can be extended to other high-dimensional biological systems and complex neural networks. Finally, two examples show the feasibility of the results.

  9. A slow pushed front in a Lotka–Volterra competition model

    International Nuclear Information System (INIS)

    Holzer, Matt; Scheel, Arnd

    2012-01-01

    We study invasion speeds in the Lotka–Volterra competition model when the rate of diffusion of one species is small. Our main result is the construction of the selected front and a rigorous asymptotic approximation of its propagation speed, valid to second order. We use techniques from geometric singular perturbation theory and geometric desingularization. The main challenge arises from the slow passage through a saddle-node bifurcation. From a perspective of linear versus nonlinear speed selection, this front provides an interesting example as the propagation speed is slower than the linear spreading speed. However, our front shares many characteristics with pushed fronts that arise when the influence of nonlinearity leads to faster than linear speeds of propagation. We show that this is a result of the linear spreading speed arising as a simple pole of the resolvent instead of as a branch pole. Using the pointwise Green's function, we show that this pole poses no a priori obstacle to marginal stability of the nonlinear travelling front, thus explaining how nonlinear systems can exhibit slower spreading that their linearization in a robust fashion

  10. Integrability and Linearizability of the Lotka-Volterra System with a Saddle Point with Rational Hyperbolicity Ratio

    Science.gov (United States)

    Gravel, Simon; Thibault, Pierre

    In this paper, we consider normalizability, integrability and linearizability properties of the Lotka-Volterra system in the neighborhood of a singular point with eigenvalues 1 and - λ. The results are obtained by generalizing and expanding two methods already known: the power expansion of the first integral or of the linearizing transformation and the transformation of the saddle into a node. With these methods we find conditions that are valid for λ∈ R+ or λ∈ Q. These conditions will allow us to find all the integrable and linearizable systems for λ= {p}/{2} and {2}/{p} with p∈ N+.

  11. Positive Periodic Solution for the Generalized Neutral Differential Equation with Multiple Delays and Impulse

    Directory of Open Access Journals (Sweden)

    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.

  12. Variational identities and Hamiltonian structures

    International Nuclear Information System (INIS)

    Ma Wenxiu

    2010-01-01

    This report is concerned with Hamiltonian structures of classical and super soliton hierarchies. In the classical case, basic tools are variational identities associated with continuous and discrete matrix spectral problems, targeted to soliton equations derived from zero curvature equations over general Lie algebras, both semisimple and non-semisimple. In the super case, a supertrace identity is presented for constructing Hamiltonian structures of super soliton equations associated with Lie superalgebras. We illustrate the general theories by the KdV hierarchy, the Volterra lattice hierarchy, the super AKNS hierarchy, and two hierarchies of dark KdV equations and dark Volterra lattices. The resulting Hamiltonian structures show the commutativity of each hierarchy discussed and thus the existence of infinitely many commuting symmetries and conservation laws.

  13. Winnerless competition principle and prediction of the transient dynamics in a Lotka-Volterra model

    Science.gov (United States)

    Afraimovich, Valentin; Tristan, Irma; Huerta, Ramon; Rabinovich, Mikhail I.

    2008-12-01

    Predicting the evolution of multispecies ecological systems is an intriguing problem. A sufficiently complex model with the necessary predicting power requires solutions that are structurally stable. Small variations of the system parameters should not qualitatively perturb its solutions. When one is interested in just asymptotic results of evolution (as time goes to infinity), then the problem has a straightforward mathematical image involving simple attractors (fixed points or limit cycles) of a dynamical system. However, for an accurate prediction of evolution, the analysis of transient solutions is critical. In this paper, in the framework of the traditional Lotka-Volterra model (generalized in some sense), we show that the transient solution representing multispecies sequential competition can be reproducible and predictable with high probability.

  14. Integrability and Poisson Structures of Three Dimensional Dynamical Systems and Equations of Hydrodynamic Type

    Science.gov (United States)

    Gumral, Hasan

    Poisson structure of completely integrable 3 dimensional dynamical systems can be defined in terms of an integrable 1-form. We take advantage of this fact and use the theory of foliations in discussing the geometrical structure underlying complete and partial integrability. We show that the Halphen system can be formulated in terms of a flat SL(2,R)-valued connection and belongs to a non-trivial Godbillon-Vey class. On the other hand, for the Euler top and a special case of 3-species Lotka-Volterra equations which are contained in the Halphen system as limiting cases, this structure degenerates into the form of globally integrable bi-Hamiltonian structures. The globally integrable bi-Hamiltonian case is a linear and the sl_2 structure is a quadratic unfolding of an integrable 1-form in 3 + 1 dimensions. We complete the discussion of the Hamiltonian structure of 2-component equations of hydrodynamic type by presenting the Hamiltonian operators for Euler's equation and a continuum limit of Toda lattice. We present further infinite sequences of conserved quantities for shallow water equations and show that their generalizations by Kodama admit bi-Hamiltonian structure. We present a simple way of constructing the second Hamiltonian operators for N-component equations admitting some scaling properties. The Kodama reduction of the dispersionless-Boussinesq equations and the Lax reduction of the Benney moment equations are shown to be equivalent by a symmetry transformation. They can be cast into the form of a triplet of conservation laws which enable us to recognize a non-trivial scaling symmetry. The resulting bi-Hamiltonian structure generates three infinite sequences of conserved densities.

  15. Remaining Useful Life Estimation of Insulated Gate Biploar Transistors (IGBTs Based on a Novel Volterra k-Nearest Neighbor Optimally Pruned Extreme Learning Machine (VKOPP Model Using Degradation Data

    Directory of Open Access Journals (Sweden)

    Zhen Liu

    2017-11-01

    Full Text Available The insulated gate bipolar transistor (IGBT is a kind of excellent performance switching device used widely in power electronic systems. How to estimate the remaining useful life (RUL of an IGBT to ensure the safety and reliability of the power electronics system is currently a challenging issue in the field of IGBT reliability. The aim of this paper is to develop a prognostic technique for estimating IGBTs’ RUL. There is a need for an efficient prognostic algorithm that is able to support in-situ decision-making. In this paper, a novel prediction model with a complete structure based on optimally pruned extreme learning machine (OPELM and Volterra series is proposed to track the IGBT’s degradation trace and estimate its RUL; we refer to this model as Volterra k-nearest neighbor OPELM prediction (VKOPP model. This model uses the minimum entropy rate method and Volterra series to reconstruct phase space for IGBTs’ ageing samples, and a new weight update algorithm, which can effectively reduce the influence of the outliers and noises, is utilized to establish the VKOPP network; then a combination of the k-nearest neighbor method (KNN and least squares estimation (LSE method is used to calculate the output weights of OPELM and predict the RUL of the IGBT. The prognostic results show that the proposed approach can predict the RUL of IGBT modules with small error and achieve higher prediction precision and lower time cost than some classic prediction approaches.

  16. HOC Based Blind Identification of Hydroturbine Shaft Volterra System

    Directory of Open Access Journals (Sweden)

    Bing Bai

    2017-01-01

    Full Text Available In order to identify the quadratic Volterra system simplified from the hydroturbine shaft system, a blind identification method based on the third-order cumulants and a reversely recursive method are proposed. The input sequence of the system under consideration is an unobservable independent identically distributed (i.i.d., zero-mean and non-Gaussian stationary signal, and the observed signals are the superposition of the system output signal and Gaussian noise. To calculate the third-order moment of the output signal, a computer loop judgment method is put forward to determine the coefficient. When using optimization method to identify the time domain kernels, we combined the traditional optimization algorithm (direct search method with genetic algorithm (GA and constituted the hybrid genetic algorithm (HGA. Finally, according to the prototype observation signal and the time domain kernel parameters obtained from identification, the input signal of the system can be gained recursively. To test the proposed method, three numerical experiments and engineering application have been carried out. The results show that the method is applicable to the blind identification of the hydroturbine shaft system and has strong universality; the input signal obtained by the reversely recursive method can be approximately taken as the random excitation acted on the runner of the hydroturbine shaft system.

  17. Dynamical insurance models with investment: Constrained singular problems for integrodifferential equations

    Science.gov (United States)

    Belkina, T. A.; Konyukhova, N. B.; Kurochkin, S. V.

    2016-01-01

    Previous and new results are used to compare two mathematical insurance models with identical insurance company strategies in a financial market, namely, when the entire current surplus or its constant fraction is invested in risky assets (stocks), while the rest of the surplus is invested in a risk-free asset (bank account). Model I is the classical Cramér-Lundberg risk model with an exponential claim size distribution. Model II is a modification of the classical risk model (risk process with stochastic premiums) with exponential distributions of claim and premium sizes. For the survival probability of an insurance company over infinite time (as a function of its initial surplus), there arise singular problems for second-order linear integrodifferential equations (IDEs) defined on a semiinfinite interval and having nonintegrable singularities at zero: model I leads to a singular constrained initial value problem for an IDE with a Volterra integral operator, while II model leads to a more complicated nonlocal constrained problem for an IDE with a non-Volterra integral operator. A brief overview of previous results for these two problems depending on several positive parameters is given, and new results are presented. Additional results are concerned with the formulation, analysis, and numerical study of "degenerate" problems for both models, i.e., problems in which some of the IDE parameters vanish; moreover, passages to the limit with respect to the parameters through which we proceed from the original problems to the degenerate ones are singular for small and/or large argument values. Such problems are of mathematical and practical interest in themselves. Along with insurance models without investment, they describe the case of surplus completely invested in risk-free assets, as well as some noninsurance models of surplus dynamics, for example, charity-type models.

  18. An introduction to mathematical population dynamics along the trail of Volterra and Lotka

    CERN Document Server

    Iannelli, Mimmo

    2014-01-01

    This book is an introduction to mathematical biology for students with no experience in biology, but who have some mathematical background. The work is focused on population dynamics and ecology, following a tradition that goes back to Lotka and Volterra, and includes a part devoted to the spread of infectious diseases, a field where mathematical modeling is extremely popular. These themes are used as the area where to understand different types of mathematical modeling and the possible meaning of qualitative agreement of modeling with data. The book also includes a collections of problems designed to approach more advanced questions. This material has been used in the courses at the University of Trento, directed at students in their fourth year of studies in Mathematics. It can also be used as a reference as it provides up-to-date developments in several areas.

  19. An hp-local Discontinuous Galerkin Method for Parabolic Integro-Differential Equations

    KAUST Repository

    Pani, Amiya K.

    2010-06-06

    In this article, a priori error bounds are derived for an hp-local discontinuous Galerkin (LDG) approximation to a parabolic integro-differential equation. It is shown that error estimates in L 2-norm of the gradient as well as of the potential are optimal in the discretizing parameter h and suboptimal in the degree of polynomial p. Due to the presence of the integral term, an introduction of an expanded mixed type Ritz-Volterra projection helps us to achieve optimal estimates. Further, it is observed that a negative norm estimate of the gradient plays a crucial role in our convergence analysis. As in the elliptic case, similar results on order of convergence are established for the semidiscrete method after suitably modifying the numerical fluxes. The optimality of these theoretical results is tested in a series of numerical experiments on two dimensional domains. © 2010 Springer Science+Business Media, LLC.

  20. An hp-local Discontinuous Galerkin Method for Parabolic Integro-Differential Equations

    KAUST Repository

    Pani, Amiya K.; Yadav, Sangita

    2010-01-01

    In this article, a priori error bounds are derived for an hp-local discontinuous Galerkin (LDG) approximation to a parabolic integro-differential equation. It is shown that error estimates in L 2-norm of the gradient as well as of the potential are optimal in the discretizing parameter h and suboptimal in the degree of polynomial p. Due to the presence of the integral term, an introduction of an expanded mixed type Ritz-Volterra projection helps us to achieve optimal estimates. Further, it is observed that a negative norm estimate of the gradient plays a crucial role in our convergence analysis. As in the elliptic case, similar results on order of convergence are established for the semidiscrete method after suitably modifying the numerical fluxes. The optimality of these theoretical results is tested in a series of numerical experiments on two dimensional domains. © 2010 Springer Science+Business Media, LLC.

  1. Non-equilibrium relaxation in a stochastic lattice Lotka-Volterra model

    Science.gov (United States)

    Chen, Sheng; Täuber, Uwe C.

    2016-04-01

    We employ Monte Carlo simulations to study a stochastic Lotka-Volterra model on a two-dimensional square lattice with periodic boundary conditions. If the (local) prey carrying capacity is finite, there exists an extinction threshold for the predator population that separates a stable active two-species coexistence phase from an inactive state wherein only prey survive. Holding all other rates fixed, we investigate the non-equilibrium relaxation of the predator density in the vicinity of the critical predation rate. As expected, we observe critical slowing-down, i.e., a power law dependence of the relaxation time on the predation rate, and algebraic decay of the predator density at the extinction critical point. The numerically determined critical exponents are in accord with the established values of the directed percolation universality class. Following a sudden predation rate change to its critical value, one finds critical aging for the predator density autocorrelation function that is also governed by universal scaling exponents. This aging scaling signature of the active-to-absorbing state phase transition emerges at significantly earlier times than the stationary critical power laws, and could thus serve as an advanced indicator of the (predator) population’s proximity to its extinction threshold.

  2. Volterra integral equation-factorisation method and nucleus ...

    Indian Academy of Sciences (India)

    U LAHA

    1Department of Physics, National Institute of Technology, Jamshedpur 831 014, India. 2Department of Physics ... published online 28 February 2018. Abstract. ... Woods–Saxon [11], Gaussian [12], energy-dependent. [13] and so on.

  3. A Nonlinear Hyperbolic Volterra Equation in Viscoelasticity.

    Science.gov (United States)

    1980-06-01

    states that k(t) e L (0,-) if -nd only if (3.7) P(Z) def .’’(3.7) P(z) d ;’(0) + ’(0)a’(z) = X( 0 ) + (0)za(z) does not vanish on the half plane Rez ; 0...For w(t,x) e X(M,T), (2.5) and the Poincare inequality yield (2.6) w 2 (t,x) + w2x(t,x) + w 2(t,x) ( M , 0 4 t ( T, 0 4 x ( I x tx xx We now consider...2.6), the Poincare inequality and Schwarz’s inequality, every term on the right-hand side of (2.12), (2.15), and (2.16) can be majorized by one of p

  4. Positive periodic solutions of periodic neutral Lotka-Volterra system with distributed delays

    International Nuclear Information System (INIS)

    Li Yongkun

    2008-01-01

    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 i (t))/(dt) =x i (t)[a i (t)-Σ j=1 n b ij (t)∫ -T ij 0 K ij (θ)x j ( t+θ)dθ-Σ j=1 n c ij (t)∫ -T ij 0 K ij (θ) x j ' (t+θ)dθ],i=1,2,...,n, where a i ,b ij ,c ij element of C(R,R + ) (i, j = 1, 2, ..., n) are ω-periodic functions, T ij ,T ij element of (0,∞) (i, j = 1, 2, ..., n) and K ij ,K ij element of (R,R + ) satisfying ∫ -T ij 0 K ij (θ)dθ=1,∫ -T ij 0 K ij (θ)dθ=1, i, j = 1, 2, ..., n

  5. The Port Service Ecosystem Research Based on the Lotka-Volterra Model

    Directory of Open Access Journals (Sweden)

    Li Wenjuan

    2017-11-01

    Full Text Available Under the new normal of China’s economy, the competition among the port enterprises is not only the competition of the core competence of the port, the port industry chain or the port supply chain, but also the competition of the port service ecosystem. In this paper, the concept and characteristics of the port service ecosystem is discussed, a hierarchical model of the port service ecosystem is constructed. As an extended logistic model, Lotka-Volterra model is applied to study the competitive co-evolution and mutually beneficial co-evolution of enterprises in the port service ecosystem. This paper simulates the co-evolution of enterprises in the port service ecosystem by using MATLAB programming. The simulation results show that the breadth of the niche of the enterprises is changing with the change of the competition coefficient and the coefficient of mutual benefit in the port service ecosystem. Based on that, some proposals are put forward to ensure the healthy and orderly development of the port service ecosystem.

  6. Lagrangian structures, integrability and chaos for 3D dynamical equations 45.20.Jj Lagrangian and Hamiltonian mechanics; 02.30.Ik Integrable systems; 05.45.Ac Low-dimensional chaos;

    CERN Document Server

    Bustamante, M D

    2003-01-01

    In this paper, we consider the general setting for constructing action principles for three-dimensional first-order autonomous equations. We present the results for some integrable and non-integrable cases of the Lotka-Volterra equation, and show Lagrangian descriptions which are valid for systems satisfying Shil'nikov criteria on the existence of strange attractors, though chaotic behaviour has not been verified up to now. The Euler-Lagrange equations we get for these systems usually present 'time reparametrization' invariance, though other kinds of invariance may be found according to the kernel of the associated symplectic 2-form. The formulation of a Hamiltonian structure (Poisson brackets and Hamiltonians) for these systems from the Lagrangian viewpoint leads to a method of finding new constants of the motion starting from known ones, which is applied to some systems found in the literature known to possess a constant of the motion, to find the other and thus showing their integrability. In particular, w...

  7. Lotka-Volterra systems in environments with randomly disordered temporal periodicity

    Science.gov (United States)

    Naess, Arvid; Dimentberg, Michael F.; Gaidai, Oleg

    2008-08-01

    A generalized Lotka-Volterra model for a pair of interacting populations of predators and prey is studied. The model accounts for the prey’s interspecies competition and therefore is asymptotically stable, whereas its oscillatory behavior is induced by temporal variations in environmental conditions simulated by those in the prey’s reproduction rate. Two models of the variations are considered, each of them combining randomness with “hidden” periodicity. The stationary joint probability density function (PDF) of the number of predators and prey is calculated numerically by the path integration (PI) method based on the use of characteristic functions and the fast Fourier transform. The numerical results match those for the asymptotic case of white-noise variations for which an analytical solution is available. Several examples are studied, with calculations of important characteristics of oscillations, for example the expected rate of up-crossings given the level of the predator number. The calculated PDFs may be of predominantly random (unimodal) or predominantly periodic nature (bimodal). Thus, the PI method has been demonstrated to be a powerful tool for studies of the dynamics of predator-prey pairs. The method captures the random oscillations as observed in nature, taking into account potential periodicity in the environmental conditions.

  8. A discrete variational identity on semi-direct sums of Lie algebras

    Energy Technology Data Exchange (ETDEWEB)

    M, Wenxiu [Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620-5700 (United States)

    2007-12-14

    The discrete variational identity under general bilinear forms on semi-direct sums of Lie algebras is established. The constant {gamma} involved in the variational identity is determined through the corresponding solution to the stationary discrete zero-curvature equation. An application of the resulting variational identity to a class of semi-direct sums of Lie algebras in the Volterra lattice case furnishes Hamiltonian structures for the associated integrable couplings of the Volterra lattice hierarchy.

  9. A discrete variational identity on semi-direct sums of Lie algebras

    International Nuclear Information System (INIS)

    M, Wenxiu

    2007-01-01

    The discrete variational identity under general bilinear forms on semi-direct sums of Lie algebras is established. The constant γ involved in the variational identity is determined through the corresponding solution to the stationary discrete zero-curvature equation. An application of the resulting variational identity to a class of semi-direct sums of Lie algebras in the Volterra lattice case furnishes Hamiltonian structures for the associated integrable couplings of the Volterra lattice hierarchy

  10. Complex dynamics of Holling type II Lotka-Volterra predator-prey system with impulsive perturbations on the predator

    International Nuclear Information System (INIS)

    Liu Xianning; Chen Lansun

    2003-01-01

    This paper develops the Holling type II Lotka-Volterra predator-prey system, which may inherently oscillate, by introducing periodic constant impulsive immigration of predator. Condition for the system to be extinct is given and permanence condition is established via the method of comparison involving multiple Liapunov functions. Further influences of the impulsive perturbations on the inherent oscillation are studied numerically, which shows that with the increasing of the amount of the immigration, the system experiences process of quasi-periodic oscillating→cycles→periodic doubling cascade→chaos→periodic halfing cascade→cycles, which is characterized by (1) quasi-periodic oscillating, (2) period doubling, (3) period halfing, (4) non-unique dynamics, meaning that several attractors coexist

  11. Emergence of a complex and stable network in a model ecosystem with extinction and mutation.

    Science.gov (United States)

    Tokita, Kei; Yasutomi, Ayumu

    2003-03-01

    We propose a minimal model of the dynamics of diversity-replicator equations with extinction, invasion and mutation. We numerically study the behavior of this simple model and show that it displays completely different behavior from the conventional replicator equation and the generalized Lotka-Volterra equation. We reach several significant conclusions as follows: (1) a complex ecosystem can emerge when mutants with respect to species-specific interaction are introduced; (2) such an ecosystem possesses strong resistance to invasion; (3) a typical fixation process of mutants is realized through the rapid growth of a group of mutualistic mutants with higher fitness than majority species; (4) a hierarchical taxonomic structure (like family-genus-species) emerges; and (5) the relative abundance of species exhibits a typical pattern widely observed in nature. Several implications of these results are discussed in connection with the relationship of the present model to the generalized Lotka-Volterra equation.

  12. Kinetic Monte Carlo simulations of travelling pulses and spiral waves in the lattice Lotka-Volterra model.

    Science.gov (United States)

    Makeev, Alexei G; Kurkina, Elena S; Kevrekidis, Ioannis G

    2012-06-01

    Kinetic Monte Carlo simulations are used to study the stochastic two-species Lotka-Volterra model on a square lattice. For certain values of the model parameters, the system constitutes an excitable medium: travelling pulses and rotating spiral waves can be excited. Stable solitary pulses travel with constant (modulo stochastic fluctuations) shape and speed along a periodic lattice. The spiral waves observed persist sometimes for hundreds of rotations, but they are ultimately unstable and break-up (because of fluctuations and interactions between neighboring fronts) giving rise to complex dynamic behavior in which numerous small spiral waves rotate and interact with each other. It is interesting that travelling pulses and spiral waves can be exhibited by the model even for completely immobile species, due to the non-local reaction kinetics.

  13. Global stability results for a generalized Lotka-Volterra system with distributed delays. Applications to predator-prey and to epidemic systems.

    Science.gov (United States)

    Beretta, E; Capasso, V; Rinaldi, F

    1988-01-01

    The paper contains an extension of the general ODE system proposed in previous papers by the same authors, to include distributed time delays in the interaction terms. The new system describes a large class of Lotka-Volterra like population models and epidemic models with continuous time delays. Sufficient conditions for the boundedness of solutions and for the global asymptotic stability of nontrivial equilibrium solutions are given. A detailed analysis of the epidemic system is given with respect to the conditions for global stability. For a relevant subclass of these systems an existence criterion for steady states is also given.

  14. Existence of limit cycles in a three level trophic chain with Lotka–Volterra and Holling type II functional responses

    International Nuclear Information System (INIS)

    Castellanos, Víctor; Chan-López, Ramón E.

    2017-01-01

    In this paper we analyze a three level trophic chain model, considering a logistic growth for the lowest trophic level, a Lotka–Volterra and Holling type II functional responses for predators in the middle and in the cusp in the chain, respectively. The differential system is based on the Leslie–Gower scheme. We establish conditions on the parameters that guarantee the coexistence of populations in the habitat. We find that an Andronov–Hopf bifurcation takes place. The first Lyapunov coefficient is computed explicitly and we show the existence of a stable limit cycle. Numerically, we observe a strange attractor and there exist evidence of the model to exhibit chaotic dynamics.

  15. An asymptotic analysis for an integrable variant of the Lotka–Volterra prey–predator model via a determinant expansion technique

    Directory of Open Access Journals (Sweden)

    Masato Shinjo

    2015-12-01

    Full Text Available The Hankel determinant appears in representations of solutions to several integrable systems. An asymptotic expansion of the Hankel determinant thus plays a key role in the investigation of asymptotic analysis of such integrable systems. This paper presents an asymptotic expansion formula of a certain Casorati determinant as an extension of the Hankel case. This Casorati determinant is then shown to be associated with the solution to the discrete hungry Lotka–Volterra (dhLV system, which is an integrable variant of the famous prey–predator model in mathematical biology. Finally, the asymptotic behavior of the dhLV system is clarified using the expansion formula for the Casorati determinant.

