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Sample records for volterra integrodifferential equations

  1. An existence theorem for Volterra integrodifferential equations with infinite delay

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    Ferenc Izsak

    2003-01-01

    Full Text Available Using Schauder's fixed point theorem, we prove an existence theorem for Volterra integrodifferential equations with infinite delay. As an appplication, we consider an $n$ species Lotka-Volterra competitive system.

  2. Splitting methods for partial Volterra integro-differential equations

    NARCIS (Netherlands)

    Brunner, H.; Houwen, P.J. van der; Sommeijer, B.P.

    1999-01-01

    The spatial discretization of initial-value problems for (nonlinear) parabolic or hyperbolic PDEs with memory terms leads to (large) systems of Volterra integro-differential equations (VIDEs). In this paper we study the efficient numerical solution of such systems by methods based on linear multiste

  3. Application of fuzzy Laplace transforms for solving fuzzy partial Volterra integro-differential equations

    OpenAIRE

    Ullah, Saif; Farooq, Muhammad; Ahmad, Latif; Abdullah, Saleem

    2014-01-01

    Fuzzy partial integro-differential equations have a major role in the fields of science and engineering. In this paper, we propose the solution of fuzzy partial Volterra integro-differential equation with convolution type kernel using fuzzy Laplace transform method (FLTM) under Hukuhara differentiability. It is shown that FLTM is a simple and reliable approach for solving such equations analytically. Finally, the method is illustrated with few examples to show the ability of the proposed method.

  4. 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 .

  5. Volterra integrodifferential systems

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    K. Balachandran

    1995-01-01

    Full Text Available Sufficient conditions for the complete controllability of nonlinear perturbations of Volterra integrodifferential systems with implicit derivative are established. The results generalize the results of Dauer and Balachandran [9] and are obtained through the notions of condensing map and measure of noncompactness of a set.

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

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    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.

  7. LOCAL FRACTIONAL VARIATIONAL ITERATION METHOD FOR SOLVING VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS WITHIN LOCAL FRACTIONAL OPERATORS

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    Ammar Ali Neamah

    2014-01-01

    Full Text Available The paper uses the Local fractional variational Iteration Method for solving the second kind Volterra integro-differential equations within the local fractional integral operators. The analytical solutions within the non-differential terms are discussed. Some illustrative examples will be discussed. The obtained results show the simplicity and efficiency of the present technique with application to the problems for the integral equations.

  8. Comparison Theorem for General Volterra-Stieltjes Integro-differential Equations%一般Volterra-Stieltjes微积分方程的比较定理

    Institute of Scientific and Technical Information of China (English)

    娄梅枝

    2003-01-01

    In this paper, A.B.Mingarelli's result is generalized to General Volterra-Stieltjes Integro-differential Equations. Comparison theorem and equivalence condition of non-oscillation are obtained. Classical Sturm comparison theorem and some conclusions are generalized.

  9. Numerical solution of nonlinear fractional-order Volterra integro-differential equations by SCW

    Science.gov (United States)

    Zhu, Li; Fan, Qibin

    2013-05-01

    Fractional calculus is an extension of derivatives and integrals to non-integer orders and has been widely used to model scientific and engineering problems. In this paper, we describe the fractional derivative in the Caputo sense and give the second kind Chebyshev wavelet (SCW) operational matrix of fractional integration. Then based on above results we propose the SCW operational matrix method to solve a kind of nonlinear fractional-order Volterra integro-differential equations. The main characteristic of this approach is that it reduces the integro-differential equations into a nonlinear system of algebraic equations. Thus, it can simplify the problem of fractional order equation solving. The obtained numerical results indicate that the proposed method is efficient and accurate for this kind equations.

  10. Systems of nonlinear Volterra integro-differential equations of arbitrary order

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    Kourosh Parand

    2018-10-01

    Full Text Available In this paper, a new approximate method for solving of systems of nonlinear Volterra integro-differential equations of arbitrary (integer and fractional order is introduced. For this purpose, the generalized fractional order of the Chebyshev orthogonal functions (GFCFs based on the classical Chebyshev polynomials of the first kind has been introduced that can be used to obtain the solution of the integro-differential equations (IDEs. Also, we construct the fractional derivative operational matrix of order $\\alpha$ in the Caputo's definition for GFCFs. This method reduced a system of IDEs by collocation method into a system of algebraic equations. Some examples to illustrate the simplicity and the effectiveness of the propose method have been presented.

  11. Stability of Runge-Kutta-Pouzet methods for Volterra integro-differential equations with delays

    Institute of Scientific and Technical Information of China (English)

    Chengming HUANG; Stefan VANDEWALLE

    2009-01-01

    This paper is concerned with the study of the stability of Runge Kutta-Pouzet methods for Volterra integro-differential equations with delays.We are interested in the comparison between the analytical and numerical stability regions.First,we focus on scalar equations with real coefficients.It is proved that all Gauss-Pouzet methods can retain the asymptotic stability of the analytical solution.Then,we consider the multidimensional case.A new stability condition for the stability of the analytical solution is given.Under this condition,the asymptotic stability of Gauss-Pouzet methods is investigated.

  12. One-step block method for solving Volterra integro-differential equations

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    Mohamed, Nurul Atikah binti; Majid, Zanariah Abdul

    2015-10-01

    One-step block method for solving linear Volterra integro-differential equations (VIDEs) is presented in this paper. In VIDEs, the unknown function appears in the form of derivative and under the integral sign. The popular methods for solving VIDEs are the method of quadrature or quadrature method combined with numerical method. The proposed block method will solve the ordinary differential equations (ODEs) part and Newton-Cotes quadrature rule is applied to calculate the integral part of VIDEs. Numerical problems are presented to illustrate the performance of the proposed method.

  13. 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

  14. 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.

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

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    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.

  16. The Use of Iterative Methods to Solve Two-Dimensional Nonlinear Volterra-Fredholm Integro-Differential Equations

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    shadan sadigh behzadi

    2012-03-01

    Full Text Available In this present paper, we solve a two-dimensional nonlinear Volterra-Fredholm integro-differential equation by using the following powerful, efficient but simple methods: (i Modified Adomian decomposition method (MADM, (ii Variational iteration method (VIM, (iii Homotopy analysis method (HAM and (iv Modified homotopy perturbation method (MHPM. The uniqueness of the solution and the convergence of the proposed methods are proved in detail. Numerical examples are studied to demonstrate the accuracy of the presented methods.

  17. Existence and uniqueness of solutions to fractional semilinear mixed Volterra-Fredholm integrodifferential equations with nonlocal conditions

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    Mohammed M. Matar

    2009-12-01

    Full Text Available In this article we study the fractional semilinear mixed Volterra-Fredholm integrodifferential equation $$ frac{d^{alpha }x(t}{dt^{alpha }} =Ax(t+fBig(t,x(t, int_{t_0}^tk(t,s,x(sds,int_{t_0}^{T}h(t,s,x(sdsBig , $$ where $tin [t_0,T]$, $t_0geq 0$, $0equation, with a nonlocal condition.

  18. Existence and Uniqueness Theorem of Fractional Mixed Volterra-Fredholm Integrodifferential Equation with Integral Boundary Conditions

    OpenAIRE

    Shayma Adil Murad; Hussein Jebrail Zekri; Samir Hadid

    2011-01-01

    We study the existence and uniqueness of the solutions of mixed Volterra-Fredholm type integral equations with integral boundary condition in Banach space. Our analysis is based on an application of the Krasnosel'skii fixed-point theorem.

  19. Existence and Uniqueness Theorem of Fractional Mixed Volterra-Fredholm Integrodifferential Equation with Integral Boundary Conditions

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    Shayma Adil Murad

    2011-01-01

    Full Text Available We study the existence and uniqueness of the solutions of mixed Volterra-Fredholm type integral equations with integral boundary condition in Banach space. Our analysis is based on an application of the Krasnosel'skii fixed-point theorem.