  16. Lagrangian structures, integrability and chaos for 3D dynamical equations[45.20.Jj Lagrangian and Hamiltonian mechanics; 02.30.Ik Integrable systems; 05.45.Ac Low-dimensional chaos;

    Energy Technology Data Exchange (ETDEWEB)

    Bustamante, Miguel D [Departamento de Fisica, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago, Chile (Chile); Hojman, Sergio A [Departamento de Fisica, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago, Chile (Chile)

    2003-01-10

    In this paper, we consider the general setting for constructing action principles for three-dimensional first-order autonomous equations. We present the results for some integrable and non-integrable cases of the Lotka-Volterra equation, and show Lagrangian descriptions which are valid for systems satisfying Shil'nikov criteria on the existence of strange attractors, though chaotic behaviour has not been verified up to now. The Euler-Lagrange equations we get for these systems usually present 'time reparametrization' invariance, though other kinds of invariance may be found according to the kernel of the associated symplectic 2-form. The formulation of a Hamiltonian structure (Poisson brackets and Hamiltonians) for these systems from the Lagrangian viewpoint leads to a method of finding new constants of the motion starting from known ones, which is applied to some systems found in the literature known to possess a constant of the motion, to find the other and thus showing their integrability. In particular, we show that the so-called ABC system is completely integrable if it possesses one constant of the motion.

  17. A Weak Comparison Principle for Reaction-Diffusion Systems

    Directory of Open Access Journals (Sweden)

    José Valero

    2012-01-01

    Full Text Available We prove a weak comparison principle for a reaction-diffusion system without uniqueness of solutions. We apply the abstract results to the Lotka-Volterra system with diffusion, a generalized logistic equation, and to a model of fractional-order chemical autocatalysis with decay. Moreover, in the case of the Lotka-Volterra system a weak maximum principle is given, and a suitable estimate in the space of essentially bounded functions L∞ is proved for at least one solution of the problem.

  18. Liouvillian integrability of gravitating static isothermal fluid spheres

    International Nuclear Information System (INIS)

    Iacono, Roberto; Llibre, Jaume

    2014-01-01

    We examine the integrability properties of the Einstein field equations for static, spherically symmetric fluid spheres, complemented with an isothermal equation of state, ρ = np. In this case, Einstein's equations can be reduced to a nonlinear, autonomous second order ordinary differential equation (ODE) for m/R (m is the mass inside the radius R) that has been solved analytically only for n = −1 and n = −3, yielding the cosmological solutions by De Sitter and Einstein, respectively, and for n = −5, case for which the solution can be derived from the De Sitter's one using a symmetry of Einstein's equations. The solutions for these three cases are of Liouvillian type, since they can be expressed in terms of elementary functions. Here, we address the question of whether Liouvillian solutions can be obtained for other values of n. To do so, we transform the second order equation into an equivalent autonomous Lotka–Volterra quadratic polynomial differential system in R 2 , and characterize the Liouvillian integrability of this system using Darboux theory. We find that the Lotka–Volterra system possesses Liouvillian first integrals for n = −1, −3, −5, which descend from the existence of invariant algebraic curves of degree one, and for n = −6, a new solvable case, associated to an invariant algebraic curve of higher degree (second). For any other value of n, eventual first integrals of the Lotka–Volterra system, and consequently of the second order ODE for the mass function must be non-Liouvillian. This makes the existence of other solutions of the isothermal fluid sphere problem with a Liouvillian metric quite unlikely

  19. Liouvillian integrability of gravitating static isothermal fluid spheres

    Energy Technology Data Exchange (ETDEWEB)

    Iacono, Roberto, E-mail: roberto.iacono@enea.it [ENEA-C. R. Casaccia, Via Anguillarese 301, 00123 Roma (Italy); Llibre, Jaume, E-mail: jllibre@mat.uab.cat [Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia (Spain)

    2014-10-01

    We examine the integrability properties of the Einstein field equations for static, spherically symmetric fluid spheres, complemented with an isothermal equation of state, ρ = np. In this case, Einstein's equations can be reduced to a nonlinear, autonomous second order ordinary differential equation (ODE) for m/R (m is the mass inside the radius R) that has been solved analytically only for n = -1 and n = -3, yielding the cosmological solutions by De Sitter and Einstein, respectively, and for n = -5, case for which the solution can be derived from the De Sitter's one using a symmetry of Einstein's equations. The solutions for these three cases are of Liouvillian type, since they can be expressed in terms of elementary functions. Here, we address the question of whether Liouvillian solutions can be obtained for other values of n. To do so, we transform the second order equation into an equivalent autonomous Lotka–Volterra quadratic polynomial differential system in R² and characterize the Liouvillian integrability of this system using Darboux theory. We find that the Lotka–Volterra system possesses Liouvillian first integrals for n = -1, -3, -5, which descend from the existence of invariant algebraic curves of degree one, and for n = -6, a new solvable case, associated to an invariant algebraic curve of higher degree (second). For any other value of n, eventual first integrals of the Lotka–Volterra system, and consequently of the second order ODE for the mass function must be non-Liouvillian. This makes the existence of other solutions of the isothermal fluid sphere problem with a Liouvillian metric quite unlikely.

  20. Limit Cycles in Predator-Prey Models

    OpenAIRE

    Puchuri Medina, Liliana

    2017-01-01

    The classic Lotka-Volterra model belongs to a family of differential equations known as “Generalized Lotka-Volterra”, which is part of a classification of four models of quadratic fields with center. These models have been studied to address the Hilbert infinitesimal problem, which consists in determine the number of limit cycles of a perturbed hamiltonian system with center. In this work, we first present an alternative proof of the existence of centers in Lotka-Volterra predator-prey models...

  1. A Baecklund transformation between two integrable discrete hungry systems

    International Nuclear Information System (INIS)

    Fukuda, Akiko; Yamamoto, Yusaku; Iwasaki, Masashi; Ishiwata, Emiko; Nakamura, Yoshimasa

    2011-01-01

    The discrete hungry Toda (dhToda) equation and the discrete hungry Lotka-Volterra (dhLV) system are known as integrable discrete hungry systems. In this Letter, through finding the LR transformations associated with the dhToda equation and the dhLV system, we present a Baecklund transformation between these integrable systems.

  2. A Baecklund transformation between two integrable discrete hungry systems

    Energy Technology Data Exchange (ETDEWEB)

    Fukuda, Akiko, E-mail: j1409704@ed.kagu.tus.ac.j [Department of Mathematical Information Science, Graduate School of Science, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601 (Japan); Yamamoto, Yusaku [Graduate School of System Informatics, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe 657-8501 (Japan); Iwasaki, Masashi [Department of Informatics and Environmental Science, Kyoto Prefectural University, 1-5, Nakaragi-cho, Shimogamo, Sakyo-ku, Kyoto 606-8522 (Japan); Ishiwata, Emiko [Department of Mathematical Information Science, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601 (Japan); Nakamura, Yoshimasa [Graduate School of Informatics, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501 (Japan)

    2011-01-17

    The discrete hungry Toda (dhToda) equation and the discrete hungry Lotka-Volterra (dhLV) system are known as integrable discrete hungry systems. In this Letter, through finding the LR transformations associated with the dhToda equation and the dhLV system, we present a Baecklund transformation between these integrable systems.

  3. Volterra representation enables modeling of complex synaptic nonlinear dynamics in large-scale simulations.

    Science.gov (United States)

    Hu, Eric Y; Bouteiller, Jean-Marie C; Song, Dong; Baudry, Michel; Berger, Theodore W

    2015-01-01

    Chemical synapses are comprised of a wide collection of intricate signaling pathways involving complex dynamics. These mechanisms are often reduced to simple spikes or exponential representations in order to enable computer simulations at higher spatial levels of complexity. However, these representations cannot capture important nonlinear dynamics found in synaptic transmission. Here, we propose an input-output (IO) synapse model capable of generating complex nonlinear dynamics while maintaining low computational complexity. This IO synapse model is an extension of a detailed mechanistic glutamatergic synapse model capable of capturing the input-output relationships of the mechanistic model using the Volterra functional power series. We demonstrate that the IO synapse model is able to successfully track the nonlinear dynamics of the synapse up to the third order with high accuracy. We also evaluate the accuracy of the IO synapse model at different input frequencies and compared its performance with that of kinetic models in compartmental neuron models. Our results demonstrate that the IO synapse model is capable of efficiently replicating complex nonlinear dynamics that were represented in the original mechanistic model and provide a method to replicate complex and diverse synaptic transmission within neuron network simulations.

  4. Stochastic differential equations as a tool to regularize the parameter estimation problem for continuous time dynamical systems given discrete time measurements.

    Science.gov (United States)

    Leander, Jacob; Lundh, Torbjörn; Jirstrand, Mats

    2014-05-01

    In this paper we consider the problem of estimating parameters in ordinary differential equations given discrete time experimental data. The impact of going from an ordinary to a stochastic differential equation setting is investigated as a tool to overcome the problem of local minima in the objective function. Using two different models, it is demonstrated that by allowing noise in the underlying model itself, the objective functions to be minimized in the parameter estimation procedures are regularized in the sense that the number of local minima is reduced and better convergence is achieved. The advantage of using stochastic differential equations is that the actual states in the model are predicted from data and this will allow the prediction to stay close to data even when the parameters in the model is incorrect. The extended Kalman filter is used as a state estimator and sensitivity equations are provided to give an accurate calculation of the gradient of the objective function. The method is illustrated using in silico data from the FitzHugh-Nagumo model for excitable media and the Lotka-Volterra predator-prey system. The proposed method performs well on the models considered, and is able to regularize the objective function in both models. This leads to parameter estimation problems with fewer local minima which can be solved by efficient gradient-based methods. Copyright © 2014 The Authors. Published by Elsevier Inc. All rights reserved.

  5. A Multiple Iterated Integral Inequality and Applications

    Directory of Open Access Journals (Sweden)

    Zongyi Hou

    2014-01-01

    Full Text Available We establish new multiple iterated Volterra-Fredholm type integral inequalities, where the composite function w(u(s of the unknown function u with nonlinear function w in integral functions in [Ma, QH, Pečarić, J: Estimates on solutions of some new nonlinear retarded Volterra-Fredholm type integral inequalities. Nonlinear Anal. 69 (2008 393–407] is changed into the composite functions w1(u(s,w2(u(s,…, wn (u(s of the unknown function u with different nonlinear functions w1,w2,…,wn, respectively. By adopting novel analysis techniques, the upper bounds of the embedded unknown functions are estimated explicitly. The derived results can be applied in the study of solutions of ordinary differential equations and integral equations.

  6. Existence and properties of semi-bounded global solutions to the functional differential equation with Volterra-type operators on the real line

    Czech Academy of Sciences Publication Activity Database

    Hakl, Robert; Aguerrea, M.

    2017-01-01

    Roč. 147, č. 6 (2017), s. 1119-1168 ISSN 0308-2105 Institutional support: RVO:67985840 Keywords : functional differential equations * boundary-value problems * global existence Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 1.158, year: 2016

  7. On Weakly Singular Versions of Discrete Nonlinear Inequalities and Applications

    Directory of Open Access Journals (Sweden)

    Kelong Cheng

    2014-01-01

    Full Text Available Some new weakly singular versions of discrete nonlinear inequalities are established, which generalize some existing weakly singular inequalities and can be used in the analysis of nonlinear Volterra type difference equations with weakly singular kernels. A few applications to the upper bound and the uniqueness of solutions of nonlinear difference equations are also involved.

  8. Lax pairs and conservation laws for two differential-difference systems

    International Nuclear Information System (INIS)

    Li Chunxia

    2003-01-01

    A coupled extended Lotka-Volterra lattice and a special Toda lattice are derived from the existing bilinear equations. Starting from the corresponding bilinear Baecklund transformation, Lax pairs for these two differential-difference systems are obtained. Furthermore, an infinite number of conservation laws for the differential-difference equations are deduced from the Lax pairs in a systematic way

  9. General two-species interacting Lotka-Volterra system: Population dynamics and wave propagation

    Science.gov (United States)

    Zhu, Haoqi; Wang, Mao-Xiang; Lai, Pik-Yin

    2018-05-01

    The population dynamics of two interacting species modeled by the Lotka-Volterra (LV) model with general parameters that can promote or suppress the other species is studied. It is found that the properties of the two species' isoclines determine the interaction of species, leading to six regimes in the phase diagram of interspecies interaction; i.e., there are six different interspecific relationships described by the LV model. Four regimes allow for nontrivial species coexistence, among which it is found that three of them are stable, namely, weak competition, mutualism, and predator-prey scenarios can lead to win-win coexistence situations. The Lyapunov function for general nontrivial two-species coexistence is also constructed. Furthermore, in the presence of spatial diffusion of the species, the dynamics can lead to steady wavefront propagation and can alter the population map. Propagating wavefront solutions in one dimension are investigated analytically and by numerical solutions. The steady wavefront speeds are obtained analytically via nonlinear dynamics analysis and verified by numerical solutions. In addition to the inter- and intraspecific interaction parameters, the intrinsic speed parameters of each species play a decisive role in species populations and wave properties. In some regimes, both species can copropagate with the same wave speeds in a finite range of parameters. Our results are further discussed in the light of possible biological relevance and ecological implications.

  10. Food Web Assembly Rules for Generalized Lotka-Volterra Equations

    DEFF Research Database (Denmark)

    Härter, Jan Olaf Mirko; Mitarai, Namiko; Sneppen, Kim

    2016-01-01

    the lack of niches, corresponding to unpaired species. For the species richness at each trophic level, we derive the food web assembly rules, which specify sustainable combinations. In neighboring levels, these rules allow the higher level to avert competitive exclusion at the lower, thereby incorporating...

  11. Interpolation method for the transport theory and its application in fusion-neutronics analysis

    International Nuclear Information System (INIS)

    Jung, J.

    1981-09-01

    This report presents an interpolation method for the solution of the Boltzmann transport equation. The method is based on a flux synthesis technique using two reference-point solutions. The equation for the interpolated solution results in a Volterra integral equation which is proved to have a unique solution. As an application of the present method, tritium breeding ratio is calculated for a typical D-T fusion reactor system. The result is compared to that of a variational technique

  12. An asymptotic problem in renewal theory

    NARCIS (Netherlands)

    Klamkin, M.S.; van Lint, J.H.

    1972-01-01

    A special problem in renewal theory is considered. The asymptotic behavior of the renewal function was studied by W. L. Smith. Here we show that his result with an exponentially small remainder term follows from a theorem of De Bruijn on Volterra integral equations.

  13. Nonlinear detection of disordered voice productions from short time series based on a Volterra-Wiener-Korenberg model

    Energy Technology Data Exchange (ETDEWEB)

    Zhang Yu, E-mail: yuzhang@xmu.edu.cn [Key Laboratory of Underwater Acoustic Communication and Marine Information Technology of the Ministry of Education, Xiamen University, Xiamen Fujian 361005 (China); Sprecher, Alicia J. [Department of Surgery, Division of Otolaryngology - Head and Neck Surgery, University of Wisconsin School of Medicine and Public Health, Madison, WI 53792-7375 (United States); Zhao Zongxi [Key Laboratory of Underwater Acoustic Communication and Marine Information Technology of the Ministry of Education, Xiamen University, Xiamen Fujian 361005 (China); Jiang, Jack J. [Department of Surgery, Division of Otolaryngology - Head and Neck Surgery, University of Wisconsin School of Medicine and Public Health, Madison, WI 53792-7375 (United States)

    2011-09-15

    Highlights: > The VWK method effectively detects the nonlinearity of a discrete map. > The method describes the chaotic time series of a biomechanical vocal fold model. > Nonlinearity in laryngeal pathology is detected from short and noisy time series. - Abstract: In this paper, we apply the Volterra-Wiener-Korenberg (VWK) model method to detect nonlinearity in disordered voice productions. The VWK method effectively describes the nonlinearity of a third-order nonlinear map. It allows for the analysis of short and noisy data sets. The extracted VWK model parameters show an agreement with the original nonlinear map parameters. Furthermore, the VWK mode method is applied to successfully assess the nonlinearity of a biomechanical voice production model simulating irregular vibratory dynamics of vocal folds with a unilateral vocal polyp. Finally, we show the clinical applicability of this nonlinear detection method to analyze the electroglottographic data generated by 14 patients with vocal nodules or polyps. The VWK model method shows potential in describing the nonlinearity inherent in disordered voice productions from short and noisy time series that are common in the clinical setting.

  14. Nonlinear detection of disordered voice productions from short time series based on a Volterra-Wiener-Korenberg model

    International Nuclear Information System (INIS)

    Zhang Yu; Sprecher, Alicia J.; Zhao Zongxi; Jiang, Jack J.

    2011-01-01

    Highlights: → The VWK method effectively detects the nonlinearity of a discrete map. → The method describes the chaotic time series of a biomechanical vocal fold model. → Nonlinearity in laryngeal pathology is detected from short and noisy time series. - Abstract: In this paper, we apply the Volterra-Wiener-Korenberg (VWK) model method to detect nonlinearity in disordered voice productions. The VWK method effectively describes the nonlinearity of a third-order nonlinear map. It allows for the analysis of short and noisy data sets. The extracted VWK model parameters show an agreement with the original nonlinear map parameters. Furthermore, the VWK mode method is applied to successfully assess the nonlinearity of a biomechanical voice production model simulating irregular vibratory dynamics of vocal folds with a unilateral vocal polyp. Finally, we show the clinical applicability of this nonlinear detection method to analyze the electroglottographic data generated by 14 patients with vocal nodules or polyps. The VWK model method shows potential in describing the nonlinearity inherent in disordered voice productions from short and noisy time series that are common in the clinical setting.

  15. Competitive or weak cooperative stochastic Lotka-Volterra systems conditioned on non-extinction.

    Science.gov (United States)

    Cattiaux, Patrick; Méléard, Sylvie

    2010-06-01

    We are interested in the long time behavior of a two-type density-dependent biological population conditioned on non-extinction, in both cases of competition or weak cooperation between the two species. This population is described by a stochastic Lotka-Volterra system, obtained as limit of renormalized interacting birth and death processes. The weak cooperation assumption allows the system not to blow up. We study the existence and uniqueness of a quasi-stationary distribution, that is convergence to equilibrium conditioned on non-extinction. To this aim we generalize in two-dimensions spectral tools developed for one-dimensional generalized Feller diffusion processes. The existence proof of a quasi-stationary distribution is reduced to the one for a d-dimensional Kolmogorov diffusion process under a symmetry assumption. The symmetry we need is satisfied under a local balance condition relying the ecological rates. A novelty is the outlined relation between the uniqueness of the quasi-stationary distribution and the ultracontractivity of the killed semi-group. By a comparison between the killing rates for the populations of each type and the one of the global population, we show that the quasi-stationary distribution can be either supported by individuals of one (the strongest one) type or supported by individuals of the two types. We thus highlight two different long time behaviors depending on the parameters of the model: either the model exhibits an intermediary time scale for which only one type (the dominant trait) is surviving, or there is a positive probability to have coexistence of the two species.

  16. Stochastic hybrid systems with renewal transitions

    NARCIS (Netherlands)

    Guerreiro Tome Antunes, D.J.; Hespanha, J.P.; Silvestre, C.J.

    2010-01-01

    We consider Stochastic Hybrid Systems (SHSs) for which the lengths of times that the system stays in each mode are independent random variables with given distributions. We propose an analysis framework based on a set of Volterra renewal-type equations, which allows us to compute any statistical

  17. Stochastic motion from a forced plasma-maser interaction

    International Nuclear Information System (INIS)

    Honjo, Haruo; Nambu, Mitsuhiro

    1986-01-01

    A model of forced plasma-maser effects is examined numerically. The model represents a conservative system and reduces to the forced type of the original Lotka-Volterra equation. A stochastic motion is found to occur when the density of a cold ion beam becomes larger. (author)

  18. An Improved Global Harmony Search Algorithm for the Identification of Nonlinear Discrete-Time Systems Based on Volterra Filter Modeling

    Directory of Open Access Journals (Sweden)

    Zongyan Li

    2016-01-01

    Full Text Available This paper describes an improved global harmony search (IGHS algorithm for identifying the nonlinear discrete-time systems based on second-order Volterra model. The IGHS is an improved version of the novel global harmony search (NGHS algorithm, and it makes two significant improvements on the NGHS. First, the genetic mutation operation is modified by combining normal distribution and Cauchy distribution, which enables the IGHS to fully explore and exploit the solution space. Second, an opposition-based learning (OBL is introduced and modified to improve the quality of harmony vectors. The IGHS algorithm is implemented on two numerical examples, and they are nonlinear discrete-time rational system and the real heat exchanger, respectively. The results of the IGHS are compared with those of the other three methods, and it has been verified to be more effective than the other three methods on solving the above two problems with different input signals and system memory sizes.

  19. Survival behavior in the cyclic Lotka-Volterra model with a randomly switching reaction rate.

    Science.gov (United States)

    West, Robert; Mobilia, Mauro; Rucklidge, Alastair M

    2018-02-01

    We study the influence of a randomly switching reproduction-predation rate on the survival behavior of the nonspatial cyclic Lotka-Volterra model, also known as the zero-sum rock-paper-scissors game, used to metaphorically describe the cyclic competition between three species. In large and finite populations, demographic fluctuations (internal noise) drive two species to extinction in a finite time, while the species with the smallest reproduction-predation rate is the most likely to be the surviving one (law of the weakest). Here we model environmental (external) noise by assuming that the reproduction-predation rate of the strongest species (the fastest to reproduce and predate) in a given static environment randomly switches between two values corresponding to more and less favorable external conditions. We study the joint effect of environmental and demographic noise on the species survival probabilities and on the mean extinction time. In particular, we investigate whether the survival probabilities follow the law of the weakest and analyze their dependence on the external noise intensity and switching rate. Remarkably, when, on average, there is a finite number of switches prior to extinction, the survival probability of the predator of the species whose reaction rate switches typically varies nonmonotonically with the external noise intensity (with optimal survival about a critical noise strength). We also outline the relationship with the case where all reaction rates switch on markedly different time scales.

  20. Survival behavior in the cyclic Lotka-Volterra model with a randomly switching reaction rate

    Science.gov (United States)

    West, Robert; Mobilia, Mauro; Rucklidge, Alastair M.

    2018-02-01

    We study the influence of a randomly switching reproduction-predation rate on the survival behavior of the nonspatial cyclic Lotka-Volterra model, also known as the zero-sum rock-paper-scissors game, used to metaphorically describe the cyclic competition between three species. In large and finite populations, demographic fluctuations (internal noise) drive two species to extinction in a finite time, while the species with the smallest reproduction-predation rate is the most likely to be the surviving one (law of the weakest). Here we model environmental (external) noise by assuming that the reproduction-predation rate of the strongest species (the fastest to reproduce and predate) in a given static environment randomly switches between two values corresponding to more and less favorable external conditions. We study the joint effect of environmental and demographic noise on the species survival probabilities and on the mean extinction time. In particular, we investigate whether the survival probabilities follow the law of the weakest and analyze their dependence on the external noise intensity and switching rate. Remarkably, when, on average, there is a finite number of switches prior to extinction, the survival probability of the predator of the species whose reaction rate switches typically varies nonmonotonically with the external noise intensity (with optimal survival about a critical noise strength). We also outline the relationship with the case where all reaction rates switch on markedly different time scales.

  1. Power Laws are Disguised Boltzmann Laws

    Science.gov (United States)

    Richmond, Peter; Solomon, Sorin

    Using a previously introduced model on generalized Lotka-Volterra dynamics together with some recent results for the solution of generalized Langevin equations, we derive analytically the equilibrium mean field solution for the probability distribution of wealth and show that it has two characteristic regimes. For large values of wealth, it takes the form of a Pareto style power law. For small values of wealth, wGeneralized Lotka-Volterra type of stochastic dynamics. The power law that arises in the distribution function is identified with new additional logarithmic terms in the familiar Boltzmann distribution function for the system. These are a direct consequence of the multiplicative stochastic dynamics and are absent for the usual additive stochastic processes.

  2. Instabilities in numerical solutions to Fredholm and Volterra integral equations of the first kind. Resolution by Tchebycheff polynomials. Application to photonuclear cross-sections; Instabilite des solutions numeriques d'equations integrales de Fredholm et Volterra de premiere espece. Resolution par les polynomes de Tchebycheff. Application aux sections efficaces photonucleaires

    Energy Technology Data Exchange (ETDEWEB)

    Moriceau, Y [Commissariat a l' Energie Atomique, Centre d' Etudes de Limeil, 94 - Villeneuve-Saint-Georges (France)

    1968-03-01

    It is well known, if not well explained, that photo cross-sections curves depend on numerical resolution; as well as many other physical solutions from integral equations of the first kind, they are oscillating. In the first part of this report, a typical example points out how oscillations are growing. In the second part, a new method is explained yielding a smooth resolution. From experimental data on equidistant intervals, we build functions expanded in Tchebycheff polynomials; the solution is of this kind. Then, the third part points out that semi-analytical resolutions of this problem are illusive. (author) [French] C'est un fait reconnu mais mal explique, que les courbes de sections efficaces photonucleaires dependent de la resolution numerique adoptee. Beaucoup d'autres solutions physiques extraites d'une equation integrale de 1ere espece sont dans ce cas; elles sont arbitraires et oscillatoires. Dans la 1ere partie de ce rapport, on montre, dans un cas particulier typique, comment se forment les oscillations. Dans la 2eme partie, on presente une methode originale qui permet d'obtenir une resolution exempte d'oscillations. A partir de donnees experimentales a intervalles equidistants, on construit des fonctions developpees en polynomes de Tchebycheff; la solution est de ce type. Enfin, on montre dans la 3eme partie que les resolutions semi-analytiques de ce probleme sont illusoires. (auteur)

  3. Finite-Time Attractivity for Diagonally Dominant Systems with Off-Diagonal Delays

    Directory of Open Access Journals (Sweden)

    T. S. Doan

    2012-01-01

    Full Text Available We introduce a notion of attractivity for delay equations which are defined on bounded time intervals. Our main result shows that linear delay equations are finite-time attractive, provided that the delay is only in the coupling terms between different components, and the system is diagonally dominant. We apply this result to a nonlinear Lotka-Volterra system and show that the delay is harmless and does not destroy finite-time attractivity.

  4. Approximation for limit cycles and their isochrons.

    Science.gov (United States)

    Demongeot, Jacques; Françoise, Jean-Pierre

    2006-12-01

    Local analysis of trajectories of dynamical systems near an attractive periodic orbit displays the notion of asymptotic phase and isochrons. These notions are quite useful in applications to biosciences. In this note, we give an expression for the first approximation of equations of isochrons in the setting of perturbations of polynomial Hamiltonian systems. This method can be generalized to perturbations of systems that have a polynomial integral factor (like the Lotka-Volterra equation).

  5. Hamiltonian description and quantization of dissipative systems

    Science.gov (United States)

    Enz, Charles P.

    1994-09-01

    Dissipative systems are described by a Hamiltonian, combined with a “dynamical matrix” which generalizes the simplectic form of the equations of motion. Criteria for dissipation are given and the examples of a particle with friction and of the Lotka-Volterra model are presented. Quantization is first introduced by translating generalized Poisson brackets into commutators and anticommutators. Then a generalized Schrödinger equation expressed by a dynamical matrix is constructed and discussed.

  6. Discrete Weighted Pseudo-Almost Automorphy and Applications

    Directory of Open Access Journals (Sweden)

    Zhinan Xia

    2014-01-01

    Full Text Available We deal with discrete weighted pseudo almost automorphy which extends some classical concepts and systematically explore its properties in Banach space including a composition result. As an application, we establish some sufficient criteria for the existence and uniqueness of the discrete weighted pseudo almost automorphic solutions to the Volterra difference equations of convolution type and also to nonautonomous semilinear difference equations. Some examples are presented to illustrate the main findings.

  7. Continuous stochastic approach to birth and death processes and co-operative behaviour of systems far from equilibrium

    Energy Technology Data Exchange (ETDEWEB)

    Chechetkin, V.R.; Lutovinov, V.S.

    1986-09-11

    The continuous stochastic formalism for the description of systems with birth and death processes randomly distributed in space is developed with the use of local birth and death operators and local generalization of the corresponding Chapman-Kolmogorov equation. The functional stochastic equation for the evolution of the probability functional is derived and its modifications for evolution of the characteristic functional and the first passage time problem are given. The corresponding evolution equations for equal-time correlators are also derived. The results are generalized then on the exothermic and endothermic chemical reactions. As examples of the particular applications of the results the small fluctuations near stable equilibrium state and fluctuations in mono-molecular reactions, Lotka-Volterra model, Schloegl reaction and brusselator are considered. It is shown that the two-dimensional Lotka-Volterra model may exhibit synergetic phase transition analogous to the topological transition of the Kosterlitz-Thouless-Berezinskii type. At the end of the paper some general consequences from stochastic evolution of the birth and death processes are discussed and the arguments on their importance in evolution of populations, cellular dynamics and in applications to various chemical and biological problems are presented.

  8. Nambu-Poisson reformulation of the finite dimensional dynamical systems

    International Nuclear Information System (INIS)

    Baleanu, D.; Makhaldiani, N.

    1998-01-01

    A system of nonlinear ordinary differential equations which in a particular case reduces to Volterra's system is introduced. We found in two simplest cases the complete sets of the integrals of motion using Nambu-Poisson reformulation of the Hamiltonian dynamics. In these cases we have solved the systems by quadratures

  9. Application of homotopy-perturbation method to nonlinear population dynamics models

    International Nuclear Information System (INIS)

    Chowdhury, M.S.H.; Hashim, I.; Abdulaziz, O.

    2007-01-01

    In this Letter, the homotopy-perturbation method (HPM) is employed to derive approximate series solutions of nonlinear population dynamics models. The nonlinear models considered are the multispecies Lotka-Volterra equations. The accuracy of this method is examined by comparison with the available exact and the fourth-order Runge-Kutta method (RK4)

  10. Persistence and stability for the three species ratio-dependent food ...

    African Journals Online (AJOL)

    user

    This can be expressed in terms of “Persistence”. Biologically ... provided necessary and sufficient condition for the persistence of Lotka-Volterra food chain model. Gard and ... ordinary differential equations. ⎟. ⎟. ⎠. ⎞. ⎜. ⎜ .... To do so, we compute the variational matrix of system (4). The signs ...... and Evolution, Vol. 15, pp.

  11. Fields of rational constants of cyclic factorizable derivations

    Directory of Open Access Journals (Sweden)

    Janusz Zielinski

    2015-12-01

    Full Text Available We describe all rational constants of a large family of four-variable cyclic factorizable derivations. Thus, we determine all rational first integrals of their corresponding systems of differential equations. Moreover, we give a characteristic of all four-variable Lotka-Volterra derivations with a nontrivial rational constant. All considerations are over an arbitrary field of characteristic zero. Our main tool is the investigation of the cofactors of strict Darboux polynomials. Factorizable derivations are important in derivation theory. Namely, we may associate the factorizable derivation with any given derivation of a polynomial ring and that construction helps to determine rational constants of arbitrary derivations. Besides, Lotka-Volterra systems play a significant role in population biology, laser physics and plasma physics.

  12. Stability and Hopf bifurcation in a delayed competitive web sites model

    International Nuclear Information System (INIS)

    Xiao Min; Cao Jinde

    2006-01-01

    The delayed differential equations modeling competitive web sites, based on the Lotka-Volterra competition equations, are considered. Firstly, the linear stability is investigated. It is found that there is a stability switch for time delay, and Hopf bifurcation occurs when time delay crosses through a critical value. Then the direction and stability of the bifurcated periodic solutions are determined, using the normal form theory and the center manifold reduction. Finally, some numerical simulations are carried out to illustrate the results found

  13. Approximate representations of propagators in an external field

    International Nuclear Information System (INIS)

    Fried, H.M.

    1979-01-01

    A method of forming approximate representations for propagators with external field dependence is suggested and discussed in the context of potential scattering. An integro-differential equation in D+1 variables, where D represents the dimensionality of Euclidian space-time, is replaced by a Volterra equation in one variable. Approximate solutions to the latter provide a generalization of the Bloch-Nordsieck representation, containing the effects of all powers of hard-potential interactions, each modified by a characteristic soft-potential dependence [fr

  14. Factorization and the synthesis of optimal feedback kernels for differential-delay systems

    Science.gov (United States)

    Milman, Mark M.; Scheid, Robert E.

    1987-01-01

    A combination of ideas from the theories of operator Riccati equations and Volterra factorizations leads to the derivation of a novel, relatively simple set of hyperbolic equations which characterize the optimal feedback kernel for the finite-time regulator problem for autonomous differential-delay systems. Analysis of these equations elucidates the underlying structure of the feedback kernel and leads to the development of fast and accurate numerical methods for its computation. Unlike traditional formulations based on the operator Riccati equation, the gain is characterized by means of classical solutions of the derived set of equations. This leads to the development of approximation schemes which are analogous to what has been accomplished for systems of ordinary differential equations with given initial conditions.

  15. Differential Equations Compatible with KZ Equations

    International Nuclear Information System (INIS)

    Felder, G.; Markov, Y.; Tarasov, V.; Varchenko, A.

    2000-01-01

    We define a system of 'dynamical' differential equations compatible with the KZ differential equations. The KZ differential equations are associated to a complex simple Lie algebra g. These are equations on a function of n complex variables z i taking values in the tensor product of n finite dimensional g-modules. The KZ equations depend on the 'dual' variable in the Cartan subalgebra of g. The dynamical differential equations are differential equations with respect to the dual variable. We prove that the standard hypergeometric solutions of the KZ equations also satisfy the dynamical equations. As an application we give a new determinant formula for the coordinates of a basis of hypergeometric solutions

  16. Analytic solutions of a class of nonlinearly dynamic systems

    International Nuclear Information System (INIS)

    Wang, M-C; Zhao, X-S; Liu, X

    2008-01-01

    In this paper, the homotopy perturbation method (HPM) is applied to solve a coupled system of two nonlinear differential with first-order similar model of Lotka-Volterra and a Bratus equation with a source term. The analytic approximate solutions are derived. Furthermore, the analytic approximate solutions obtained by the HPM with the exact solutions reveals that the present method works efficiently

  17. Application of multi-scale wavelet entropy and multi-resolution Volterra models for climatic downscaling

    Science.gov (United States)

    Sehgal, V.; Lakhanpal, A.; Maheswaran, R.; Khosa, R.; Sridhar, Venkataramana

    2018-01-01

    This study proposes a wavelet-based multi-resolution modeling approach for statistical downscaling of GCM variables to mean monthly precipitation for five locations at Krishna Basin, India. Climatic dataset from NCEP is used for training the proposed models (Jan.'69 to Dec.'94) and are applied to corresponding CanCM4 GCM variables to simulate precipitation for the validation (Jan.'95-Dec.'05) and forecast (Jan.'06-Dec.'35) periods. The observed precipitation data is obtained from the India Meteorological Department (IMD) gridded precipitation product at 0.25 degree spatial resolution. This paper proposes a novel Multi-Scale Wavelet Entropy (MWE) based approach for clustering climatic variables into suitable clusters using k-means methodology. Principal Component Analysis (PCA) is used to obtain the representative Principal Components (PC) explaining 90-95% variance for each cluster. A multi-resolution non-linear approach combining Discrete Wavelet Transform (DWT) and Second Order Volterra (SoV) is used to model the representative PCs to obtain the downscaled precipitation for each downscaling location (W-P-SoV model). The results establish that wavelet-based multi-resolution SoV models perform significantly better compared to the traditional Multiple Linear Regression (MLR) and Artificial Neural Networks (ANN) based frameworks. It is observed that the proposed MWE-based clustering and subsequent PCA, helps reduce the dimensionality of the input climatic variables, while capturing more variability compared to stand-alone k-means (no MWE). The proposed models perform better in estimating the number of precipitation events during the non-monsoon periods whereas the models with clustering without MWE over-estimate the rainfall during the dry season.

  18. A very efficient approach for pricing barrier options on an underlying described by the mixed fractional Brownian motion

    International Nuclear Information System (INIS)

    Ballestra, Luca Vincenzo; Pacelli, Graziella; Radi, Davide

    2016-01-01

    We deal with the problem of pricing barrier options on an underlying described by the mixed fractional Brownian model. To this aim, we consider the initial-boundary value partial differential problem that yields the option price and we derive an integral representation of it in which the integrand functions must be obtained solving Volterra equations of the first kind. In addition, we develop an ad-hoc numerical procedure to solve the integral equations obtained. Numerical simulations reveal that the proposed method is extremely accurate and fast, and performs significantly better than the finite difference method.

  19. Application of the Banach Fixed-Point Theorem to the Scattering Problem at a Nonlinear Three-Layer Structure with Absorption

    Directory of Open Access Journals (Sweden)

    V. S. Serov

    2010-01-01

    Full Text Available A method based on the Banach fixed-point theorem is proposed for obtaining certain solutions (TE-polarized electromagnetic waves of the Helmholtz equation describing the reflection and transmission of a plane monochromatic wave at a nonlinear lossy dielectric film situated between two lossless linear semiinfinite media. All three media are assumed to be nonmagnetic and isotropic. The permittivity of the film is modelled by a continuously differentiable function of the transverse coordinate with a saturating Kerr nonlinearity. It is shown that the solution of the Helmholtz equation exists in form of a uniformly convergent sequence of iterations of the equivalent Volterra integral equation. Numerical results are presented.

  20. Setting and solving several factorization problems for integral operators

    International Nuclear Information System (INIS)

    Engibaryan, N B

    2000-01-01

    The problem of factorization I-K=(I-U - )(I-U + ), is considered. Here I is the identity operator, K is a fixed integral operator of Fredholm type: (Kf)(x)=∫ a b k(x,t)f(t)dt, -∞≤a ± are unknown upper and lower Volterra operators. Classes of generalized Volterra operators U ± are introduced such that I-U ± are not necessarily invertible operators in the spaces of functions on (a,b) under consideration. A combination of the method of non-linear factorization equations and a priori estimates brings forth new results on the existence and properties of the solution to this problem for k≥0, both in the subcritical case μ + and U - vanish on some parts S - and S + of the domain S=(a,b) 2 such that S + union S - =S

  1. Application of pert

    Directory of Open Access Journals (Sweden)

    Yiğit Aksoy

    2016-06-01

    Full Text Available Perturbation–iteration method is generalized for systems of first order differential equations. Approximate solutions of Lotka–Volterra systems are obtained using the method. Comparisons of our results with each other and with numerical solutions are given. The method is implemented in Mathematica, a major computer algebra system. The package PerturbationIteration.m automatically carries out the tedious calculations of the method.

  2. Nonlinear problems in fluid dynamics and inverse scattering: Nonlinear waves and inverse scattering

    Science.gov (United States)

    Ablowitz, Mark J.

    1994-12-01

    Research investigations involving the fundamental understanding and applications of nonlinear wave motion and related studies of inverse scattering and numerical computation have been carried out and a number of significant results have been obtained. A class of nonlinear wave equations which can be solved by the inverse scattering transform (IST) have been studied, including the Kadaomtsev-Petviashvili (KP) equation, the Davey-Stewartson equation, and the 2+1 Toda system. The solutions obtained by IST correspond to the Cauchy initial value problem with decaying initial data. We have also solved two important systems via the IST method: a 'Volterra' system in 2+1 dimensions and a new one dimensional nonlinear equation which we refer to as the Toda differential-delay equation. Research in computational chaos in moderate to long time numerical simulations continues.

  3. [The incidence of caries in a school-age population sample of U.S.L. n. 15 Alta Val di Cecina-Volterra].

    Science.gov (United States)

    Benetti, G L; Dini, M

    1990-01-01

    It was made a screening on children of some filter classes (1st and 3d class of primary school and 1st class of secondary school) of the Volterra's schools to estimate the incidence of caries and, if necessary, to activate programs for an adequate prevention. We examined 749 children arrived to the Dental Department of the Sanitary District owing an invitation letter; a set of question was given to their parents testing mainly alimentary and oral hygienic uses of the children examined by dentists. Elaboration of data obtained from replies and demonstrated that caries incidence in our population is of 65.29%, prevailing on male sex, and that this pathology is predominant on people taking insufficient care of oral hygiene, making no use of fluoridated toothpaste and eating any of cakes (especially between meals). These data show the high incidence of caries in evolutional age and how much this is strictly connected with wrong alimentary and hygienic uses. Therefore, to reduce this phenomenon, it's necessary to operate interventions of sanitary education and dental checking examinations, at least every 6-12 months, beginning in preschool age.

  4. Cross-talk dynamics of optical solitons in a broadband Kerr nonlinear system with weak cubic loss

    International Nuclear Information System (INIS)

    Peleg, Avner; Nguyen, Quan M.; Chung, Yeojin

    2010-01-01

    We study the dynamics of fast soliton collisions in a Kerr nonlinear optical waveguide with weak cubic loss. We obtain analytic expressions for the amplitude and frequency shifts in a single two-soliton collision and show that the impact of a fast three-soliton collision is given by the sum of the two-soliton interactions. Our analytic predictions are confirmed by numerical simulations with the perturbed nonlinear Schroedinger (NLS) equation. Furthermore, we show that the deterministic collision-induced dynamics of soliton amplitudes in a broadband waveguide system with N frequency channels is described by a Lotka-Volterra model for N competing species. For a two-channel system we find that stable transmission with equal prescribed amplitudes can be achieved by a proper choice of linear amplifier gain. The predictions of the Lotka-Volterra model are confirmed by numerical solution of a perturbed coupled-NLS model.

  5. Dynamics of a prey-predator system under Poisson white noise excitation

    Science.gov (United States)

    Pan, Shan-Shan; Zhu, Wei-Qiu

    2014-10-01

    The classical Lotka-Volterra (LV) model is a well-known mathematical model for prey-predator ecosystems. In the present paper, the pulse-type version of stochastic LV model, in which the effect of a random natural environment has been modeled as Poisson white noise, is investigated by using the stochastic averaging method. The averaged generalized Itô stochastic differential equation and Fokker-Planck-Kolmogorov (FPK) equation are derived for prey-predator ecosystem driven by Poisson white noise. Approximate stationary solution for the averaged generalized FPK equation is obtained by using the perturbation method. The effect of prey self-competition parameter ɛ2 s on ecosystem behavior is evaluated. The analytical result is confirmed by corresponding Monte Carlo (MC) simulation.

  6. Controlling chaos in dynamical systems described by maps

    International Nuclear Information System (INIS)

    Crispin, Y.; Marduel, C.

    1994-01-01

    The problem of suppressing chaotic behavior in dynamical systems is treated using a feedback control method with limited control effort. The proposed method is validated on archetypal systems described by maps, i.e. discrete-time difference equations. The method is also applicable to dynamical systems described by flows, i.e. by systems of ordinary differential equations. Results are presented for the one-dimensional logistic map and for a two-dimensional Lotka-Volterra map describing predator-prey population dynamics. It is shown that chaos can be suppressed and the system stabilized about a period-1 fixed point of the maps

  7. Building Deformation Assessment by Means of Persistent Scatterer Interferometry Analysis on a Landslide-Affected Area: The Volterra (Italy Case Study

    Directory of Open Access Journals (Sweden)

    Silvia Bianchini

    2015-04-01

    Full Text Available In recent years, space-borne InSAR (interferometric synthetic aperture radar techniques have shown their capabilities to provide precise measurements of Earth surface displacements for monitoring natural processes. Landslides threaten human lives and structures, especially in urbanized areas, where the density of elements at risk sensitive to ground movements is high. The methodology described in this paper aims at detecting terrain motions and building deformations at the local scale, by means of satellite radar data combined with in situ validation campaigns. The proposed approach consists of deriving maximum settlement directions of the investigated buildings from displacement data revealed by radar measurements and then in the cross-comparison of these values with background geological data, constructive features and on-field evidence. This validation permits better understanding whether or not the detected movements correspond to visible and effective damages to buildings. The method has been applied to the southwestern sector of Volterra (Tuscany region, Italy, which is a landslide-affected and partially urbanized area, through the use of COSMO-SkyMed satellite images as input data. Moreover, we discuss issues and possible misinterpretations when dealing with PSI (Persistent Scatterer Interferometry data referring to single manufactures and the consequent difficulty of attributing the motion rate to ground displacements, rather than to structural failures.

  8. p-Euler equations and p-Navier-Stokes equations

    Science.gov (United States)

    Li, Lei; Liu, Jian-Guo

    2018-04-01

    We propose in this work new systems of equations which we call p-Euler equations and p-Navier-Stokes equations. p-Euler equations are derived as the Euler-Lagrange equations for the action represented by the Benamou-Brenier characterization of Wasserstein-p distances, with incompressibility constraint. p-Euler equations have similar structures with the usual Euler equations but the 'momentum' is the signed (p - 1)-th power of the velocity. In the 2D case, the p-Euler equations have streamfunction-vorticity formulation, where the vorticity is given by the p-Laplacian of the streamfunction. By adding diffusion presented by γ-Laplacian of the velocity, we obtain what we call p-Navier-Stokes equations. If γ = p, the a priori energy estimates for the velocity and momentum have dual symmetries. Using these energy estimates and a time-shift estimate, we show the global existence of weak solutions for the p-Navier-Stokes equations in Rd for γ = p and p ≥ d ≥ 2 through a compactness criterion.

  9. Equating error in observed-score equating

    NARCIS (Netherlands)

    van der Linden, Willem J.

    2006-01-01

    Traditionally, error in equating observed scores on two versions of a test is defined as the difference between the transformations that equate the quantiles of their distributions in the sample and population of test takers. But it is argued that if the goal of equating is to adjust the scores of

  10. Degeneracy-driven self-structuring dynamics in selective repertoires.

    Science.gov (United States)

    Atamas, Sergei P; Bell, Jonathan

    2009-08-01

    Numerous biological interactions, such as interactions between T cell receptors or antibodies with antigens, interactions between enzymes and substrates, or interactions between predators and prey are often not strictly specific. In such less specific, or "sloppy," systems, referred to here as degenerate systems, a given unit of a diverse resource (antigens, enzymatic substrates, prey) is at risk of being recognized and consumed by multiple consumers (lymphocytes, enzymes, predators). In this study, we model generalized degenerate consumer-resource systems of Lotka-Volterra and Verhulst types. In the degenerate systems of Lotka-Volterra, there is a continuum of types of consumer and resource based on variation of a single trait (characteristic, or preference). The consumers experience competition for a continuum of resource types. This non-local interaction system is modeled with partial differential-integral equations and shows spontaneous self-structuring of the consumer population that depends on the degree of interaction degeneracy between resource and consumer, but does not mirror the distribution of resource. We also show that the classical Verhulst (i.e. logistic) single population model can be generalized to a degenerate model, which shows qualitative behavior similar to that in the degenerate Lotka-Volterra model. These results provide better insight into the dynamics of selective systems in biology, suggesting that adaptation of degenerate repertoires is not a simple "mirroring" of the environment by the "fittest" elements of population.

  11. Explicit integration of some integrable systems of classical mechanics

    OpenAIRE

    Basak Gancheva, Inna

    2011-01-01

    The main objective of the thesis is the analytical and geometrical study of several integrable finite-dimentional dynamical systems of classical mechanics, which are closely related, namely: - the classical generalization of the Euler top: the Zhukovski-Volterra (ZV) system describing the free motion of a gyrostat, i.e., a rigid body carrying a symmetric rotator whose axis is fixed in the body; - the Steklov-Lyapunov integrable case of the Kirchhoff equations describing the motio...

  12. equateIRT: An R Package for IRT Test Equating

    Directory of Open Access Journals (Sweden)

    Michela Battauz

    2015-12-01

    Full Text Available The R package equateIRT implements item response theory (IRT methods for equating different forms composed of dichotomous items. In particular, the IRT models included are the three-parameter logistic model, the two-parameter logistic model, the one-parameter logistic model and the Rasch model. Forms can be equated when they present common items (direct equating or when they can be linked through a chain of forms that present common items in pairs (indirect or chain equating. When two forms can be equated through different paths, a single conversion can be obtained by averaging the equating coefficients. The package calculates direct and chain equating coefficients. The averaging of direct and chain coefficients that link the same two forms is performed through the bisector method. Furthermore, the package provides analytic standard errors of direct, chain and average equating coefficients.