  20. EXTRAPOLATION AND A-POSTERIORI ERROR ESTIMATORS OF PETROV-GALERKIN METHODS FOR NON-LINEAR VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    Shu-hua Zhang; Tao Lin; Yan-ping Lin; Ming Rao

    2001-01-01

    In this paper we will show that the Richardson extrapolation can be used to enhance the numerical solution generated by a Petrov-Galerkin finite element method for the initialvalue problem for a nonlinear Volterra integro-differential equation. As by-products, we will also show that these enhanced approximations can be used to form a class of aposteriori estimators for this Petrov-Galerkin finite element method. Numerical examples are supplied to illustrate the theoretical results.

  1. Reliability of difference analogues to preserve stability properties of stochastic Volterra integro-differential equations

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    Roberts Jason A

    2006-01-01

    Full Text Available We consider the reliability of some numerical methods in preserving the stability properties of the linear stochastic functional differential equation , where α, β, σ, τ ≥ 0 are real constants, and W(t is a standard Wiener process. The areas of the regions of asymptotic stability for the class of methods considered, indicated by the sufficient conditions for the discrete system, are shown to be equal in size to each other and we show that an upper bound can be put on the time-step parameter for the numerical method for which the system is asymptotically mean-square stable. We illustrate our results by means of numerical experiments and various stability diagrams. We examine the extent to which the continuous system can tolerate stochastic perturbations before losing its stability properties and we illustrate how one may accurately choose a numerical method to preserve the stability properties of the original problem in the numerical solution. Our numerical experiments also indicate that the quality of the sufficient conditions is very high.

  2. Asymptotic Behavior of Solutions to a Linear Volterra Integrodifferential System

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    Yue-Wen Cheng

    2013-01-01

    Full Text Available We investigate the asymptotic behavior of solutions to a linear Volterra integrodifferential system , We show that under some suitable conditions, there exists a solution for the above integrodifferential system, which is asymptotically equivalent to some given functions. Two examples are given to illustrate our theorem.

  3. Nonlocal Cauchy problem for nonlinear mixed integrodifferential equations

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    H.L. Tidke

    2010-12-01

    Full Text Available The present paper investigates the existence and uniqueness of mild and strong solutions of a nonlinear mixed Volterra-Fredholm integrodifferential equation with nonlocal condition. The results obtained by using Schauder fixed point theorem and the theory of semigroups.

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

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    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.

  5. Approximations of solutions to retarded integrodifferential equations

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    Dhirendra Bahuguna

    2004-11-01

    Full Text Available In this paper we consider a retarded integrodifferential equation and prove existence, uniqueness and convergence of approximate solutions. We also give some examples to illustrate the applications of the abstract results.

  6. Rothe's method to semilinear hyperbolic integrodifferential equations

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    D. Bahaguna

    1990-01-01

    Full Text Available In this paper we consider an application of Rothe's method to abstract semi-linear hyperbolic integrodifferential equations in Hilbert spaces. With the aid of Rothe's method we establish the existence of a unique strong solution.

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

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    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.

  8. Error estimates for finite element solution for parabolic integro-differential equations

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    Hasan N. Ymeri

    1993-05-01

    Full Text Available In this paper we first study the stability of Ritz-Volterra projection and its maximum norm estimates, and then we use these results to derive some L\\infty error estimates for finite element methods for parabolic partial integro-differential equations.

  9. Application of the hybrid method with constant coefficients to solving the integro-differential equations of first order

    Science.gov (United States)

    Mehdiyeva, Galina; Imanova, Mehriban; Ibrahimov, Vagif

    2012-11-01

    As is well known investigation of many processes of natural sciences reduce to the solving of initial value problem for integro-differential equations which are one of the priority areas of modern mathematics. To define the exact solution of such problems is not always possible. Therefore the scientists constructed approximate methods for solving them. There are a number of papers devoted to finding approximate solutions of integro-differential equations. Unlike at papers investigated, here the numerical solution of initial value problem for Volterra integro-differential equations by the hybrid methods, constructed concrete methods with the degree p ≤ 6 and suggested algorithm for using them.

  10. Discrete multiscale wavelet shrinkage and integrodifferential equations

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    Didas, S.; Steidl, G.; Weickert, J.