  13. Computing anticipatory systems with incursion and hyperincursion

    Science.gov (United States)

    Dubois, Daniel M.

    1998-07-01

    An anticipatory system is a system which contains a model of itself and/or of its environment in view of computing its present state as a function of the prediction of the model. With the concepts of incursion and hyperincursion, anticipatory discrete systems can be modelled, simulated and controlled. By definition an incursion, an inclusive or implicit recursion, can be written as: x(t+1)=F[…,x(t-1),x(t),x(t+1),…] where the value of a variable x(t+1) at time t+1 is a function of this variable at past, present and future times. This is an extension of recursion. Hyperincursion is an incursion with multiple solutions. For example, chaos in the Pearl-Verhulst map model: x(t+1)=a.x(t).[1-x(t)] is controlled by the following anticipatory incursive model: x(t+1)=a.x(t).[1-x(t+1)] which corresponds to the differential anticipatory equation: dx(t)/dt=a.x(t).[1-x(t+1)]-x(t). The main part of this paper deals with the discretisation of differential equation systems of linear and non-linear oscillators. The non-linear oscillator is based on the Lotka-Volterra equations model. The discretisation is made by incursion. The incursive discrete equation system gives the same stability condition than the original differential equations without numerical instabilities. The linearisation of the incursive discrete non-linear Lotka-Volterra equation system gives rise to the classical harmonic oscillator. The incursive discretisation of the linear oscillator is similar to define backward and forward discrete derivatives. A generalized complex derivative is then considered and applied to the harmonic oscillator. Non-locality seems to be a property of anticipatory systems. With some mathematical assumption, the Schrödinger quantum equation is derived for a particle in a uniform potential. Finally an hyperincursive system is given in the case of a neural stack memory.

  14. About several classes of bi-orthogonal polynomials and discrete integrable systems

    International Nuclear Information System (INIS)

    Chang, Xiang-Ke; Chen, Xiao-Min; Hu, Xing-Biao; Tam, Hon-Wah

    2015-01-01

    By introducing some special bi-orthogonal polynomials, we derive the so-called discrete hungry quotient-difference (dhQD) algorithm and a system related to the QD-type discrete hungry Lotka–Volterra (QD-type dhLV) system, together with their Lax pairs. These two known equations can be regarded as extensions of the QD algorithm. When this idea is applied to a higher analogue of the discrete-time Toda (HADT) equation and the quotient–quotient-difference (QQD) scheme proposed by Spicer, Nijhoff and van der Kamp, two extended systems are constructed. We call these systems the hungry forms of the higher analogue discrete-time Toda (hHADT) equation and the quotient-quotient-difference (hQQD) scheme, respectively. In addition, the corresponding Lax pairs are provided. (paper)

  15. Noncommutative operational calculus

    Directory of Open Access Journals (Sweden)

    Henry E. Heatherly

    1999-12-01

    Full Text Available Oliver Heaviside's operational calculus was placed on a rigorous mathematical basis by Jan Mikusinski, who constructed an algebraic setting for the operational methods. In this paper, we generalize Mikusi'{n}ski's methods to solve linear ordinary differential equations in which the unknown is a matrix- or linear operator-valued function. Because these functions can be zero-divisors and do not necessarily commute, Mikusi'{n}ski's one-dimensional calculus cannot be used. The noncommuative operational calculus developed here,however, is used to solve a wide class of such equations. In addition, we provide new proofs of existence and uniqueness theorems for certain matrix- and operator valued Volterra integral and integro-differential equations. Several examples are given which demonstrate these new methods.

  16. Computing generalized Langevin equations and generalized Fokker-Planck equations.

    Science.gov (United States)

    Darve, Eric; Solomon, Jose; Kia, Amirali

    2009-07-07

    The Mori-Zwanzig formalism is an effective tool to derive differential equations describing the evolution of a small number of resolved variables. In this paper we present its application to the derivation of generalized Langevin equations and generalized non-Markovian Fokker-Planck equations. We show how long time scales rates and metastable basins can be extracted from these equations. Numerical algorithms are proposed to discretize these equations. An important aspect is the numerical solution of the orthogonal dynamics equation which is a partial differential equation in a high dimensional space. We propose efficient numerical methods to solve this orthogonal dynamics equation. In addition, we present a projection formalism of the Mori-Zwanzig type that is applicable to discrete maps. Numerical applications are presented from the field of Hamiltonian systems.

  17. A novel method for non-parametric identification of nonlinear restoring forces in nonlinear vibrations from noisy response data: A conservative system

    International Nuclear Information System (INIS)

    Jang, T. S.; Kwon, S. H.; Han, S. L.

    2009-01-01

    A novel procedure is proposed to identify the functional form of nonlinear restoring forces in the nonlinear oscillatory motion of a conservative system. Although the problem of identification has a unique solution, formulation results in a Volterra-type of integral equation of the 'first' kind: the solution lacks stability because the integral equation is the 'first' kind. Thus, the new problem at hand is ill-posed. Inevitable small errors during the identification procedure can make the prediction of nonlinear restoring forces useless. We overcome the difficulty by using a stabilization technique of Landweber's regularization in this study. The capability of the proposed procedure is investigated through numerical examples

  18. Development of kinetics equations from the Boltzmann equation; Etablissement des equations de la cinetique a partir de l'equation de Boltzmann

    Energy Technology Data Exchange (ETDEWEB)

    Plas, R.

    1962-07-01

    The author reports a study on kinetics equations for a reactor. He uses the conventional form of these equations but by using a dynamic multiplication factor. Thus, constants related to delayed neutrons are not modified by efficiency factors. The author first describes the theoretic kinetic operation of a reactor and develops the associated equations. He reports the development of equations for multiplication factors.

  19. Nonlinear Relaxation in Population Dynamics

    Science.gov (United States)

    Cirone, Markus A.; de Pasquale, Ferdinando; Spagnolo, Bernardo

    We analyze the nonlinear relaxation of a complex ecosystem composed of many interacting species. The ecological system is described by generalized Lotka-Volterra equations with a multiplicative noise. The transient dynamics is studied in the framework of the mean field theory and with random interaction between the species. We focus on the statistical properties of the asymptotic behaviour of the time integral of the ith population and on the distribution of the population and of the local field.

  20. Simple equation method for nonlinear partial differential equations and its applications

    Directory of Open Access Journals (Sweden)

    Taher A. Nofal

    2016-04-01

    Full Text Available In this article, we focus on the exact solution of the some nonlinear partial differential equations (NLPDEs such as, Kodomtsev–Petviashvili (KP equation, the (2 + 1-dimensional breaking soliton equation and the modified generalized Vakhnenko equation by using the simple equation method. In the simple equation method the trial condition is the Bernoulli equation or the Riccati equation. It has been shown that the method provides a powerful mathematical tool for solving nonlinear wave equations in mathematical physics and engineering problems.

  1. Extended rate equations

    International Nuclear Information System (INIS)

    Shore, B.W.

    1981-01-01

    The equations of motion are discussed which describe time dependent population flows in an N-level system, reviewing the relationship between incoherent (rate) equations, coherent (Schrodinger) equations, and more general partially coherent (Bloch) equations. Approximations are discussed which replace the elaborate Bloch equations by simpler rate equations whose coefficients incorporate long-time consequences of coherence

  2. When the feasibility of an ecosystem is sufficient for global stability?

    Science.gov (United States)

    Porati, A; Granero, M I

    2000-01-01

    We show via a Liapunov function that in every model ecosystem governed by generalized Lotka-Volterra equations, a feasible steady state is globally asymptotically stable if the number of interaction branches equals n-1, where n is the number of species. This means that the representative graph for which the theorem holds is a 'tree' and not only an alimentary chain. Our result is valid also in the case of non-homogeneous systems, which model situations in which input fluxes are present.

  3. Complexified dynamical systems

    International Nuclear Information System (INIS)

    Bender, Carl M; Holm, Darryl D; Hook, Daniel W

    2007-01-01

    Many dynamical systems, such as the Lotka-Volterra predator-prey model and the Euler equations for the free rotation of a rigid body, are PT symmetric. The standard and well-known real solutions to such dynamical systems constitute an infinitessimal subclass of the full set of complex solutions. This paper examines a subset of the complex solutions that contains the real solutions, namely those having PT symmetry. The condition of PT symmetry selects out complex solutions that are periodic. (fast track communication)

  4. A phase-transition induced by the struggle for life in a competitive coexistence model in ecology

    International Nuclear Information System (INIS)

    Wio, H.S.; Kuperman, M.N.

    1994-07-01

    We have studied a spatially homogeneous model of an ecological system consisting of two species: a strong and a weak one, competing for a single food resource. The inclusion of a term corresponding to intraspecies competition, in particular for the strong species, shows that, it a certain threshold value is overcome, the classical result on extinction and coexistence of Lotka-Volterra type equations can drastically change yielding a kind of phase-transition to a coexistence phase. (author). 18 refs, 2 figs

  5. Comparison of the Short-Term Forecasting Accuracy on Battery Electric Vehicle between Modified Bass and Lotka-Volterra Model: A Case Study of China

    Directory of Open Access Journals (Sweden)

    Shunxi Li

    2017-01-01

    Full Text Available The potential demand of battery electric vehicle (BEV is the base of the decision-making to the government policy formulation, enterprise manufacture capacity expansion, and charging infrastructure construction. How to predict the future amount of BEV accurately is very important to the development of BEV both in practice and in theory. The present paper tries to compare the short-term accuracy of a proposed modified Bass model and Lotka-Volterra (LV model, by taking China’s BEV development as the case study. Using the statistics data of China’s BEV amount of 21 months from Jan 2015 to Sep 2016, we compare the simulation accuracy based on the value of mean absolute percentage error (MAPE and discuss the forecasting capacity of the two models according to China’s government expectation. According to the MAPE value, the two models have good prediction accuracy, but the Bass model is more accurate than LV model. Bass model has only one dimension and focuses on the diffusion trend, while LV model has two dimensions and mainly describes the relationship and competing process between the two populations. In future research, the forecasting advantages of Bass model and LV model should be combined to get more accurate predicting effect.

  6. Numerical Solution of Heun Equation Via Linear Stochastic Differential Equation

    Directory of Open Access Journals (Sweden)

    Hamidreza Rezazadeh

    2014-05-01

    Full Text Available In this paper, we intend to solve special kind of ordinary differential equations which is called Heun equations, by converting to a corresponding stochastic differential equation(S.D.E.. So, we construct a stochastic linear equation system from this equation which its solution is based on computing fundamental matrix of this system and then, this S.D.E. is solved by numerically methods. Moreover, its asymptotic stability and statistical concepts like expectation and variance of solutions are discussed. Finally, the attained solutions of these S.D.E.s compared with exact solution of corresponding differential equations.

  7. A generalization of the simplest equation method and its application to (3+1)-dimensional KP equation and generalized Fisher equation

    International Nuclear Information System (INIS)

    Zhao, Zhonglong; Zhang, Yufeng; Han, Zhong; Rui, Wenjuan

    2014-01-01

    In this paper, the simplest equation method is used to construct exact traveling solutions of the (3+1)-dimensional KP equation and generalized Fisher equation. We summarize the main steps of the simplest equation method. The Bernoulli and Riccati equation are used as simplest equations. This method is straightforward and concise, and it can be applied to other nonlinear partial differential equations

  8. A multiple-scale power series method for solving nonlinear ordinary differential equations

    Directory of Open Access Journals (Sweden)

    Chein-Shan Liu

    2016-02-01

    Full Text Available The power series solution is a cheap and effective method to solve nonlinear problems, like the Duffing-van der Pol oscillator, the Volterra population model and the nonlinear boundary value problems. A novel power series method by considering the multiple scales $R_k$ in the power term $(t/R_k^k$ is developed, which are derived explicitly to reduce the ill-conditioned behavior in the data interpolation. In the method a huge value times a tiny value is avoided, such that we can decrease the numerical instability and which is the main reason to cause the failure of the conventional power series method. The multiple scales derived from an integral can be used in the power series expansion, which provide very accurate numerical solutions of the problems considered in this paper.

  9. Two competing species in super-diffusive dynamical regimes

    Science.gov (United States)

    La Cognata, A.; Valenti, D.; Spagnolo, B.; Dubkov, A. A.

    2010-09-01

    The dynamics of two competing species within the framework of the generalized Lotka-Volterra equations, in the presence of multiplicative α-stable Lévy noise sources and a random time dependent interaction parameter, is studied. The species dynamics is characterized by two different dynamical regimes, exclusion of one species and coexistence of both, depending on the values of the interaction parameter, which obeys a Langevin equation with a periodically fluctuating bistable potential and an additive α-stable Lévy noise. The stochastic resonance phenomenon is analyzed for noise sources asymmetrically distributed. Finally, the effects of statistical dependence between multiplicative noise and additive noise on the dynamics of the two species are studied.

  10. Stochastic resonance and noise delayed extinction in a model of two competing species

    Science.gov (United States)

    Valenti, D.; Fiasconaro, A.; Spagnolo, B.

    2004-01-01

    We study the role of the noise in the dynamics of two competing species. We consider generalized Lotka-Volterra equations in the presence of a multiplicative noise, which models the interaction between the species and the environment. The interaction parameter between the species is a random process which obeys a stochastic differential equation with a generalized bistable potential in the presence of a periodic driving term, which accounts for the environment temperature variation. We find noise-induced periodic oscillations of the species concentrations and stochastic resonance phenomenon. We find also a nonmonotonic behavior of the mean extinction time of one of the two competing species as a function of the additive noise intensity.

  11. On the numerical treatment of selected oscillatory evolutionary problems

    Science.gov (United States)

    Cardone, Angelamaria; Conte, Dajana; D'Ambrosio, Raffaele; Paternoster, Beatrice

    2017-07-01

    We focus on evolutionary problems whose qualitative behaviour is known a-priori and exploited in order to provide efficient and accurate numerical schemes. For classical numerical methods, depending on constant coefficients, the required computational effort could be quite heavy, due to the necessary employ of very small stepsizes needed to accurately reproduce the qualitative behaviour of the solution. In these situations, it may be convenient to use special purpose formulae, i.e. non-polynomially fitted formulae on basis functions adapted to the problem (see [16, 17] and references therein). We show examples of special purpose strategies to solve two families of evolutionary problems exhibiting periodic solutions, i.e. partial differential equations and Volterra integral equations.

  12. On identification of dynamic system parameters from experimental data

    CSIR Research Space (South Africa)

    Shatalov, M

    2007-08-01

    Full Text Available -linear differen- tial equations frequently used to describe the dynamics of biological systems in which two species interact. They were proposed independently by Alfred J. Lotka [1] and Vito Volterra in 1926 [2]. This system can be written in the form x′1(t...) = x1 (a11 − a12x2) x′2(t) = x2 (ηa12x1 − a22) When solved for x1 and x2 the above system of equations yields x1 = 0, x1 = 0 and 1 x1 = a22 ηa12 , x1 = a11 a12 hence there are two equilibria. The solution in the neighborhood of the first...

  13. Logistic map with memory from economic model

    International Nuclear Information System (INIS)

    Tarasova, Valentina V.; Tarasov, Vasily E.

    2017-01-01

    A generalization of the economic model of logistic growth, which takes into account the effects of memory and crises, is suggested. Memory effect means that the economic factors and parameters at any given time depend not only on their values at that time, but also on their values at previous times. For the mathematical description of the memory effects, we use the theory of derivatives of non-integer order. Crises are considered as sharp splashes (bursts) of the price, which are mathematically described by the delta-functions. Using the equivalence of fractional differential equations and the Volterra integral equations, we obtain discrete maps with memory that are exact discrete analogs of fractional differential equations of economic processes. We derive logistic map with memory, its generalizations, and “economic” discrete maps with memory from the fractional differential equations, which describe the economic natural growth with competition, power-law memory and crises.

  14. Orthogonality preserving infinite dimensional quadratic stochastic operators

    International Nuclear Information System (INIS)

    Akın, Hasan; Mukhamedov, Farrukh

    2015-01-01

    In the present paper, we consider a notion of orthogonal preserving nonlinear operators. We introduce π-Volterra quadratic operators finite and infinite dimensional settings. It is proved that any orthogonal preserving quadratic operator on finite dimensional simplex is π-Volterra quadratic operator. In infinite dimensional setting, we describe all π-Volterra operators in terms orthogonal preserving operators

  15. Analysis of wave equation in electromagnetic field by Proca equation

    International Nuclear Information System (INIS)

    Pamungkas, Oky Rio; Soeparmi; Cari

    2017-01-01

    This research is aimed to analyze wave equation for the electric and magnetic field, vector and scalar potential, and continuity equation using Proca equation. Then, also analyze comparison of the solution on Maxwell and Proca equation for scalar potential and electric field, both as a function of distance and constant wave number. (paper)

  16. Comparison of Kernel Equating and Item Response Theory Equating Methods

    Science.gov (United States)

    Meng, Yu

    2012-01-01

    The kernel method of test equating is a unified approach to test equating with some advantages over traditional equating methods. Therefore, it is important to evaluate in a comprehensive way the usefulness and appropriateness of the Kernel equating (KE) method, as well as its advantages and disadvantages compared with several popular item…

  17. Integral equations

    CERN Document Server

    Moiseiwitsch, B L

    2005-01-01

    Two distinct but related approaches hold the solutions to many mathematical problems--the forms of expression known as differential and integral equations. The method employed by the integral equation approach specifically includes the boundary conditions, which confers a valuable advantage. In addition, the integral equation approach leads naturally to the solution of the problem--under suitable conditions--in the form of an infinite series.Geared toward upper-level undergraduate students, this text focuses chiefly upon linear integral equations. It begins with a straightforward account, acco

  18. Partial Differential Equations

    CERN Document Server

    1988-01-01

    The volume contains a selection of papers presented at the 7th Symposium on differential geometry and differential equations (DD7) held at the Nankai Institute of Mathematics, Tianjin, China, in 1986. Most of the contributions are original research papers on topics including elliptic equations, hyperbolic equations, evolution equations, non-linear equations from differential geometry and mechanics, micro-local analysis.

  19. Nonlinear evolution equations

    CERN Document Server

    Uraltseva, N N

    1995-01-01

    This collection focuses on nonlinear problems in partial differential equations. Most of the papers are based on lectures presented at the seminar on partial differential equations and mathematical physics at St. Petersburg University. Among the topics explored are the existence and properties of solutions of various classes of nonlinear evolution equations, nonlinear imbedding theorems, bifurcations of solutions, and equations of mathematical physics (Navier-Stokes type equations and the nonlinear Schrödinger equation). The book will be useful to researchers and graduate students working in p

  20. FMTLxLyLz DIMENSIONAL EQUAT DIMENSIONAL EQUATION ...

    African Journals Online (AJOL)

    eobe

    plant made of 12mm thick steel plate was used in de steel plate ... water treatment plant. ... ameters affecting filtration processes were used to derive an equation usin ..... system. However, in deriving the equation onl terms are incorporated.

  1. Integrodifferential equations and delay models in population dynamics

    CERN Document Server

    Cushing, Jim M

    1977-01-01

    These notes are, for the most part, the result of a course I taught at the University of Arizona during the Spring of 1977. Their main purpose is to inves­ tigate the effect that delays (of Volterra integral type) have when placed in the differential models of mathematical ecology, as far as stability of equilibria and the nature of oscillations of species densities are concerned. A secondary pur­ pose of the course out of which they evolved was to give students an (at least elementary) introduction to some mathematical modeling in ecology as well as to some purely mathematical subjects, such as stability theory for integrodifferentia1 systems, bifurcation theory, and some simple topics in perturbation theory. The choice of topics of course reflects my personal interests; and while these notes were not meant to exhaust the topics covered, I think they and the list of refer­ ences come close to covering the literature to date, as far as integrodifferentia1 models in ecology are concerned. I would like to th...

  2. Kinetic equations for an unstable plasma; Equations cinetiques d'un plasma instable

    Energy Technology Data Exchange (ETDEWEB)

    Laval, G; Pellat, R [Commissariat a l' Energie Atomique, Fontenay-aux-Roses (France). Centre d' Etudes Nucleaires

    1968-07-01

    In this work, we establish the plasma kinetic equations starting from the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy of equations. We demonstrate that relations existing between correlation functions may help to justify the truncation of the hierarchy. Then we obtain the kinetic equations of a stable or unstable plasma. They do not reduce to an equation for the one-body distribution function, but generally involve two coupled equations for the one-body distribution function and the spectral density of the fluctuating electric field. We study limiting cases where the Balescu-Lenard equation, the quasi-linear theory, the Pines-Schrieffer equations and the equations of weak turbulence in the random phase approximation are recovered. At last we generalise the H-theorem for the system of equations and we define conditions for irreversible behaviour. (authors) [French] Dans ce travail nous etablissons les equations cinetiques d'un plasma a partir des equations de la recurrence de Bogoliubov, Born, Green, Kirkwood et Yvon. Nous demontrons qu'entre les fonctions de correlation d'un plasma existent des relations qui permettent de justifier la troncature de la recurrence. Nous obtenons alors les equations cinetiques d'un plasma stable ou instable. En general elles ne se reduisent pas a une equation d'evolution pour la densite simple, mais se composent de deux equations couplees portant sur la densite simple et la densite spectrale du champ electrique fluctuant. Nous etudions le cas limites ou l'on retrouve l'equation de Balescu-Lenard, les equations de la theorie quasi-lineaire, les equations de Pines et Schrieffer et les equations de la turbulence faible dans l'approximation des phases aleatoires. Enfin, nous generalisons le theoreme H pour ce systeme d'equations et nous precisons les conditions d'evolution irreversible. (auteurs)

  3. equate: An R Package for Observed-Score Linking and Equating

    Directory of Open Access Journals (Sweden)

    Anthony D. Albano

    2016-10-01

    Full Text Available The R package equate contains functions for observed-score linking and equating under single-group, equivalent-groups, and nonequivalent-groups with anchor test(s designs. This paper introduces these designs and provides an overview of observed-score equating with details about each of the supported methods. Examples demonstrate the basic functionality of the equate package.

  4. Chemical Equation Balancing.

    Science.gov (United States)

    Blakley, G. R.

    1982-01-01

    Reviews mathematical techniques for solving systems of homogeneous linear equations and demonstrates that the algebraic method of balancing chemical equations is a matter of solving a system of homogeneous linear equations. FORTRAN programs using this matrix method to chemical equation balancing are available from the author. (JN)

  5. A new auxiliary equation and exact travelling wave solutions of nonlinear equations

    International Nuclear Information System (INIS)

    Sirendaoreji

    2006-01-01

    A new auxiliary ordinary differential equation and its solutions are used for constructing exact travelling wave solutions of nonlinear partial differential equations in a unified way. The main idea of this method is to take full advantage of the auxiliary equation which has more new exact solutions. More new exact travelling wave solutions are obtained for the quadratic nonlinear Klein-Gordon equation, the combined KdV and mKdV equation, the sine-Gordon equation and the Whitham-Broer-Kaup equations

  6. Optimal control of non-Markovian dynamics in a single-mode cavity strongly coupled to an inhomogeneously broadened spin ensemble

    Science.gov (United States)

    Krimer, Dmitry O.; Hartl, Benedikt; Mintert, Florian; Rotter, Stefan

    2017-10-01

    Ensembles of quantum-mechanical spins offer a promising platform for quantum memories, but proper functionality requires accurate control of unavoidable system imperfections. We present an efficient control scheme for a spin ensemble strongly coupled to a single-mode cavity based on a set of Volterra equations relying solely on weak classical control pulses. The viability of our approach is demonstrated in terms of explicit storage and readout sequences that will serve as a starting point towards the realization of more demanding full quantum-mechanical optimal control schemes.

  7. An Efficient UD-Based Algorithm for the Computation of Maximum Likelihood Sensitivity of Continuous-Discrete Systems

    DEFF Research Database (Denmark)

    Boiroux, Dimitri; Juhl, Rune; Madsen, Henrik

    2016-01-01

    This paper addresses maximum likelihood parameter estimation of continuous-time nonlinear systems with discrete-time measurements. We derive an efficient algorithm for the computation of the log-likelihood function and its gradient, which can be used in gradient-based optimization algorithms....... This algorithm uses UD decomposition of symmetric matrices and the array algorithm for covariance update and gradient computation. We test our algorithm on the Lotka-Volterra equations. Compared to the maximum likelihood estimation based on finite difference gradient computation, we get a significant speedup...

  8. On a functional equation related to the intermediate long wave equation

    International Nuclear Information System (INIS)

    Hone, A N W; Novikov, V S

    2004-01-01

    We resolve an open problem stated by Ablowitz et al (1982 J. Phys. A: Math. Gen. 15 781) concerning the integral operator appearing in the intermediate long wave equation. We explain how this is resolved using the perturbative symmetry approach introduced by one of us with Mikhailov. By solving a certain functional equation, we prove that the intermediate long wave equation and the Benjamin-Ono equation are the unique integrable cases within a particular class of integro-differential equations. Furthermore, we explain how the perturbative symmetry approach is naturally extended to treat equations on a periodic domain. (letter to the editor)

  9. Some New Integrable Equations from the Self-Dual Yang-Mills Equations

    International Nuclear Information System (INIS)

    Ivanova, T.A.; Popov, A.D.

    1994-01-01

    Using the symmetry reductions of the self-dual Yang-Mills (SDYM) equations in (2+2) dimensions, we introduce new integrable equations which are 'deformations' of the chiral model in (2+1) dimensions, generalized nonlinear Schroedinger, Korteweg-de Vries, Toda lattice, Garnier, Euler-Arnold, generalized Calogero-Moser and Euler-Calogero-Moser equations. The Lax pairs for all of these equations are derived by the symmetry reductions of the Lax pair for the SDYM equations. 34 refs

  10. Auxiliary equation method for solving nonlinear partial differential equations

    International Nuclear Information System (INIS)

    Sirendaoreji,; Jiong, Sun

    2003-01-01

    By using the solutions of an auxiliary ordinary differential equation, a direct algebraic method is described to construct several kinds of exact travelling wave solutions for some nonlinear partial differential equations. By this method some physically important nonlinear equations are investigated and new exact travelling wave solutions are explicitly obtained with the aid of symbolic computation

  11. 40-Gb/s PAM4 with low-complexity equalizers for next-generation PON systems

    Science.gov (United States)

    Tang, Xizi; Zhou, Ji; Guo, Mengqi; Qi, Jia; Hu, Fan; Qiao, Yaojun; Lu, Yueming

    2018-01-01

    In this paper, we demonstrate 40-Gb/s four-level pulse amplitude modulation (PAM4) transmission with 10 GHz devices and low-complexity equalizers for next-generation passive optical network (PON) systems. Simple feed-forward equalizer (FFE) and decision feedback equalizer (DFE) enable 20 km fiber transmission while high-complexity Volterra algorithm in combination with FFE and DFE can extend the transmission distance to 40 km. A simplified Volterra algorithm is proposed for reducing computational complexity. Simulation results show that the simplified Volterra algorithm reduces up to ∼75% computational complexity at a relatively low cost of only 0.4 dB power budget. At a forward error correction (FEC) threshold of 10-3 , we achieve 31.2 dB and 30.8 dB power budget over 40 km fiber transmission using traditional FFE-DFE-Volterra and our simplified FFE-DFE-Volterra, respectively.

  12. The equationally-defined commutator a study in equational logic and algebra

    CERN Document Server

    Czelakowski, Janusz

    2015-01-01

    This monograph introduces and explores the notions of a commutator equation and the equationally-defined commutator from the perspective of abstract algebraic logic.  An account of the commutator operation associated with equational deductive systems is presented, with an emphasis placed on logical aspects of the commutator for equational systems determined by quasivarieties of algebras.  The author discusses the general properties of the equationally-defined commutator, various centralization relations for relative congruences, the additivity and correspondence properties of the equationally-defined commutator, and its behavior in finitely generated quasivarieties. Presenting new and original research not yet considered in the mathematical literature, The Equationally-Defined Commutator will be of interest to professional algebraists and logicians, as well as graduate students and other researchers interested in problems of modern algebraic logic.

  13. A Comparison between Linear IRT Observed-Score Equating and Levine Observed-Score Equating under the Generalized Kernel Equating Framework

    Science.gov (United States)

    Chen, Haiwen

    2012-01-01

    In this article, linear item response theory (IRT) observed-score equating is compared under a generalized kernel equating framework with Levine observed-score equating for nonequivalent groups with anchor test design. Interestingly, these two equating methods are closely related despite being based on different methodologies. Specifically, when…

  14. Scattering of Ricci scalar perturbations from Schwarzschild black holes in modified gravity

    Energy Technology Data Exchange (ETDEWEB)

    Sibandze, Dan B.; Goswami, Rituparno; Maharaj, Sunil D.; Nzioki, Anne Marie [University of KwaZulu-Natal, Astrophysics and Cosmology Research Unit, School of Mathematics Statistics and Computer Science, Private Bag X54001, Durban (South Africa); Dunsby, Peter K.S. [University of Cape Town, Department of Mathematics and Applied Mathematics and ACGC, Cape Town (South Africa)

    2017-06-15

    It has already been shown that the gravitational waves emitted from a Schwarzschild black hole in f(R) gravity have no signatures of the modification of gravity from General Relativity, as the Regge-Wheeler equation remains invariant. In this paper we consider the perturbations of Ricci scalar in a vacuum Schwarzschild spacetime, which is unique to higher order theories of gravity and is absent in General Relativity. We show that the equation that governs these perturbations can be reduced to a Volterra integral equation. We explicitly calculate the reflection coefficients for the Ricci scalar perturbations, when they are scattered by the black hole potential barrier. Our analysis shows that a larger fraction of these Ricci scalar waves are reflected compared to the gravitational waves. This may provide a novel observational signature for fourth order gravity. (orig.)

  15. On the complete and partial integrability of non-Hamiltonian systems

    Science.gov (United States)

    Bountis, T. C.; Ramani, A.; Grammaticos, B.; Dorizzi, B.

    1984-11-01

    The methods of singularity analysis are applied to several third order non-Hamiltonian systems of physical significance including the Lotka-Volterra equations, the three-wave interaction and the Rikitake dynamo model. Complete integrability is defined and new completely integrable systems are discovered by means of the Painlevé property. In all these cases we obtain integrals, which reduce the equations either to a final quadrature or to an irreducible second order ordinary differential equation (ODE) solved by Painlevé transcendents. Relaxing the Painlevé property we find many partially integrable cases whose movable singularities are poles at leading order, with In( t- t0) terms entering at higher orders. In an Nth order, generalized Rössler model a precise relation is established between the partial fulfillment of the Painlevé conditions and the existence of N - 2 integrals of the motion.

  16. Five-dimensional Monopole Equation with Hedge-Hog Ansatz and Abel's Differential Equation

    OpenAIRE

    Kihara, Hironobu

    2008-01-01

    We review the generalized monopole in the five-dimensional Euclidean space. A numerical solution with the Hedge-Hog ansatz is studied. The Bogomol'nyi equation becomes a second order autonomous non-linear differential equation. The equation can be translated into the Abel's differential equation of the second kind and is an algebraic differential equation.

  17. Differential equations a dynamical systems approach ordinary differential equations

    CERN Document Server

    Hubbard, John H

    1991-01-01

    This is a corrected third printing of the first part of the text Differential Equations: A Dynamical Systems Approach written by John Hubbard and Beverly West. The authors' main emphasis in this book is on ordinary differential equations. The book is most appropriate for upper level undergraduate and graduate students in the fields of mathematics, engineering, and applied mathematics, as well as the life sciences, physics and economics. Traditional courses on differential equations focus on techniques leading to solutions. Yet most differential equations do not admit solutions which can be written in elementary terms. The authors have taken the view that a differential equations defines functions; the object of the theory is to understand the behavior of these functions. The tools the authors use include qualitative and numerical methods besides the traditional analytic methods. The companion software, MacMath, is designed to bring these notions to life.

  18. Differential equations

    CERN Document Server

    Barbu, Viorel

    2016-01-01

    This textbook is a comprehensive treatment of ordinary differential equations, concisely presenting basic and essential results in a rigorous manner. Including various examples from physics, mechanics, natural sciences, engineering and automatic theory, Differential Equations is a bridge between the abstract theory of differential equations and applied systems theory. Particular attention is given to the existence and uniqueness of the Cauchy problem, linear differential systems, stability theory and applications to first-order partial differential equations. Upper undergraduate students and researchers in applied mathematics and systems theory with a background in advanced calculus will find this book particularly useful. Supplementary topics are covered in an appendix enabling the book to be completely self-contained.

  19. New Equating Methods and Their Relationships with Levine Observed Score Linear Equating under the Kernel Equating Framework

    Science.gov (United States)

    Chen, Haiwen; Holland, Paul

    2010-01-01

    In this paper, we develop a new curvilinear equating for the nonequivalent groups with anchor test (NEAT) design under the assumption of the classical test theory model, that we name curvilinear Levine observed score equating. In fact, by applying both the kernel equating framework and the mean preserving linear transformation of…

  20. Relations between nonlinear Riccati equations and other equations in fundamental physics

    International Nuclear Information System (INIS)

    Schuch, Dieter

    2014-01-01

    Many phenomena in the observable macroscopic world obey nonlinear evolution equations while the microscopic world is governed by quantum mechanics, a fundamental theory that is supposedly linear. In order to combine these two worlds in a common formalism, at least one of them must sacrifice one of its dogmas. Linearizing nonlinear dynamics would destroy the fundamental property of this theory, however, it can be shown that quantum mechanics can be reformulated in terms of nonlinear Riccati equations. In a first step, it will be shown that the information about the dynamics of quantum systems with analytical solutions can not only be obtainable from the time-dependent Schrödinger equation but equally-well from a complex Riccati equation. Comparison with supersymmetric quantum mechanics shows that even additional information can be obtained from the nonlinear formulation. Furthermore, the time-independent Schrödinger equation can also be rewritten as a complex Riccati equation for any potential. Extension of the Riccati formulation to include irreversible dissipative effects is straightforward. Via (real and complex) Riccati equations, other fields of physics can also be treated within the same formalism, e.g., statistical thermodynamics, nonlinear dynamical systems like those obeying a logistic equation as well as wave equations in classical optics, Bose- Einstein condensates and cosmological models. Finally, the link to abstract ''quantizations'' such as the Pythagorean triples and Riccati equations connected with trigonometric and hyperbolic functions will be shown

  1. Bridging the Knowledge Gaps between Richards' Equation and Budyko Equation

    Science.gov (United States)

    Wang, D.

    2017-12-01

    The empirical Budyko equation represents the partitioning of mean annual precipitation into evaporation and runoff. Richards' equation, based on Darcy's law, represents the movement of water in unsaturated soils. The linkage between Richards' equation and Budyko equation is presented by invoking the empirical Soil Conservation Service curve number (SCS-CN) model for computing surface runoff at the event-scale. The basis of the SCS-CN method is the proportionality relationship, i.e., the ratio of continuing abstraction to its potential is equal to the ratio of surface runoff to its potential value. The proportionality relationship can be derived from the Richards' equation for computing infiltration excess and saturation excess models at the catchment scale. Meanwhile, the generalized proportionality relationship is demonstrated as the common basis of SCS-CN method, monthly "abcd" model, and Budyko equation. Therefore, the linkage between Darcy's law and the emergent pattern of mean annual water balance at the catchment scale is presented through the proportionality relationship.

  2. Partial differential equations

    CERN Document Server

    Evans, Lawrence C

    2010-01-01

    This text gives a comprehensive survey of modern techniques in the theoretical study of partial differential equations (PDEs) with particular emphasis on nonlinear equations. The exposition is divided into three parts: representation formulas for solutions; theory for linear partial differential equations; and theory for nonlinear partial differential equations. Included are complete treatments of the method of characteristics; energy methods within Sobolev spaces; regularity for second-order elliptic, parabolic, and hyperbolic equations; maximum principles; the multidimensional calculus of variations; viscosity solutions of Hamilton-Jacobi equations; shock waves and entropy criteria for conservation laws; and, much more.The author summarizes the relevant mathematics required to understand current research in PDEs, especially nonlinear PDEs. While he has reworked and simplified much of the classical theory (particularly the method of characteristics), he primarily emphasizes the modern interplay between funct...

  3. Nonlinear Dirac Equations

    Directory of Open Access Journals (Sweden)

    Wei Khim Ng

    2009-02-01

    Full Text Available We construct nonlinear extensions of Dirac's relativistic electron equation that preserve its other desirable properties such as locality, separability, conservation of probability and Poincaré invariance. We determine the constraints that the nonlinear term must obey and classify the resultant non-polynomial nonlinearities in a double expansion in the degree of nonlinearity and number of derivatives. We give explicit examples of such nonlinear equations, studying their discrete symmetries and other properties. Motivated by some previously suggested applications we then consider nonlinear terms that simultaneously violate Lorentz covariance and again study various explicit examples. We contrast our equations and construction procedure with others in the literature and also show that our equations are not gauge equivalent to the linear Dirac equation. Finally we outline various physical applications for these equations.

  4. Equalization and detection for digital communication over nonlinear bandlimited satellite communication channels. Ph.D. Thesis

    Science.gov (United States)

    Gutierrez, Alberto, Jr.

    1995-01-01

    This dissertation evaluates receiver-based methods for mitigating the effects due to nonlinear bandlimited signal distortion present in high data rate satellite channels. The effects of the nonlinear bandlimited distortion is illustrated for digitally modulated signals. A lucid development of the low-pass Volterra discrete time model for a nonlinear communication channel is presented. In addition, finite-state machine models are explicitly developed for a nonlinear bandlimited satellite channel. A nonlinear fixed equalizer based on Volterra series has previously been studied for compensation of noiseless signal distortion due to a nonlinear satellite channel. This dissertation studies adaptive Volterra equalizers on a downlink-limited nonlinear bandlimited satellite channel. We employ as figure of merits performance in the mean-square error and probability of error senses. In addition, a receiver consisting of a fractionally-spaced equalizer (FSE) followed by a Volterra equalizer (FSE-Volterra) is found to give improvement beyond that gained by the Volterra equalizer. Significant probability of error performance improvement is found for multilevel modulation schemes. Also, it is found that probability of error improvement is more significant for modulation schemes, constant amplitude and multilevel, which require higher signal to noise ratios (i.e., higher modulation orders) for reliable operation. The maximum likelihood sequence detection (MLSD) receiver for a nonlinear satellite channel, a bank of matched filters followed by a Viterbi detector, serves as a probability of error lower bound for the Volterra and FSE-Volterra equalizers. However, this receiver has not been evaluated for a specific satellite channel. In this work, an MLSD receiver is evaluated for a specific downlink-limited satellite channel. Because of the bank of matched filters, the MLSD receiver may be high in complexity. Consequently, the probability of error performance of a more practical

  5. Evaluating Equating Results: Percent Relative Error for Chained Kernel Equating

    Science.gov (United States)

    Jiang, Yanlin; von Davier, Alina A.; Chen, Haiwen

    2012-01-01

    This article presents a method for evaluating equating results. Within the kernel equating framework, the percent relative error (PRE) for chained equipercentile equating was computed under the nonequivalent groups with anchor test (NEAT) design. The method was applied to two data sets to obtain the PRE, which can be used to measure equating…

  6. On the reduction of the degree of linear differential operators

    International Nuclear Information System (INIS)

    Bobieński, Marcin; Gavrilov, Lubomir

    2011-01-01

    Let L be a linear differential operator with coefficients in some differential field k of characteristic zero with algebraically closed field of constants. Let k a be the algebraic closure of k. For a solution y 0 , Ly 0 = 0, we determine the linear differential operator of minimal degree L-tilde and coefficients in k a , such that L-tilde y 0 =0. This result is then applied to some Picard–Fuchs equations which appear in the study of perturbations of plane polynomial vector fields of Lotka–Volterra type

  7. Quantum mechanical analogy for solving a competitive coexistence model in ecology

    International Nuclear Information System (INIS)

    Wio, H.S.; Kuperman, M.N.; Haeften, B. von

    1994-07-01

    We have studied an ecological system of three species: a strong and a weak one, competing for a single food resource, modelled as a reaction-diffusion process. An exact analytical solution has been found through a quantum mechanical analogy. Such solution indicates that in certain situations the classical results on extinction and coexistence of Lotka-Volterra type equations are no longer valid, essentially, as a consequence of the weak species mobility. A stability analysis of this solution against changes in different parameters has been carried out. (author). 19 refs, 5 figs

  8. Stability properties of a general class of nonlinear dynamical systems

    Science.gov (United States)

    Gléria, I. M.; Figueiredo, A.; Rocha Filho, T. M.

    2001-05-01

    We establish sufficient conditions for the boundedness of the trajectories and the stability of the fixed points in a class of general nonlinear systems, the so-called quasi-polynomial vector fields, with the help of a natural embedding of such systems in a family of generalized Lotka-Volterra (LV) equations. A purely algebraic procedure is developed to determine such conditions. We apply our method to obtain new results for LV systems, by a reparametrization in time variable, and to study general nonlinear vector fields, originally far from the LV format.

  9. Stability properties of a general class of nonlinear dynamical systems

    Energy Technology Data Exchange (ETDEWEB)

    Gleria, I.M. [Filho Instituto de Fisica, Universidade de Brasilia, Campus Universitario Darcy Ribeiro, Brasilia (Brazil). E-mail: iram@ucb.br; Figueiredo, A. [Filho Instituto de Fisica, Universidade de Brasilia, Campus Universitario Darcy Ribeiro, Brasilia (Brazil). E-mail: annibal@helium.fis.unb.br; Rocha, T.M. [Filho Instituto de Fisica, Universidade de Brasilia, Campus Universitario Darcy Ribeiro, Brasilia (Brazil). E-mail: marciano@helium.fis.unb.br

    2001-05-04

    We establish sufficient conditions for the boundedness of the trajectories and the stability of the fixed points in a class of general nonlinear systems, the so-called quasi-polynomial vector fields, with the help of a natural embedding of such systems in a family of generalized Lotka-Volterra (LV) equations. A purely algebraic procedure is developed to determine such conditions. We apply our method to obtain new results for LV systems, by a reparametrization in time variable, and to study general nonlinear vector fields, originally far from the LV format. (author)

  10. Becker and Lomnitz rheological models: A comparison

    Science.gov (United States)

    Mainardi, Francesco; Spada, Giorgio

    2012-07-01

    The viscoelastic material functions for the Becker and the Lomnitz rheological models, sometimes employed to describe the transient flow of rocks, are studied and compared. Their creep functions, which are known in a closed form, share a similar time dependence and asymptotic behavior. This is also found for the relaxation functions, obtained by solving numerically a Volterra equation of the second kind. We show that the two rheologies constitute a clear example of broadly similar creep and relaxation patterns associated with neatly distinct retardation spectra, for which analytical expressions are available.

  11. Ordinary differential equations

    CERN Document Server

    Greenberg, Michael D

    2014-01-01

    Features a balance between theory, proofs, and examples and provides applications across diverse fields of study Ordinary Differential Equations presents a thorough discussion of first-order differential equations and progresses to equations of higher order. The book transitions smoothly from first-order to higher-order equations, allowing readers to develop a complete understanding of the related theory. Featuring diverse and interesting applications from engineering, bioengineering, ecology, and biology, the book anticipates potential difficulties in understanding the various solution steps

  12. Fractional Schroedinger equation

    International Nuclear Information System (INIS)

    Laskin, Nick

    2002-01-01

    Some properties of the fractional Schroedinger equation are studied. We prove the Hermiticity of the fractional Hamilton operator and establish the parity conservation law for fractional quantum mechanics. As physical applications of the fractional Schroedinger equation we find the energy spectra of a hydrogenlike atom (fractional 'Bohr atom') and of a fractional oscillator in the semiclassical approximation. An equation for the fractional probability current density is developed and discussed. We also discuss the relationships between the fractional and standard Schroedinger equations

  13. Introduction to differential equations

    CERN Document Server

    Taylor, Michael E

    2011-01-01

    The mathematical formulations of problems in physics, economics, biology, and other sciences are usually embodied in differential equations. The analysis of the resulting equations then provides new insight into the original problems. This book describes the tools for performing that analysis. The first chapter treats single differential equations, emphasizing linear and nonlinear first order equations, linear second order equations, and a class of nonlinear second order equations arising from Newton's laws. The first order linear theory starts with a self-contained presentation of the exponen

  14. Stochastic optimal control, forward-backward stochastic differential equations and the Schroedinger equation

    Energy Technology Data Exchange (ETDEWEB)

    Paul, Wolfgang; Koeppe, Jeanette [Institut fuer Physik, Martin Luther Universitaet, 06099 Halle (Germany); Grecksch, Wilfried [Institut fuer Mathematik, Martin Luther Universitaet, 06099 Halle (Germany)

    2016-07-01

    The standard approach to solve a non-relativistic quantum problem is through analytical or numerical solution of the Schroedinger equation. We show a way to go around it. This way is based on the derivation of the Schroedinger equation from conservative diffusion processes and the establishment of (several) stochastic variational principles leading to the Schroedinger equation under the assumption of a kinematics described by Nelson's diffusion processes. Mathematically, the variational principle can be considered as a stochastic optimal control problem linked to the forward-backward stochastic differential equations of Nelson's stochastic mechanics. The Hamilton-Jacobi-Bellmann equation of this control problem is the Schroedinger equation. We present the mathematical background and how to turn it into a numerical scheme for analyzing a quantum system without using the Schroedinger equation and exemplify the approach for a simple 1d problem.

  15. Averaged RMHD equations

    International Nuclear Information System (INIS)

    Ichiguchi, Katsuji

    1998-01-01

    A new reduced set of resistive MHD equations is derived by averaging the full MHD equations on specified flux coordinates, which is consistent with 3D equilibria. It is confirmed that the total energy is conserved and the linearized equations for ideal modes are self-adjoint. (author)

  16. Relaxation Cycles in a Generalized Neuron Model with Two Delays

    Directory of Open Access Journals (Sweden)

    S. D. Glyzin

    2013-01-01

    Full Text Available A method of modeling the phenomenon of bursting behavior in neural systems based on delay equations is proposed. A singularly perturbed scalar nonlinear differentialdifference equation of Volterra type is a mathematical model of a neuron and a separate pulse containing one function without delay and two functions with different lags. It is established that this equation, for a suitable choice of parameters, has a stable periodic motion with any preassigned number of bursts in the time interval of the period length. To prove this assertion we first go to a relay-type equation and then determine the asymptotic solutions of a singularly perturbed equation. On the basis of this asymptotics the Poincare operator is constructed. The resulting operator carries a closed bounded convex set of initial conditions into itself, which suggests that it has at least one fixed point. The Frechet derivative evaluation of the succession operator, made in the paper, allows us to prove the uniqueness and stability of the resulting relax of the periodic solution.

  17. Differential equations

    CERN Document Server

    Tricomi, FG

    2013-01-01

    Based on his extensive experience as an educator, F. G. Tricomi wrote this practical and concise teaching text to offer a clear idea of the problems and methods of the theory of differential equations. The treatment is geared toward advanced undergraduates and graduate students and addresses only questions that can be resolved with rigor and simplicity.Starting with a consideration of the existence and uniqueness theorem, the text advances to the behavior of the characteristics of a first-order equation, boundary problems for second-order linear equations, asymptotic methods, and diff

  18. How to obtain the covariant form of Maxwell's equations from the continuity equation

    International Nuclear Information System (INIS)

    Heras, Jose A

    2009-01-01

    The covariant Maxwell equations are derived from the continuity equation for the electric charge. This result provides an axiomatic approach to Maxwell's equations in which charge conservation is emphasized as the fundamental axiom underlying these equations

  19. A generalized simplest equation method and its application to the Boussinesq-Burgers equation.

    Science.gov (United States)

    Sudao, Bilige; Wang, Xiaomin

    2015-01-01

    In this paper, a generalized simplest equation method is proposed to seek exact solutions of nonlinear evolution equations (NLEEs). In the method, we chose a solution expression with a variable coefficient and a variable coefficient ordinary differential auxiliary equation. This method can yield a Bäcklund transformation between NLEEs and a related constraint equation. By dealing with the constraint equation, we can derive infinite number of exact solutions for NLEEs. These solutions include the traveling wave solutions, non-traveling wave solutions, multi-soliton solutions, rational solutions, and other types of solutions. As applications, we obtained wide classes of exact solutions for the Boussinesq-Burgers equation by using the generalized simplest equation method.

  20. On separable Pauli equations

    International Nuclear Information System (INIS)

    Zhalij, Alexander

    2002-01-01

    We classify (1+3)-dimensional Pauli equations for a spin-(1/2) particle interacting with the electro-magnetic field, that are solvable by the method of separation of variables. As a result, we obtain the 11 classes of vector-potentials of the electro-magnetic field A(t,x(vector sign))=(A 0 (t,x(vector sign)), A(vector sign)(t,x(vector sign))) providing separability of the corresponding Pauli equations. It is established, in particular, that the necessary condition for the Pauli equation to be separable into second-order matrix ordinary differential equations is its equivalence to the system of two uncoupled Schroedinger equations. In addition, the magnetic field has to be independent of spatial variables. We prove that coordinate systems and the vector-potentials of the electro-magnetic field providing the separability of the corresponding Pauli equations coincide with those for the Schroedinger equations. Furthermore, an efficient algorithm for constructing all coordinate systems providing the separability of Pauli equation with a fixed vector-potential of the electro-magnetic field is developed. Finally, we describe all vector-potentials A(t,x(vector sign)) that (a) provide the separability of Pauli equation, (b) satisfy vacuum Maxwell equations without currents, and (c) describe non-zero magnetic field

  1. Modified Method of Simplest Equation Applied to the Nonlinear Schrödinger Equation

    Science.gov (United States)

    Vitanov, Nikolay K.; Dimitrova, Zlatinka I.

    2018-03-01

    We consider an extension of the methodology of the modified method of simplest equation to the case of use of two simplest equations. The extended methodology is applied for obtaining exact solutions of model nonlinear partial differential equations for deep water waves: the nonlinear Schrödinger equation. It is shown that the methodology works also for other equations of the nonlinear Schrödinger kind.

  2. Elliptic and solitary wave solutions for Bogoyavlenskii equations system, couple Boiti-Leon-Pempinelli equations system and Time-fractional Cahn-Allen equation

    Directory of Open Access Journals (Sweden)

    Mostafa M.A. Khater

    Full Text Available In this article and for the first time, we introduce and describe Khater method which is a new technique for solving nonlinear partial differential equations (PDEs.. We apply this method for each of the following models Bogoyavlenskii equation, couple Boiti-Leon-Pempinelli system and Time-fractional Cahn-Allen equation. Khater method is very powerful, Effective, felicitous and fabulous method to get exact and solitary wave solution of (PDEs.. Not only just like that but it considers too one of the general methods for solving that kind of equations since it involves some methods as we will see in our discuss of the results. We make a comparison between the results of this new method and another method. Keywords: Bogoyavlenskii equations system, Couple Boiti-Leon-Pempinelli equations system, Time-fractional Cahn-Allen equation, Khater method, Traveling wave solutions, Solitary wave solutions

  3. Modified Method of Simplest Equation Applied to the Nonlinear Schrödinger Equation

    Directory of Open Access Journals (Sweden)

    Vitanov Nikolay K.

    2018-03-01

    Full Text Available We consider an extension of the methodology of the modified method of simplest equation to the case of use of two simplest equations. The extended methodology is applied for obtaining exact solutions of model nonlinear partial differential equations for deep water waves: the nonlinear Schrödinger equation. It is shown that the methodology works also for other equations of the nonlinear Schrödinger kind.

  4. Feedback coupling in dynamical systems

    Science.gov (United States)

    Trimper, Steffen; Zabrocki, Knud

    2003-05-01

    Different evolution models are considered with feedback-couplings. In particular, we study the Lotka-Volterra system under the influence of a cumulative term, the Ginzburg-Landau model with a convolution memory term and chemical rate equations with time delay. The memory leads to a modified dynamical behavior. In case of a positive coupling the generalized Lotka-Volterra system exhibits a maximum gain achieved after a finite time, but the population will die out in the long time limit. In the opposite case, the time evolution is terminated in a crash. Due to the nonlinear feedback coupling the two branches of a bistable model are controlled by the the strength and the sign of the memory. For a negative coupling the system is able to switch over between both branches of the stationary solution. The dynamics of the system is further controlled by the initial condition. The diffusion-limited reaction is likewise studied in case the reacting entities are not available simultaneously. Whereas for an external feedback the dynamics is altered, but the stationary solution remain unchanged, a self-organized internal feedback leads to a time persistent solution.

  5. Integrable dissipative nonlinear second order differential equations via factorizations and Abel equations

    Energy Technology Data Exchange (ETDEWEB)

    Mancas, Stefan C. [Department of Mathematics, Embry–Riddle Aeronautical University, Daytona Beach, FL 32114-3900 (United States); Rosu, Haret C., E-mail: hcr@ipicyt.edu.mx [IPICYT, Instituto Potosino de Investigacion Cientifica y Tecnologica, Apdo Postal 3-74 Tangamanga, 78231 San Luis Potosí, SLP (Mexico)

    2013-09-02

    We emphasize two connections, one well known and another less known, between the dissipative nonlinear second order differential equations and the Abel equations which in their first-kind form have only cubic and quadratic terms. Then, employing an old integrability criterion due to Chiellini, we introduce the corresponding integrable dissipative equations. For illustration, we present the cases of some integrable dissipative Fisher, nonlinear pendulum, and Burgers–Huxley type equations which are obtained in this way and can be of interest in applications. We also show how to obtain Abel solutions directly from the factorization of second order nonlinear equations.

  6. On the Existence and the Applications of Modified Equations for Stochastic Differential Equations

    KAUST Repository

    Zygalakis, K. C.

    2011-01-01

    In this paper we describe a general framework for deriving modified equations for stochastic differential equations (SDEs) with respect to weak convergence. Modified equations are derived for a variety of numerical methods, such as the Euler or the Milstein method. Existence of higher order modified equations is also discussed. In the case of linear SDEs, using the Gaussianity of the underlying solutions, we derive an SDE which the numerical method solves exactly in the weak sense. Applications of modified equations in the numerical study of Langevin equations is also discussed. © 2011 Society for Industrial and Applied Mathematics.

  7. An Auxiliary Equation for the Bellman Equation in a One-Dimensional Ergodic Control

    International Nuclear Information System (INIS)

    Fujita, Y.

    2001-01-01

    In this paper we consider the Bellman equation in a one-dimensional ergodic control. Our aim is to show the existence and the uniqueness of its solution under general assumptions. For this purpose we introduce an auxiliary equation whose solution gives the invariant measure of the diffusion corresponding to an optimal control. Using this solution, we construct a solution to the Bellman equation. Our method of using this auxiliary equation has two advantages in the one-dimensional case. First, we can solve the Bellman equation under general assumptions. Second, this auxiliary equation gives an optimal Markov control explicitly in many examples

  8. Covariant field equations in supergravity

    Energy Technology Data Exchange (ETDEWEB)

    Vanhecke, Bram [KU Leuven, Institute for Theoretical Physics, Leuven (Belgium); Ghent University, Faculty of Physics, Gent (Belgium); Proeyen, Antoine van [KU Leuven, Institute for Theoretical Physics, Leuven (Belgium)

    2017-12-15

    Covariance is a useful property for handling supergravity theories. In this paper, we prove a covariance property of supergravity field equations: under reasonable conditions, field equations of supergravity are covariant modulo other field equations. We prove that for any supergravity there exist such covariant equations of motion, other than the regular equations of motion, that are equivalent to the latter. The relations that we find between field equations and their covariant form can be used to obtain multiplets of field equations. In practice, the covariant field equations are easily found by simply covariantizing the ordinary field equations. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

  9. Covariant field equations in supergravity

    International Nuclear Information System (INIS)

    Vanhecke, Bram; Proeyen, Antoine van

    2017-01-01

    Covariance is a useful property for handling supergravity theories. In this paper, we prove a covariance property of supergravity field equations: under reasonable conditions, field equations of supergravity are covariant modulo other field equations. We prove that for any supergravity there exist such covariant equations of motion, other than the regular equations of motion, that are equivalent to the latter. The relations that we find between field equations and their covariant form can be used to obtain multiplets of field equations. In practice, the covariant field equations are easily found by simply covariantizing the ordinary field equations. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

  10. Reduction of lattice equations to the Painlevé equations: PIV and PV

    Science.gov (United States)

    Nakazono, Nobutaka

    2018-02-01

    In this paper, we construct a new relation between Adler-Bobenko-Suris equations and Painlevé equations. Moreover, using this connection we construct the difference-differential Lax representations of the fourth and fifth Painlevé equations.

  11. Test equating methods and practices

    CERN Document Server

    Kolen, Michael J

    1995-01-01

    In recent years, many researchers in the psychology and statistical communities have paid increasing attention to test equating as issues of using multiple test forms have arisen and in response to criticisms of traditional testing techniques This book provides a practically oriented introduction to test equating which both discusses the most frequently used equating methodologies and covers many of the practical issues involved The main themes are - the purpose of equating - distinguishing between equating and related methodologies - the importance of test equating to test development and quality control - the differences between equating properties, equating designs, and equating methods - equating error, and the underlying statistical assumptions for equating The authors are acknowledged experts in the field, and the book is based on numerous courses and seminars they have presented As a result, educators, psychometricians, professionals in measurement, statisticians, and students coming to the subject for...

  12. On generalized fractional vibration equation

    International Nuclear Information System (INIS)

    Dai, Hongzhe; Zheng, Zhibao; Wang, Wei

    2017-01-01

    Highlights: • The paper presents a generalized fractional vibration equation for arbitrary viscoelastically damped system. • Some classical vibration equations can be derived from the developed equation. • The analytic solution of developed equation is derived under some special cases. • The generalized equation is particularly useful for developing new fractional equivalent linearization method. - Abstract: In this paper, a generalized fractional vibration equation with multi-terms of fractional dissipation is developed to describe the dynamical response of an arbitrary viscoelastically damped system. It is shown that many classical equations of motion, e.g., the Bagley–Torvik equation, can be derived from the developed equation. The Laplace transform is utilized to solve the generalized equation and the analytic solution under some special cases is derived. Example demonstrates the generalized transfer function of an arbitrary viscoelastic system.

  13. Differential equations for dummies

    CERN Document Server

    Holzner, Steven

    2008-01-01

    The fun and easy way to understand and solve complex equations Many of the fundamental laws of physics, chemistry, biology, and economics can be formulated as differential equations. This plain-English guide explores the many applications of this mathematical tool and shows how differential equations can help us understand the world around us. Differential Equations For Dummies is the perfect companion for a college differential equations course and is an ideal supplemental resource for other calculus classes as well as science and engineering courses. It offers step-by-step techniques, practical tips, numerous exercises, and clear, concise examples to help readers improve their differential equation-solving skills and boost their test scores.

  14. Every Equation Tells a Story: Using Equation Dictionaries in Introductory Geophysics

    Science.gov (United States)

    Caplan-Auerbach, Jacqueline

    2009-01-01

    Many students view equations as a series of variables and operators into which numbers should be plugged rather than as representative of a physical process. To solve a problem they may simply look for an equation with the correct variables and assume it meets their needs, rather than selecting an equation that represents the appropriate physical…

  15. Fundamental equations for two-phase flow. Part 1: general conservation equations. Part 2: complement and remarks; Equations fondamentales des ecoulements diphasiques. Premiere partie: equations generales de conservation. Deuxieme partie: complements et remarques

    Energy Technology Data Exchange (ETDEWEB)

    Delhaye, J M [Commissariat a l' Energie Atomique, 38 - Grenoble (France). Centre d' Etudes Nucleaires

    1968-12-01

    This report deals with the general equations of mass conservation, of momentum conservation, and energy conservation in the case of a two-phase flow. These equations are presented in several forms starting from integral equations which are assumed initially a priori. 1. Equations with local instantaneous variables, and interfacial conditions; 2. Equations with mean instantaneous variables in a cross-section, and practical applications: these equations include an important experimental value which is the ratio of the cross-section of passage of one phase to the total cross-section of a flow-tube. 3. Equations with a local statistical mean, and equations averaged over a period of time: A more advanced attempt to relate theory and experiment consists in taking the statistical averages of local equations. Equations are then obtained involving variables which are averaged over a period of time with the help of an ergodic assumption. 4. Combination of statistical averages and averages over a cross-section: in this study are considered the local variables averaged statistically, then averaged over the cross-section, and also the variables averaged over the section and then averaged statistically. 5. General equations concerning emulsions: In this case a phase exists in a locally very finely divided form. This peculiarity makes it possible to define a volume concentration, and to draw up equations which have numerous applications. - Certain points arising in the first part of this report concerning general mass conservation equations for two-phase flow have been completed and clarified. The terms corresponding to the interfacial tension have been introduced into the general equations. The interfacial conditions have thus been generalized. A supplementary step has still to be carried out: it has, in effect, been impossible to take the interfacial tension into account in the case of emulsions. It was then appeared interesting to compare this large group of fundamental

  16. Fundamental equations for two-phase flow. Part 1: general conservation equations. Part 2: complement and remarks; Equations fondamentales des ecoulements diphasiques. Premiere partie: equations generales de conservation. Deuxieme partie: complements et remarques

    Energy Technology Data Exchange (ETDEWEB)

    Delhaye, J.M. [Commissariat a l' Energie Atomique, 38 - Grenoble (France). Centre d' Etudes Nucleaires

    1968-12-01

    This report deals with the general equations of mass conservation, of momentum conservation, and energy conservation in the case of a two-phase flow. These equations are presented in several forms starting from integral equations which are assumed initially a priori. 1. Equations with local instantaneous variables, and interfacial conditions; 2. Equations with mean instantaneous variables in a cross-section, and practical applications: these equations include an important experimental value which is the ratio of the cross-section of passage of one phase to the total cross-section of a flow-tube. 3. Equations with a local statistical mean, and equations averaged over a period of time: A more advanced attempt to relate theory and experiment consists in taking the statistical averages of local equations. Equations are then obtained involving variables which are averaged over a period of time with the help of an ergodic assumption. 4. Combination of statistical averages and averages over a cross-section: in this study are considered the local variables averaged statistically, then averaged over the cross-section, and also the variables averaged over the section and then averaged statistically. 5. General equations concerning emulsions: In this case a phase exists in a locally very finely divided form. This peculiarity makes it possible to define a volume concentration, and to draw up equations which have numerous applications. - Certain points arising in the first part of this report concerning general mass conservation equations for two-phase flow have been completed and clarified. The terms corresponding to the interfacial tension have been introduced into the general equations. The interfacial conditions have thus been generalized. A supplementary step has still to be carried out: it has, in effect, been impossible to take the interfacial tension into account in the case of emulsions. It was then appeared interesting to compare this large group of fundamental

  17. Equating TIMSS Mathematics Subtests with Nonlinear Equating Methods Using NEAT Design: Circle-Arc Equating Approaches

    Science.gov (United States)

    Ozdemir, Burhanettin

    2017-01-01

    The purpose of this study is to equate Trends in International Mathematics and Science Study (TIMSS) mathematics subtest scores obtained from TIMSS 2011 to scores obtained from TIMSS 2007 form with different nonlinear observed score equating methods under Non-Equivalent Anchor Test (NEAT) design where common items are used to link two or more test…

  18. Solving polynomial differential equations by transforming them to linear functional-differential equations

    OpenAIRE

    Nahay, John Michael

    2008-01-01

    We present a new approach to solving polynomial ordinary differential equations by transforming them to linear functional equations and then solving the linear functional equations. We will focus most of our attention upon the first-order Abel differential equation with two nonlinear terms in order to demonstrate in as much detail as possible the computations necessary for a complete solution. We mention in our section on further developments that the basic transformation idea can be generali...

  19. Lorentz-force equations as Heisenberg equations for a quantum system in the euclidean space

    International Nuclear Information System (INIS)

    Rodriguez D, R.

    2007-01-01

    In an earlier work, the dynamic equations for a relativistic charged particle under the action of electromagnetic fields were formulated by R. Yamaleev in terms of external, as well as internal momenta. Evolution equations for external momenta, the Lorentz-force equations, were derived from the evolution equations for internal momenta. The mapping between the observables of external and internal momenta are related by Viete formulae for a quadratic polynomial, the characteristic polynomial of the relativistic dynamics. In this paper we show that the system of dynamic equations, can be cast into the Heisenberg scheme for a four-dimensional quantum system. Within this scheme the equations in terms of internal momenta play the role of evolution equations for a state vector, whereas the external momenta obey the Heisenberg equation for an operator evolution. The solutions of the Lorentz-force equation for the motion inside constant electromagnetic fields are presented via pentagonometric functions. (Author)

  20. Differential Equation over Banach Algebra

    OpenAIRE

    Kleyn, Aleks

    2018-01-01

    In the book, I considered differential equations of order $1$ over Banach $D$-algebra: differential equation solved with respect to the derivative; exact differential equation; linear homogeneous equation. In noncommutative Banach algebra, initial value problem for linear homogeneous equation has infinitely many solutions.

  1. Maximal monotone model with delay term of convolution

    Directory of Open Access Journals (Sweden)

    Claude-Henri Lamarque

    2005-01-01

    Full Text Available Mechanical models are governed either by partial differential equations with boundary conditions and initial conditions (e.g., in the frame of continuum mechanics or by ordinary differential equations (e.g., after discretization via Galerkin procedure or directly from the model description with the initial conditions. In order to study dynamical behavior of mechanical systems with a finite number of degrees of freedom including nonsmooth terms (e.g., friction, we consider here problems governed by differential inclusions. To describe effects of particular constitutive laws, we add a delay term. In contrast to previous papers, we introduce delay via a Volterra kernel. We provide existence and uniqueness results by using an Euler implicit numerical scheme; then convergence with its order is established. A few numerical examples are given.

  2. Heteroclinic dynamics of coupled semiconductor lasers with optoelectronic feedback.

    Science.gov (United States)

    Shahin, S; Vallini, F; Monifi, F; Rabinovich, M; Fainman, Y

    2016-11-15

    Generalized Lotka-Volterra (GLV) equations are important equations used in various areas of science to describe competitive dynamics among a population of N interacting nodes in a network topology. In this Letter, we introduce a photonic network consisting of three optoelectronically cross-coupled semiconductor lasers to realize a GLV model. In such a network, the interaction of intensity and carrier inversion rates, as well as phases of laser oscillator nodes, result in various dynamics. We study the influence of asymmetric coupling strength and frequency detuning between semiconductor lasers and show that inhibitory asymmetric coupling is required to achieve consecutive amplitude oscillations of the laser nodes. These studies were motivated primarily by the dynamical models used to model brain cognitive activities and their correspondence with dynamics obtained among coupled laser oscillators.

  3. Elements of partial differential equations

    CERN Document Server

    Sneddon, Ian Naismith

    1957-01-01

    Geared toward students of applied rather than pure mathematics, this volume introduces elements of partial differential equations. Its focus is primarily upon finding solutions to particular equations rather than general theory.Topics include ordinary differential equations in more than two variables, partial differential equations of the first and second orders, Laplace's equation, the wave equation, and the diffusion equation. A helpful Appendix offers information on systems of surfaces, and solutions to the odd-numbered problems appear at the end of the book. Readers pursuing independent st

  4. New exact solutions to MKDV-Burgers equation and (2 + 1)-dimensional dispersive long wave equation via extended Riccati equation method

    International Nuclear Information System (INIS)

    Kong Cuicui; Wang Dan; Song Lina; Zhang Hongqing

    2009-01-01

    In this paper, with the aid of symbolic computation and a general ansaetz, we presented a new extended rational expansion method to construct new rational formal exact solutions to nonlinear partial differential equations. In order to illustrate the effectiveness of this method, we apply it to the MKDV-Burgers equation and the (2 + 1)-dimensional dispersive long wave equation, then several new kinds of exact solutions are successfully obtained by using the new ansaetz. The method can also be applied to other nonlinear partial differential equations.

  5. Introduction to partial differential equations

    CERN Document Server

    Greenspan, Donald

    2000-01-01

    Designed for use in a one-semester course by seniors and beginning graduate students, this rigorous presentation explores practical methods of solving differential equations, plus the unifying theory underlying the mathematical superstructure. Topics include basic concepts, Fourier series, second-order partial differential equations, wave equation, potential equation, heat equation, approximate solution of partial differential equations, and more. Exercises appear at the ends of most chapters. 1961 edition.

  6. A New Fractional Projective Riccati Equation Method for Solving Fractional Partial Differential Equations

    International Nuclear Information System (INIS)

    Feng Qing-Hua

    2014-01-01

    In this paper, a new fractional projective Riccati equation method is proposed to establish exact solutions for fractional partial differential equations in the sense of modified Riemann—Liouville derivative. This method can be seen as the fractional version of the known projective Riccati equation method. For illustrating the validity of this method, we apply this method to solve the space-time fractional Whitham—Broer—Kaup (WBK) equations and the nonlinear fractional Sharma—Tasso—Olever (STO) equation, and as a result, some new exact solutions for them are obtained. (general)

  7. A new sine-Gordon equation expansion algorithm to investigate some special nonlinear differential equations

    International Nuclear Information System (INIS)

    Yan Zhenya

    2005-01-01

    A new transformation method is developed using the general sine-Gordon travelling wave reduction equation and a generalized transformation. With the aid of symbolic computation, this method can be used to seek more types of solutions of nonlinear differential equations, which include not only the known solutions derived by some known methods but new solutions. Here we choose the double sine-Gordon equation, the Magma equation and the generalized Pochhammer-Chree (PC) equation to illustrate the method. As a result, many types of new doubly periodic solutions are obtained. Moreover when using the method to these special nonlinear differential equations, some transformations are firstly needed. The method can be also extended to other nonlinear differential equations

  8. Singular stochastic differential equations

    CERN Document Server

    Cherny, Alexander S

    2005-01-01

    The authors introduce, in this research monograph on stochastic differential equations, a class of points termed isolated singular points. Stochastic differential equations possessing such points (called singular stochastic differential equations here) arise often in theory and in applications. However, known conditions for the existence and uniqueness of a solution typically fail for such equations. The book concentrates on the study of the existence, the uniqueness, and, what is most important, on the qualitative behaviour of solutions of singular stochastic differential equations. This is done by providing a qualitative classification of isolated singular points, into 48 possible types.

  9. Reactimeter dispersion equation

    OpenAIRE

    A.G. Yuferov

    2016-01-01

    The aim of this work is to derive and analyze a reactimeter metrological model in the form of the dispersion equation which connects reactimeter input/output signal dispersions with superimposed random noise at the inlet. It is proposed to standardize the reactimeter equation form, presenting the main reactimeter computing unit by a convolution equation. Hence, the reactimeter metrological characteristics are completely determined by this unit hardware function which represents a transient re...

  10. Symmetries and Invariants of the Time-dependent Oscillator Equation and the Envelope Equation

    CERN Document Server

    Qin, Hong

    2005-01-01

    Single-particle dynamics in a time-dependent focusing field is examined. The existence of the Courant-Snyder invariant* is fundamentally the result of the corresponding symmetry admitted by the oscillator equation with time-dependent frequency.** A careful analysis of the admitted symmetries reveals a deeper connection between the nonlinear envelope equation and the oscillator equation. A general theorem regarding the symmetries and invariants of the envelope equation, which includes the existence of the Courant-Snyder invariant as a special case, is demonstrated. The symmetries of the envelope equation enable a fast algorithm for finding matched solutions without using the conventional iterative shooting method.

  11. A generalized fractional sub-equation method for fractional differential equations with variable coefficients

    International Nuclear Information System (INIS)

    Tang, Bo; He, Yinnian; Wei, Leilei; Zhang, Xindong

    2012-01-01

    In this Letter, a generalized fractional sub-equation method is proposed for solving fractional differential equations with variable coefficients. Being concise and straightforward, this method is applied to the space–time fractional Gardner equation with variable coefficients. As a result, many exact solutions are obtained including hyperbolic function solutions, trigonometric function solutions and rational solutions. It is shown that the considered method provides a very effective, convenient and powerful mathematical tool for solving many other fractional differential equations in mathematical physics. -- Highlights: ► Study of fractional differential equations with variable coefficients plays a role in applied physical sciences. ► It is shown that the proposed algorithm is effective for solving fractional differential equations with variable coefficients. ► The obtained solutions may give insight into many considerable physical processes.

  12. True amplitude wave equation migration arising from true amplitude one-way wave equations

    Science.gov (United States)

    Zhang, Yu; Zhang, Guanquan; Bleistein, Norman

    2003-10-01

    One-way wave operators are powerful tools for use in forward modelling and inversion. Their implementation, however, involves introduction of the square root of an operator as a pseudo-differential operator. Furthermore, a simple factoring of the wave operator produces one-way wave equations that yield the same travel times as the full wave equation, but do not yield accurate amplitudes except for homogeneous media and for almost all points in heterogeneous media. Here, we present augmented one-way wave equations. We show that these equations yield solutions for which the leading order asymptotic amplitude as well as the travel time satisfy the same differential equations as the corresponding functions for the full wave equation. Exact representations of the square-root operator appearing in these differential equations are elusive, except in cases in which the heterogeneity of the medium is independent of the transverse spatial variables. Here, we address the fully heterogeneous case. Singling out depth as the preferred direction of propagation, we introduce a representation of the square-root operator as an integral in which a rational function of the transverse Laplacian appears in the integrand. This allows us to carry out explicit asymptotic analysis of the resulting one-way wave equations. To do this, we introduce an auxiliary function that satisfies a lower dimensional wave equation in transverse spatial variables only. We prove that ray theory for these one-way wave equations leads to one-way eikonal equations and the correct leading order transport equation for the full wave equation. We then introduce appropriate boundary conditions at z = 0 to generate waves at depth whose quotient leads to a reflector map and an estimate of the ray theoretical reflection coefficient on the reflector. Thus, these true amplitude one-way wave equations lead to a 'true amplitude wave equation migration' (WEM) method. In fact, we prove that applying the WEM imaging condition

  13. Non-commuting variations in mathematics and physics a survey

    CERN Document Server

    Preston, Serge

    2016-01-01

    This text presents and studies the method of so –called noncommuting variations in Variational Calculus. This method was pioneered by Vito Volterra who noticed that the conventional Euler-Lagrange (EL-) equations are not applicable in Non-Holonomic Mechanics and suggested to modify the basic rule used in Variational Calculus. This book presents a survey of Variational Calculus with non-commutative variations and shows that most basic properties of conventional Euler-Lagrange Equations are, with some modifications, preserved for EL-equations with K-twisted (defined by K)-variations. Most of the book can be understood by readers without strong mathematical preparation (some knowledge of Differential Geometry is necessary). In order to make the text more accessible the definitions and several necessary results in Geometry are presented separately in Appendices I and II Furthermore in Appendix III a short presentation of the Noether Theorem describing the relation between the symmetries of the differential equa...

  14. Defining strategies to win in the Internet market

    Science.gov (United States)

    López, Luis; Sanjuán, Miguel A. F.

    2001-12-01

    This paper analyzes a model for the competition dynamics of web sites in the Internet, based on the Lotka-Volterra competition equations. This model shows the well known appearance of a winner-take-all characteristic and is based in the nonvalidity of traditional offer and demand equilibrium theory of these kinds of markets. From the stability analysis of the model, we establish a series of rules which are useful for defining strategies in the Internet market. One of the most important results that emerge from this simple model is the appearance of some unexpected phenomena related to the collaboration and competition between sites.

  15. Dynamics of two competing species in the presence of Lévy noise sources

    Science.gov (United States)

    La Cognata, A.; Valenti, D.; Dubkov, A. A.; Spagnolo, B.

    2010-07-01

    We consider a Lotka-Volterra system of two competing species subject to multiplicative α -stable Lévy noise. The interaction parameter between the species is a random process which obeys a stochastic differential equation with a generalized bistable potential in the presence both of a periodic driving term and an additive α -stable Lévy noise. We study the species dynamics, which is characterized by two different regimes, exclusion of one species and coexistence of both. We find quasiperiodic oscillations and stochastic resonance phenomenon in the dynamics of the competing species, analyzing the role of the Lévy noise sources.

  16. First-order partial differential equations

    CERN Document Server

    Rhee, Hyun-Ku; Amundson, Neal R

    2001-01-01

    This first volume of a highly regarded two-volume text is fully usable on its own. After going over some of the preliminaries, the authors discuss mathematical models that yield first-order partial differential equations; motivations, classifications, and some methods of solution; linear and semilinear equations; chromatographic equations with finite rate expressions; homogeneous and nonhomogeneous quasilinear equations; formation and propagation of shocks; conservation equations, weak solutions, and shock layers; nonlinear equations; and variational problems. Exercises appear at the end of mo

  17. Equating Multidimensional Tests under a Random Groups Design: A Comparison of Various Equating Procedures

    Science.gov (United States)

    Lee, Eunjung

    2013-01-01

    The purpose of this research was to compare the equating performance of various equating procedures for the multidimensional tests. To examine the various equating procedures, simulated data sets were used that were generated based on a multidimensional item response theory (MIRT) framework. Various equating procedures were examined, including…

  18. Comparing the IRT Pre-equating and Section Pre-equating: A Simulation Study.

    Science.gov (United States)

    Hwang, Chi-en; Cleary, T. Anne

    The results obtained from two basic types of pre-equatings of tests were compared: the item response theory (IRT) pre-equating and section pre-equating (SPE). The simulated data were generated from a modified three-parameter logistic model with a constant guessing parameter. Responses of two replication samples of 3000 examinees on two 72-item…

  19. Exactly and completely integrable nonlinear dynamical systems

    International Nuclear Information System (INIS)

    Leznov, A.N.; Savel'ev, M.V.

    1987-01-01

    The survey is devoted to a consitent exposition of the group-algebraic methods for the integration of systems of nonlinear partial differential equations possessing a nontrivial internal symmetry algebra. Samples of exactly and completely integrable wave and evolution equations are considered in detail, including generalized (periodic and finite nonperiodic Toda lattice, nonlinear Schroedinger, Korteweg-de Vries, Lotka-Volterra equations, etc.) For exactly integrable systems the general solutions of the Cauchy and Goursat problems are given in an explicit form, while for completely integrable systems an effective method for the construction of their soliton solutions is developed. Application of the developed methods to a differential geometry problem of classification of the integrable manifolds embeddings is discussed. For exactly integrable systems the supersymmetric extensions are constructed. By the example of the generalized Toda lattice a quantization scheme is developed. It includes an explicit derivation of the corresponding Heisenberg operators and their desription in terms of the quantum algebras of the Hopf type. Among multidimensional systems the four-dimensional self-dual Yang-Mills equations are investigated most attentively with a goal of constructing their general solutions

  20. Beginning partial differential equations

    CERN Document Server

    O'Neil, Peter V

    2014-01-01

    A broad introduction to PDEs with an emphasis on specialized topics and applications occurring in a variety of fields Featuring a thoroughly revised presentation of topics, Beginning Partial Differential Equations, Third Edition provides a challenging, yet accessible,combination of techniques, applications, and introductory theory on the subjectof partial differential equations. The new edition offers nonstandard coverageon material including Burger's equation, the telegraph equation, damped wavemotion, and the use of characteristics to solve nonhomogeneous problems. The Third Edition is or

  1. A new formulation of equations of compressible fluids by analogy with Maxwell's equations

    International Nuclear Information System (INIS)

    Kambe, Tsutomu

    2010-01-01

    A compressible ideal fluid is governed by Euler's equation of motion and equations of continuity, entropy and vorticity. This system can be reformulated in a form analogous to that of electromagnetism governed by Maxwell's equations with source terms. The vorticity plays the role of magnetic field, while the velocity field plays the part of a vector potential and the enthalpy (of isentropic flows) plays the part of a scalar potential in electromagnetism. The evolution of source terms of fluid Maxwell equations is determined by solving the equations of motion and continuity. The equation of sound waves can be derived from this formulation, where time evolution of the sound source is determined by the equation of motion. The theory of vortex sound of aeroacoustics is included in this formulation. It is remarkable that the forces acting on a point mass moving in a velocity field of an inviscid fluid are analogous in their form to the electric force and Lorentz force in electromagnetism. The significance of the reformulation is interpreted by examples taken from fluid mechanics. This formulation can be extended to viscous fluids without difficulty. The Maxwell-type equations are unchanged by the viscosity effect, although the source terms have additional terms due to viscosities.

  2. Degenerate nonlinear diffusion equations

    CERN Document Server

    Favini, Angelo

    2012-01-01

    The aim of these notes is to include in a uniform presentation style several topics related to the theory of degenerate nonlinear diffusion equations, treated in the mathematical framework of evolution equations with multivalued m-accretive operators in Hilbert spaces. The problems concern nonlinear parabolic equations involving two cases of degeneracy. More precisely, one case is due to the vanishing of the time derivative coefficient and the other is provided by the vanishing of the diffusion coefficient on subsets of positive measure of the domain. From the mathematical point of view the results presented in these notes can be considered as general results in the theory of degenerate nonlinear diffusion equations. However, this work does not seek to present an exhaustive study of degenerate diffusion equations, but rather to emphasize some rigorous and efficient techniques for approaching various problems involving degenerate nonlinear diffusion equations, such as well-posedness, periodic solutions, asympt...

  3. Computational partial differential equations using Matlab

    CERN Document Server

    Li, Jichun

    2008-01-01

    Brief Overview of Partial Differential Equations The parabolic equations The wave equations The elliptic equations Differential equations in broader areasA quick review of numerical methods for PDEsFinite Difference Methods for Parabolic Equations Introduction Theoretical issues: stability, consistence, and convergence 1-D parabolic equations2-D and 3-D parabolic equationsNumerical examples with MATLAB codesFinite Difference Methods for Hyperbolic Equations IntroductionSome basic difference schemes Dissipation and dispersion errors Extensions to conservation lawsThe second-order hyperbolic PDE

  4. Integrable systems of partial differential equations determined by structure equations and Lax pair

    International Nuclear Information System (INIS)

    Bracken, Paul

    2010-01-01

    It is shown how a system of evolution equations can be developed both from the structure equations of a submanifold embedded in three-space as well as from a matrix SO(6) Lax pair. The two systems obtained this way correspond exactly when a constraint equation is selected and imposed on the system of equations. This allows for the possibility of selecting the coefficients in the second fundamental form in a general way.

  5. Drift-Diffusion Equation

    Directory of Open Access Journals (Sweden)

    K. Banoo

    1998-01-01

    equation in the discrete momentum space. This is shown to be similar to the conventional drift-diffusion equation except that it is a more rigorous solution to the Boltzmann equation because the current and carrier densities are resolved into M×1 vectors, where M is the number of modes in the discrete momentum space. The mobility and diffusion coefficient become M×M matrices which connect the M momentum space modes. This approach is demonstrated by simulating electron transport in bulk silicon.

  6. Symmetries of the Euler compressible flow equations for general equation of state

    Energy Technology Data Exchange (ETDEWEB)

    Boyd, Zachary M. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Ramsey, Scott D. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Baty, Roy S. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

    2015-10-15

    The Euler compressible flow equations exhibit different Lie symmetries depending on the equation of state (EOS) of the medium in which the flow occurs. This means that, in general, different types of similarity solution will be available in different flow media. We present a comprehensive classification of all EOS’s to which the Euler equations apply, based on the Lie symmetries admitted by the corresponding flow equations, restricting to the case of 1-D planar, cylindrical, or spherical geometry. The results are conveniently summarized in tables. This analysis also clarifies past work by Axford and Ovsiannikov on symmetry classification.

  7. Alternatives to the Dirac equation

    International Nuclear Information System (INIS)

    Girvin, S.M.; Brownstein, K.R.

    1975-01-01

    Recent work by Biedenharn, Han, and van Dam (BHvD) has questioned the uniqueness of the Dirac equation. BHvD have obtained a two-component equation as an alternate to the Dirac equation. Although they later show their alternative to be unitarily equivalent to the Dirac equation, certain physical differences were claimed. BHvD attribute the existence of this alternate equation to the fact that their factorizing matrices were position-dependent. To investigate this, we factor the Klein-Gordon equation in spherical coordinates allowing the factorizing matrices to depend arbitrarily upon theta and phi. It is shown that despite this additional freedom, and without involving any relativistic covariance, the conventional four-component Dirac equation is the only possibility

  8. Nonlinear differential equations

    Energy Technology Data Exchange (ETDEWEB)

    Dresner, L.

    1988-01-01

    This report is the text of a graduate course on nonlinear differential equations given by the author at the University of Wisconsin-Madison during the summer of 1987. The topics covered are: direction fields of first-order differential equations; the Lie (group) theory of ordinary differential equations; similarity solutions of second-order partial differential equations; maximum principles and differential inequalities; monotone operators and iteration; complementary variational principles; and stability of numerical methods. The report should be of interest to graduate students, faculty, and practicing scientists and engineers. No prior knowledge is required beyond a good working knowledge of the calculus. The emphasis is on practical results. Most of the illustrative examples are taken from the fields of nonlinear diffusion, heat and mass transfer, applied superconductivity, and helium cryogenics.

  9. Nonlinear differential equations

    International Nuclear Information System (INIS)

    Dresner, L.

    1988-01-01

    This report is the text of a graduate course on nonlinear differential equations given by the author at the University of Wisconsin-Madison during the summer of 1987. The topics covered are: direction fields of first-order differential equations; the Lie (group) theory of ordinary differential equations; similarity solutions of second-order partial differential equations; maximum principles and differential inequalities; monotone operators and iteration; complementary variational principles; and stability of numerical methods. The report should be of interest to graduate students, faculty, and practicing scientists and engineers. No prior knowledge is required beyond a good working knowledge of the calculus. The emphasis is on practical results. Most of the illustrative examples are taken from the fields of nonlinear diffusion, heat and mass transfer, applied superconductivity, and helium cryogenics

  10. Semilinear Schrödinger equations

    CERN Document Server

    Cazenave, Thierry

    2003-01-01

    The nonlinear Schrödinger equation has received a great deal of attention from mathematicians, in particular because of its applications to nonlinear optics. It is also a good model dispersive equation, since it is often technically simpler than other dispersive equations, such as the wave or Korteweg-de Vries equation. Particularly useful tools in studying the nonlinear Schrödinger equation are energy and Strichartz's estimates. This book presents various mathematical aspects of the nonlinear Schrödinger equation. It examines both problems of local nature (local existence of solutions, unique

  11. Quantum linear Boltzmann equation

    International Nuclear Information System (INIS)

    Vacchini, Bassano; Hornberger, Klaus

    2009-01-01

    We review the quantum version of the linear Boltzmann equation, which describes in a non-perturbative fashion, by means of scattering theory, how the quantum motion of a single test particle is affected by collisions with an ideal background gas. A heuristic derivation of this Lindblad master equation is presented, based on the requirement of translation-covariance and on the relation to the classical linear Boltzmann equation. After analyzing its general symmetry properties and the associated relaxation dynamics, we discuss a quantum Monte Carlo method for its numerical solution. We then review important limiting forms of the quantum linear Boltzmann equation, such as the case of quantum Brownian motion and pure collisional decoherence, as well as the application to matter wave optics. Finally, we point to the incorporation of quantum degeneracies and self-interactions in the gas by relating the equation to the dynamic structure factor of the ambient medium, and we provide an extension of the equation to include internal degrees of freedom.

  12. Exact Solutions to Nonlinear Schroedinger Equation and Higher-Order Nonlinear Schroedinger Equation

    International Nuclear Information System (INIS)

    Ren Ji; Ruan Hangyu

    2008-01-01

    We study solutions of the nonlinear Schroedinger equation (NLSE) and higher-order nonlinear Schroedinger equation (HONLSE) with variable coefficients. By considering all the higher-order effect of HONLSE as a new dependent variable, the NLSE and HONLSE can be changed into one equation. Using the generalized Lie group reduction method (GLGRM), the abundant solutions of NLSE and HONLSE are obtained

  13. Nonlinear diffusion equations

    CERN Document Server

    Wu Zhuo Qun; Li Hui Lai; Zhao Jun Ning

    2001-01-01

    Nonlinear diffusion equations, an important class of parabolic equations, come from a variety of diffusion phenomena which appear widely in nature. They are suggested as mathematical models of physical problems in many fields, such as filtration, phase transition, biochemistry and dynamics of biological groups. In many cases, the equations possess degeneracy or singularity. The appearance of degeneracy or singularity makes the study more involved and challenging. Many new ideas and methods have been developed to overcome the special difficulties caused by the degeneracy and singularity, which

  14. On the F-equation

    International Nuclear Information System (INIS)

    Kalinowski, M.W.; Szymanowski, L.

    1982-03-01

    A generalization of the Truesdell F-equations is proposed and some solutions to them - generalized Fox F-functions - are found. It is also shown that a non-linear difference-differential equation, which does not belong to the Truesdell class, nevertheless may be transformed into the standard F-equation. (author)

  15. How to obtain the covariant form of Maxwell's equations from the continuity equation

    Energy Technology Data Exchange (ETDEWEB)

    Heras, Jose A [Departamento de Ciencias Basicas, Universidad Autonoma Metropolitana, Unidad Azcapotzalco, Av. San Pablo No. 180, Col. Reynosa, 02200, Mexico D. F. (Mexico); Departamento de Fisica y Matematicas, Universidad Iberoamericana, Prolongacion Paseo de la Reforma 880, Mexico D. F. 01210 (Mexico)

    2009-07-15

    The covariant Maxwell equations are derived from the continuity equation for the electric charge. This result provides an axiomatic approach to Maxwell's equations in which charge conservation is emphasized as the fundamental axiom underlying these equations.

  16. Linear integral equations and soliton systems

    International Nuclear Information System (INIS)

    Quispel, G.R.W.

    1983-01-01

    A study is presented of classical integrable dynamical systems in one temporal and one spatial dimension. The direct linearizations are given of several nonlinear partial differential equations, for example the Korteweg-de Vries equation, the modified Korteweg-de Vries equation, the sine-Gordon equation, the nonlinear Schroedinger equation, and the equation of motion for the isotropic Heisenberg spin chain; the author also discusses several relations between these equations. The Baecklund transformations of these partial differential equations are treated on the basis of a singular transformation of the measure (or equivalently of the plane-wave factor) occurring in the corresponding linear integral equations, and the Baecklund transformations are used to derive the direct linearization of a chain of so-called modified partial differential equations. Finally it is shown that the singular linear integral equations lead in a natural way to the direct linearizations of various nonlinear difference-difference equations. (Auth.)

  17. Lectures on partial differential equations

    CERN Document Server

    Petrovsky, I G

    1992-01-01

    Graduate-level exposition by noted Russian mathematician offers rigorous, transparent, highly readable coverage of classification of equations, hyperbolic equations, elliptic equations and parabolic equations. Wealth of commentary and insight invaluable for deepening understanding of problems considered in text. Translated from the Russian by A. Shenitzer.

  18. Reduction operators of Burgers equation.

    Science.gov (United States)

    Pocheketa, Oleksandr A; Popovych, Roman O

    2013-02-01

    The solution of the problem on reduction operators and nonclassical reductions of the Burgers equation is systematically treated and completed. A new proof of the theorem on the special "no-go" case of regular reduction operators is presented, and the representation of the coefficients of operators in terms of solutions of the initial equation is constructed for this case. All possible nonclassical reductions of the Burgers equation to single ordinary differential equations are exhaustively described. Any Lie reduction of the Burgers equation proves to be equivalent via the Hopf-Cole transformation to a parameterized family of Lie reductions of the linear heat equation.

  19. The magnetic field experiment onboard Equator-S and its scientific possibilities

    Directory of Open Access Journals (Sweden)

    K.-H. Fornacon

    1999-12-01

    Full Text Available The special feature of the ringcore fluxgate magnetometer on Equator-S is the high time and field resolution. The scientific aim of the experiment is the investigation of waves in the 10–100 picotesla range with a time resolution up to 64 Hz. The instrument characteristics and the influence of the spacecraft on the magnetic field measurement will be discussed. The work shows that the applied pre- and inflight calibration techniques are sufficient to suppress spacecraft interferences. The offset in spin axis direction was determined for the first time with an independent field measurement by the Equator-S Electron Drift Instrument. The data presented gives an impression of the accuracy of the measurement.Key words. Magnetospheric physics (instruments and techniques · Space plasma physics (instruments and techniques

  20. The magnetic field experiment onboard Equator-S and its scientific possibilities

    Directory of Open Access Journals (Sweden)

    K.-H. Fornacon

    Full Text Available The special feature of the ringcore fluxgate magnetometer on Equator-S is the high time and field resolution. The scientific aim of the experiment is the investigation of waves in the 10–100 picotesla range with a time resolution up to 64 Hz. The instrument characteristics and the influence of the spacecraft on the magnetic field measurement will be discussed. The work shows that the applied pre- and inflight calibration techniques are sufficient to suppress spacecraft interferences. The offset in spin axis direction was determined for the first time with an independent field measurement by the Equator-S Electron Drift Instrument. The data presented gives an impression of the accuracy of the measurement.

    Key words. Magnetospheric physics (instruments and techniques · Space plasma physics (instruments and techniques

  1. Methods for Equating Mental Tests.

    Science.gov (United States)

    1984-11-01

    1983) compared conventional and IRT methods for equating the Test of English as a Foreign Language ( TOEFL ) after chaining. Three conventional and...three IRT equating methods were examined in this study; two sections of TOEFL were each (separately) equated. The IRT methods included the following: (a...group. A separate base form was established for each of the six equating methods. Instead of equating the base-form TOEFL to itself, the last (eighth

  2. Supersymmetric quasipotential equations

    International Nuclear Information System (INIS)

    Zaikov, R.P.

    1981-01-01

    A supersymmetric extension of the Logunov-Tavkhelidze quasipotential approach is suggested. The supersymmetric Bethe- Salpeter equation is an initial equation. The transition from the four-time to the two-time Green function is made in the super- center-of-mass system. The two-time Green function has no inverse function in the whole spinor space. The resolvent operator if found using the Majorana character of the spinor wave function. The supersymmetric quasipotential equation is written. The consideration is carried out in the framework of the theory of chiral scalar superfields [ru

  3. Ordinary differential equations

    CERN Document Server

    Miller, Richard K

    1982-01-01

    Ordinary Differential Equations is an outgrowth of courses taught for a number of years at Iowa State University in the mathematics and the electrical engineering departments. It is intended as a text for a first graduate course in differential equations for students in mathematics, engineering, and the sciences. Although differential equations is an old, traditional, and well-established subject, the diverse backgrounds and interests of the students in a typical modern-day course cause problems in the selection and method of presentation of material. In order to compensate for this diversity,

  4. Uncertain differential equations

    CERN Document Server

    Yao, Kai

    2016-01-01

    This book introduces readers to the basic concepts of and latest findings in the area of differential equations with uncertain factors. It covers the analytic method and numerical method for solving uncertain differential equations, as well as their applications in the field of finance. Furthermore, the book provides a number of new potential research directions for uncertain differential equation. It will be of interest to researchers, engineers and students in the fields of mathematics, information science, operations research, industrial engineering, computer science, artificial intelligence, automation, economics, and management science.

  5. Introduction to nonlinear dispersive equations

    CERN Document Server

    Linares, Felipe

    2015-01-01

    This textbook introduces the well-posedness theory for initial-value problems of nonlinear, dispersive partial differential equations, with special focus on two key models, the Korteweg–de Vries equation and the nonlinear Schrödinger equation. A concise and self-contained treatment of background material (the Fourier transform, interpolation theory, Sobolev spaces, and the linear Schrödinger equation) prepares the reader to understand the main topics covered: the initial-value problem for the nonlinear Schrödinger equation and the generalized Korteweg–de Vries equation, properties of their solutions, and a survey of general classes of nonlinear dispersive equations of physical and mathematical significance. Each chapter ends with an expert account of recent developments and open problems, as well as exercises. The final chapter gives a detailed exposition of local well-posedness for the nonlinear Schrödinger equation, taking the reader to the forefront of recent research. The second edition of Introdu...

  6. Generalized Lorentz-Force equations

    International Nuclear Information System (INIS)

    Yamaleev, R.M.

    2001-01-01

    Guided by Nambu (n+1)-dimensional phase space formalism we build a new system of dynamic equations. These equations describe a dynamic state of the corporeal system composed of n subsystems. The dynamic equations are formulated in terms of dynamic variables of the subsystems as well as in terms of dynamic variables of the corporeal system. These two sets of variables are related respectively as roots and coefficients of the n-degree polynomial equation. In the special n=2 case, this formalism reproduces relativistic dynamics for the charged spinning particles

  7. A new evolution equation

    International Nuclear Information System (INIS)

    Laenen, E.

    1995-01-01

    We propose a new evolution equation for the gluon density relevant for the region of small x B . It generalizes the GLR equation and allows deeper penetration in dense parton systems than the GLR equation does. This generalization consists of taking shadowing effects more comprehensively into account by including multigluon correlations, and allowing for an arbitrary initial gluon distribution in a hadron. We solve the new equation for fixed α s . We find that the effects of multigluon correlations on the deep-inelastic structure function are small. (orig.)

  8. Thermoviscous Model Equations in Nonlinear Acoustics

    DEFF Research Database (Denmark)

    Rasmussen, Anders Rønne

    Four nonlinear acoustical wave equations that apply to both perfect gasses and arbitrary fluids with a quadratic equation of state are studied. Shock and rarefaction wave solutions to the equations are studied. In order to assess the accuracy of the wave equations, their solutions are compared...... to solutions of the basic equations from which the wave equations are derived. A straightforward weakly nonlinear equation is the most accurate for shock modeling. A higher order wave equation is the most accurate for modeling of smooth disturbances. Investigations of the linear stability properties...... of solutions to the wave equations, reveal that the solutions may become unstable. Such instabilities are not found in the basic equations. Interacting shocks and standing shocks are investigated....

  9. Invalidity of the spectral Fokker-Planck equation forCauchy noise driven Langevin equation

    DEFF Research Database (Denmark)

    Ditlevsen, Ove Dalager

    2004-01-01

    -called alpha-stable noise (or Levy noise) the Fokker-Planck equation no longer exists as a partial differential equation for the probability density because the property of finite variance is lost. In stead it has been attempted to formulate an equation for the characteristic function (the Fourier transform...

  10. Difference equations theory, applications and advanced topics

    CERN Document Server

    Mickens, Ronald E

    2015-01-01

    THE DIFFERENCE CALCULUS GENESIS OF DIFFERENCE EQUATIONS DEFINITIONS DERIVATION OF DIFFERENCE EQUATIONS EXISTENCE AND UNIQUENESS THEOREM OPERATORS ∆ AND E ELEMENTARY DIFFERENCE OPERATORS FACTORIAL POLYNOMIALS OPERATOR ∆−1 AND THE SUM CALCULUS FIRST-ORDER DIFFERENCE EQUATIONS INTRODUCTION GENERAL LINEAR EQUATION CONTINUED FRACTIONS A GENERAL FIRST-ORDER EQUATION: GEOMETRICAL METHODS A GENERAL FIRST-ORDER EQUATION: EXPANSION TECHNIQUES LINEAR DIFFERENCE EQUATIONSINTRODUCTION LINEARLY INDEPENDENT FUNCTIONS FUNDAMENTAL THEOREMS FOR HOMOGENEOUS EQUATIONSINHOMOGENEOUS EQUATIONS SECOND-ORDER EQUATIONS STURM-LIOUVILLE DIFFERENCE EQUATIONS LINEAR DIFFERENCE EQUATIONS INTRODUCTION HOMOGENEOUS EQUATIONS CONSTRUCTION OF A DIFFERENCE EQUATION HAVING SPECIFIED SOLUTIONS RELATIONSHIP BETWEEN LINEAR DIFFERENCE AND DIFFERENTIAL EQUATIONS INHOMOGENEOUS EQUATIONS: METHOD OF UNDETERMINED COEFFICIENTS INHOMOGENEOUS EQUATIONS: OPERATOR METHODS z-TRANSFORM METHOD SYSTEMS OF DIFFERENCE EQUATIONS LINEAR PARTIAL DIFFERENCE EQUATI...

  11. Weak self-adjoint differential equations

    International Nuclear Information System (INIS)

    Gandarias, M L

    2011-01-01

    The concepts of self-adjoint and quasi self-adjoint equations were introduced by Ibragimov (2006 J. Math. Anal. Appl. 318 742-57; 2007 Arch. ALGA 4 55-60). In Ibragimov (2007 J. Math. Anal. Appl. 333 311-28), a general theorem on conservation laws was proved. In this paper, we generalize the concept of self-adjoint and quasi self-adjoint equations by introducing the definition of weak self-adjoint equations. We find a class of weak self-adjoint quasi-linear parabolic equations. The property of a differential equation to be weak self-adjoint is important for constructing conservation laws associated with symmetries of the differential equation. (fast track communication)

  12. Solutions of system of P1 equations without use of auxiliary differential equations coupled

    International Nuclear Information System (INIS)

    Martinez, Aquilino Senra; Silva, Fernando Carvalho da; Cardoso, Carlos Eduardo Santos

    2000-01-01

    The system of P1 equations is composed by two equations coupled itself one for the neutron flux and other for the current. Usually this system is solved by definitions of two integrals parameters, which are named slowing down densities of the flux and the current. Hence, the system P1 can be change from integral to only two differential equations. However, there are two new differentials equations that may be solved with the initial system. The present work analyzes this procedure and studies a method, which solve the P1 equations directly, without definitions of slowing down densities. (author)

  13. Equations of radiation hydrodynamics

    International Nuclear Information System (INIS)

    Mihalas, D.

    1982-01-01

    The purpose of this paper is to give an overview of the role of radiation in the transport of energy and momentum in a combined matter-radiation fluid. The transport equation for a moving radiating fluid is presented in both a fully Eulerian and a fully Lagrangian formulation, along with conservation equations describing the dynamics of the fluid. Special attention is paid to the problem of deriving equations that are mutually consistent in each frame, and between frames, to 0(v/c). A detailed analysis is made to show that in situations of broad interest, terms that are formally of 0(v/c) actually dominate the solution, demonstrating that it is esential (1) to pay scrupulous attention to the question of the frame dependence in formulating the equations; and (2) to solve the equations to 0(v/c) in quite general circumstances. These points are illustrated in the context of the nonequilibrium radiation diffusion limit, and a sketch of how the Lagrangian equations are to be solved will be presented

  14. The numerical solution of linear multi-term fractional differential equations: systems of equations

    Science.gov (United States)

    Edwards, John T.; Ford, Neville J.; Simpson, A. Charles

    2002-11-01

    In this paper, we show how the numerical approximation of the solution of a linear multi-term fractional differential equation can be calculated by reduction of the problem to a system of ordinary and fractional differential equations each of order at most unity. We begin by showing how our method applies to a simple class of problems and we give a convergence result. We solve the Bagley Torvik equation as an example. We show how the method can be applied to a general linear multi-term equation and give two further examples.

  15. A Comparison of Kernel Equating and Traditional Equipercentile Equating Methods and the Parametric Bootstrap Methods for Estimating Standard Errors in Equipercentile Equating

    Science.gov (United States)

    Choi, Sae Il

    2009-01-01

    This study used simulation (a) to compare the kernel equating method to traditional equipercentile equating methods under the equivalent-groups (EG) design and the nonequivalent-groups with anchor test (NEAT) design and (b) to apply the parametric bootstrap method for estimating standard errors of equating. A two-parameter logistic item response…

  16. Monge-Ampere equations and tensorial functors

    International Nuclear Information System (INIS)

    Tunitsky, Dmitry V

    2009-01-01

    We consider differential-geometric structures associated with Monge-Ampere equations on manifolds and use them to study the contact linearization of such equations. We also consider the category of Monge-Ampere equations (the morphisms are contact diffeomorphisms) and a number of subcategories. We are chiefly interested in subcategories of Monge-Ampere equations whose objects are locally contact equivalent to equations linear in the second derivatives (semilinear equations), linear in derivatives, almost linear, linear in the second derivatives and independent of the first derivatives, linear, linear and independent of the first derivatives, equations with constant coefficients or evolution equations. We construct a number of functors from the category of Monge-Ampere equations and from some of its subcategories to the category of tensorial objects (that is, multi-valued sections of tensor bundles). In particular, we construct a pseudo-Riemannian metric for every generic Monge-Ampere equation. These functors enable us to establish effectively verifiable criteria for a Monge-Ampere equation to belong to the subcategories listed above.

  17. Nonlinear integrodifferential equations as discrete systems

    Science.gov (United States)

    Tamizhmani, K. M.; Satsuma, J.; Grammaticos, B.; Ramani, A.

    1999-06-01

    We analyse a class of integrodifferential equations of the `intermediate long wave' (ILW) type. We show that these equations can be formally interpreted as discrete, differential-difference systems. This allows us to link equations of this type with previous results of ours involving differential-delay equations and, on the basis of this, propose new integrable equations of ILW type. Finally, we extend this approach to pure difference equations and propose ILW forms for the discrete lattice KdV equation.

  18. Analytic solutions of hydrodynamics equations

    International Nuclear Information System (INIS)

    Coggeshall, S.V.

    1991-01-01

    Many similarity solutions have been found for the equations of one-dimensional (1-D) hydrodynamics. These special combinations of variables allow the partial differential equations to be reduced to ordinary differential equations, which must then be solved to determine the physical solutions. Usually, these reduced ordinary differential equations are solved numerically. In some cases it is possible to solve these reduced equations analytically to obtain explicit solutions. In this work a collection of analytic solutions of the 1-D hydrodynamics equations is presented. These can be used for a variety of purposes, including (i) numerical benchmark problems, (ii) as a basis for analytic models, and (iii) to provide insight into more complicated solutions

  19. The modified simplest equation method to look for exact solutions of nonlinear partial differential equations

    OpenAIRE

    Efimova, Olga Yu.

    2010-01-01

    The modification of simplest equation method to look for exact solutions of nonlinear partial differential equations is presented. Using this method we obtain exact solutions of generalized Korteweg-de Vries equation with cubic source and exact solutions of third-order Kudryashov-Sinelshchikov equation describing nonlinear waves in liquids with gas bubbles.

  20. Equationally Noetherian property of Ershov algebras

    OpenAIRE

    Dvorzhetskiy, Yuriy

    2014-01-01

    This article is about equationally Noetherian and weak equationally Noetherian property of Ershov algebras. Here we show two canonical forms of the system of equations over Ershov algebras and two criteria of equationally Noetherian and weak equationally Noetherian properties.

  1. Differential equations extended to superspace

    International Nuclear Information System (INIS)

    Torres, J.; Rosu, H.C.

    2003-01-01

    We present a simple SUSY Ns = 2 superspace extension of the differential equations in which the sought solutions are considered to be real superfields but maintaining the common derivative operators and the coefficients of the differential equations unaltered. In this way, we get self consistent systems of coupled differential equations for the components of the superfield. This procedure is applied to the Riccati equation, for which we obtain in addition the system of coupled equations corresponding to the components of the general superfield solution. (Author)

  2. Differential equations extended to superspace

    Energy Technology Data Exchange (ETDEWEB)

    Torres, J. [Instituto de Fisica, Universidad de Guanajuato, A.P. E-143, Leon, Guanajuato (Mexico); Rosu, H.C. [Instituto Potosino de Investigacion Cientifica y Tecnologica, A.P. 3-74, Tangamanga, San Luis Potosi (Mexico)

    2003-07-01

    We present a simple SUSY Ns = 2 superspace extension of the differential equations in which the sought solutions are considered to be real superfields but maintaining the common derivative operators and the coefficients of the differential equations unaltered. In this way, we get self consistent systems of coupled differential equations for the components of the superfield. This procedure is applied to the Riccati equation, for which we obtain in addition the system of coupled equations corresponding to the components of the general superfield solution. (Author)

  3. Integral equation for inhomogeneous condensed bosons generalizing the Gross-Pitaevskii differential equation

    International Nuclear Information System (INIS)

    Angilella, G.G.N.; Pucci, R.; March, N.H.

    2004-01-01

    We give here the derivation of a Gross-Pitaevskii-type equation for inhomogeneous condensed bosons. Instead of the original Gross-Pitaevskii differential equation, we obtain an integral equation that implies less restrictive assumptions than are made in the very recent study of Pieri and Strinati [Phys. Rev. Lett. 91, 030401 (2003)]. In particular, the Thomas-Fermi approximation and the restriction to small spatial variations of the order parameter invoked in their study are avoided

  4. Iterative Splitting Methods for Differential Equations

    CERN Document Server

    Geiser, Juergen

    2011-01-01

    Iterative Splitting Methods for Differential Equations explains how to solve evolution equations via novel iterative-based splitting methods that efficiently use computational and memory resources. It focuses on systems of parabolic and hyperbolic equations, including convection-diffusion-reaction equations, heat equations, and wave equations. In the theoretical part of the book, the author discusses the main theorems and results of the stability and consistency analysis for ordinary differential equations. He then presents extensions of the iterative splitting methods to partial differential

  5. Algorithm for research of mathematical physics equations symmetries. Symmetries of the free Schroedinger equation

    International Nuclear Information System (INIS)

    Kotel'nikov, G.A.

    1994-01-01

    An algorithm id proposed for research the symmetries of mathematical physics equation. The application of this algorithm to the Schroedinger equation permitted to establish, that in addition to the known symmetry the Schroedinger equation possesses also the relativistic symmetry

  6. Generalized quantal equation of motion

    International Nuclear Information System (INIS)

    Morsy, M.W.; Embaby, M.

    1986-07-01

    In the present paper, an attempt is made for establishing a generalized equation of motion for quantal objects, in which intrinsic self adjointness is naturally built in, independently of any prescribed representation. This is accomplished by adopting Hamilton's principle of least action, after incorporating, properly, the quantal features and employing the generalized calculus of variations, without being restricted to fixed end points representation. It turns out that our proposed equation of motion is an intrinsically self-adjoint Euler-Lagrange's differential equation that ensures extremization of the quantal action as required by Hamilton's principle. Time dependence is introduced and the corresponding equation of motion is derived, in which intrinsic self adjointness is also achieved. Reducibility of the proposed equation of motion to the conventional Schroedinger equation is examined. The corresponding continuity equation is established, and both of the probability density and the probability current density are identified. (author)

  7. On orthogonality preserving quadratic stochastic operators

    Energy Technology Data Exchange (ETDEWEB)

    Mukhamedov, Farrukh; Taha, Muhammad Hafizuddin Mohd [Department of Computational and Theoretical Sciences, Faculty of Science International Islamic University Malaysia, P.O. Box 141, 25710 Kuantan, Pahang Malaysia (Malaysia)

    2015-05-15

    A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. In the present paper, we first give a simple characterization of Volterra QSO in terms of absolutely continuity of discrete measures. Further, we introduce a notion of orthogonal preserving QSO, and describe such kind of operators defined on two dimensional simplex. It turns out that orthogonal preserving QSOs are permutations of Volterra QSO. The associativity of genetic algebras generated by orthogonal preserving QSO is studied too.

  8. On orthogonality preserving quadratic stochastic operators

    International Nuclear Information System (INIS)

    Mukhamedov, Farrukh; Taha, Muhammad Hafizuddin Mohd

    2015-01-01

    A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. In the present paper, we first give a simple characterization of Volterra QSO in terms of absolutely continuity of discrete measures. Further, we introduce a notion of orthogonal preserving QSO, and describe such kind of operators defined on two dimensional simplex. It turns out that orthogonal preserving QSOs are permutations of Volterra QSO. The associativity of genetic algebras generated by orthogonal preserving QSO is studied too

  9. Higher order field equations. II

    International Nuclear Information System (INIS)

    Tolhoek, H.A.

    1977-01-01

    In a previous paper wave propagation was studied according to a sixth-order partial differential equation involving a complex mass M. The corresponding Yang-Feldman integral equations (indicated as SM-YF-equations), were formulated using modified Green's functions Gsub(R)sup(M)(x) and Gsub(A)sup(M)(x), which then incorporate the partial differential equation together with certain boundary conditions. In this paper certain limit properties of these modified Green's functions are derived: (a) It is shown that for mod(M)→infinity the Green's functions Gsub(R)sup(M)(x) and Gsub(A)sup(M)(x) approach the Green's functions Δsub(R)(x) and Δsub(A)(x) of the corresponding KG-equation (Klein-Gordon equation). (b) It is further shown that the asymptotic behaviour of Gsub(R)sup(M)(x) and Gsub(A)sup(M)(x) is the same as of Δsub(R)(x) and Δsub(A)(x)-and also the same as for Dsub(R)(x) and Dsub(A)(x) for t→+-infinity;, where Dsub(R) and Dsub(A) are the Green's functions for the KG-equation with mass zero. It is essential to take limits in the sense of distribution theory in both cases (a) and (b). The property (b) indicates that the wave propagation properties of the SM-YF-equations, the KG-equation with finite mass and the KG-equation with mass zero are closely related in an asymptotic sense. (Auth.)

  10. Bäcklund transformation of fractional Riccati equation and its applications to nonlinear fractional partial differential equations

    International Nuclear Information System (INIS)

    Lu, Bin

    2012-01-01

    In this Letter, the fractional derivatives in the sense of modified Riemann–Liouville derivative and the Bäcklund transformation of fractional Riccati equation are employed for constructing the exact solutions of nonlinear fractional partial differential equations. The power of this manageable method is presented by applying it to several examples. This approach can also be applied to other nonlinear fractional differential equations. -- Highlights: ► Backlund transformation of fractional Riccati equation is presented. ► A new method for solving nonlinear fractional differential equations is proposed. ► Three important fractional differential equations are solved successfully. ► Some new exact solutions of the fractional differential equations are obtained.

  11. Equational type logic

    NARCIS (Netherlands)

    Manca, V.; Salibra, A.; Scollo, Giuseppe

    1990-01-01

    Equational type logic is an extension of (conditional) equational logic, that enables one to deal in a single, unified framework with diverse phenomena such as partiality, type polymorphism and dependent types. In this logic, terms may denote types as well as elements, and atomic formulae are either

  12. Reduced Braginskii equations

    International Nuclear Information System (INIS)

    Yagi, M.; Horton, W.

    1994-01-01

    A set of reduced Braginskii equations is derived without assuming flute ordering and the Boussinesq approximation. These model equations conserve the physical energy. It is crucial at finite β that the perpendicular component of Ohm's law be solved to ensure ∇·j=0 for energy conservation

  13. Model Compaction Equation

    African Journals Online (AJOL)

    The currently proposed model compaction equation was derived from data sourced from the. Niger Delta and it relates porosity to depth for sandstones under hydrostatic pressure condition. The equation is useful in predicting porosity and compaction trend in hydrostatic sands of the. Niger Delta. GEOLOGICAL SETTING OF ...

  14. Reduction of infinite dimensional equations

    Directory of Open Access Journals (Sweden)

    Zhongding Li

    2006-02-01

    Full Text Available In this paper, we use the general Legendre transformation to show the infinite dimensional integrable equations can be reduced to a finite dimensional integrable Hamiltonian system on an invariant set under the flow of the integrable equations. Then we obtain the periodic or quasi-periodic solution of the equation. This generalizes the results of Lax and Novikov regarding the periodic or quasi-periodic solution of the KdV equation to the general case of isospectral Hamiltonian integrable equation. And finally, we discuss the AKNS hierarchy as a special example.

  15. Dynamical Competition of IC-Industry Clustering from Taiwan to China

    Science.gov (United States)

    Tsai, Bi-Huei; Tsai, Kuo-Hui

    2009-08-01

    Most studies employ qualitative approach to explore the industrial clusters; however, few research has objectively quantified the evolutions of industry clustering. The purpose of this paper is to quantitatively analyze clustering among IC design, IC manufacturing as well as IC packaging and testing industries by using the foreign direct investment (FDI) data. The Lotka-Volterra system equations are first adopted here to capture the competition or cooperation among such three industries, thus explaining their clustering inclinations. The results indicate that the evolution of FDI into China for IC design industry significantly inspire the subsequent FDI of IC manufacturing as well as IC packaging and testing industries. Since IC design industry lie in the upstream stage of IC production, the middle-stream IC manufacturing and downstream IC packing and testing enterprises tend to cluster together with IC design firms, in order to sustain a steady business. Finally, Taiwan IC industry's FDI amount into China is predicted to cumulatively increase, which supports the industrial clustering tendency for Taiwan IC industry. Particularly, the FDI prediction of Lotka-Volterra model performs superior to that of the conventional Bass model after the forecast accuracy of these two models are compared. The prediction ability is dramatically improved as the industrial mutualism among each IC production stage is taken into account.

  16. Construction of Chained True Score Equipercentile Equatings under the Kernel Equating (KE) Framework and Their Relationship to Levine True Score Equating. Research Report. ETS RR-09-24

    Science.gov (United States)

    Chen, Haiwen; Holland, Paul

    2009-01-01

    In this paper, we develop a new chained equipercentile equating procedure for the nonequivalent groups with anchor test (NEAT) design under the assumptions of the classical test theory model. This new equating is named chained true score equipercentile equating. We also apply the kernel equating framework to this equating design, resulting in a…

  17. Applied partial differential equations

    CERN Document Server

    Logan, J David

    2004-01-01

    This primer on elementary partial differential equations presents the standard material usually covered in a one-semester, undergraduate course on boundary value problems and PDEs. What makes this book unique is that it is a brief treatment, yet it covers all the major ideas: the wave equation, the diffusion equation, the Laplace equation, and the advection equation on bounded and unbounded domains. Methods include eigenfunction expansions, integral transforms, and characteristics. Mathematical ideas are motivated from physical problems, and the exposition is presented in a concise style accessible to science and engineering students; emphasis is on motivation, concepts, methods, and interpretation, rather than formal theory. This second edition contains new and additional exercises, and it includes a new chapter on the applications of PDEs to biology: age structured models, pattern formation; epidemic wave fronts, and advection-diffusion processes. The student who reads through this book and solves many of t...

  18. Equations of motion derived from a generalization of Einstein's equation for the gravitational field

    International Nuclear Information System (INIS)

    Mociutchi, C.

    1980-01-01

    The extended Einstein's equation, combined with a vectorial theory of maxwellian type of the gravitational field, leads to: a) the equation of motion; b) the equation of the trajectory for the static case of spherical symmetry, the test particle having a rest mass other than zero, and c) the propagation of light on null geodesics. All the basic tests of the theory given by Einstein's extended equation. Thus, the new theory of gravitation suggested by us is competitive. (author)

  19. The Wouthuysen equation

    NARCIS (Netherlands)

    M. Hazewinkel (Michiel)

    1995-01-01

    textabstractDedication: I dedicate this paper to Prof. P.C. Baayen, at the occasion of his retirement on 20 December 1994. The beautiful equation which forms the subject matter of this paper was invented by Wouthuysen after he retired. The four complex variable Wouthuysen equation arises from an

  20. Approach in Theory of Nonlinear Evolution Equations: The Vakhnenko-Parkes Equation

    Directory of Open Access Journals (Sweden)

    V. O. Vakhnenko

    2016-01-01

    Full Text Available A variety of methods for examining the properties and solutions of nonlinear evolution equations are explored by using the Vakhnenko equation (VE as an example. The VE, which arises in modelling the propagation of high-frequency waves in a relaxing medium, has periodic and solitary traveling wave solutions some of which are loop-like in nature. The VE can be written in an alternative form, known as the Vakhnenko-Parkes equation (VPE, by a change of independent variables. The VPE has an N-soliton solution which is discussed in detail. Individual solitons are hump-like in nature whereas the corresponding solution to the VE comprises N-loop-like solitons. Aspects of the inverse scattering transform (IST method, as applied originally to the KdV equation, are used to find one- and two-soliton solutions to the VPE even though the VPE’s spectral equation is third-order and not second-order. A Bäcklund transformation for the VPE is used to construct conservation laws. The standard IST method for third-order spectral problems is used to investigate solutions corresponding to bound states of the spectrum and to a continuous spectrum. This leads to N-soliton solutions and M-mode periodic solutions, respectively. Interactions between these types of solutions are investigated.