    2008-04-01

    We investigate the relation between discrete wavelet shrinkage and integrodifferential equations in the context of simplification and denoising of one-dimensional signals. In the continuous setting, strong connections between these two approaches were discovered in 6 (see references). The key observation is that the wavelet transform can be understood as derivative operator after the convolution with a smoothing kernel. In this paper, we extend these ideas to the practically relevant discrete setting with both orthogonal and biorthogonal wavelets. In the discrete case, the behaviour of the smoothing kernels for different scales requires additional investigation. The results of discrete multiscale wavelet shrinkage and related discrete versions of integrodifferential equations are compared with respect to their denoising quality by numerical experiments.

  11. Sherman-Morrison-Woodbury Formula for Linear Integrodifferential Equations

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    Feng Wu

    2016-01-01

    Full Text Available The well-known Sherman-Morrison-Woodbury formula is a powerful device for calculating the inverse of a square matrix. The paper finds that the Sherman-Morrison-Woodbury formula can be extended to the linear integrodifferential equation, which results in an unified scheme to decompose the linear integrodifferential equation into sets of differential equations and one integral equation. Two examples are presented to illustrate the Sherman-Morrison-Woodbury formula for the linear integrodifferential equation.

  12. An abstract partial functional integrodifferential equations

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    Khalil Ezzinbi

    2016-10-01

    Full Text Available In this work, we investigate the existence and regularity of solutions for some partial functional integrodifferential equations with finite delay. The continuous dependence upen initial values and asymptotic stability are also studied. Firstly, we show the existence of the mild solutions. Secondly, we give sufficient conditions ensuring the existence of the strict solutions. The method used treats the equations in the domain of A with the graph norm employing results from linear semigroup theory. To illustrate our abstract result, we conclude this work with an application.

  13. Approximate Controllability of Fractional Integrodifferential Evolution Equations

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    R. Ganesh

    2013-01-01

    Full Text Available This paper addresses the issue of approximate controllability for a class of control system which is represented by nonlinear fractional integrodifferential equations with nonlocal conditions. By using semigroup theory, p-mean continuity and fractional calculations, a set of sufficient conditions, are formulated and proved for the nonlinear fractional control systems. More precisely, the results are established under the assumption that the corresponding linear system is approximately controllable and functions satisfy non-Lipschitz conditions. The results generalize and improve some known results.

  14. Qualitative permanence of Lotka-Volterra equations.

    Science.gov (United States)

    Hofbauer, Josef; Kon, Ryusuke; Saito, Yasuhisa

    2008-12-01

    In this paper, we consider permanence of Lotka-Volterra equations. We investigate the sign structure of the interaction matrix that guarantees the permanence of a Lotka-Volterra equation whenever it has a positive equilibrium point. An interaction matrix with this property is said to be qualitatively permanent. Our results provide both necessary and sufficient conditions for qualitative permanence.

  15. 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.

  16. B-Theory of Runge-Kutta methods for stiff Volterra functional differential equations

    Institute of Scientific and Technical Information of China (English)

    LI; Shoufu(李寿佛)

    2003-01-01

    B-stability and B-convergence theories of Runge-Kutta methods for nonlinear stiff Volterra func-tional differential equations (VFDEs) are established which provide unified theoretical foundation for the studyof Runge-Kutta methods when applied to nonlinear stiff initial value problems (IVPs) in ordinary differentialequations (ODEs), delay differential equations (DDEs), integro-differential equations (IDEs) and VFDEs ofother type which appear in practice.

  17. Inequalities applicable to retarded Volterra integral equations

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    B. G. Pachpatte

    2004-12-01

    Full Text Available The main objective of this paper is to establish explicit bounds on certain integral inequialities which can be used as tools in the study of certain classes of retarded Volterra integral equations.

  18. Current work and open problems in the numerical analysis of Volterra functional equations with vanishing delays

    Institute of Scientific and Technical Information of China (English)

    Hermann BRUNNER

    2009-01-01

    The aims of this paper are (i) to present a survey of recent advances in the analysis of superconvergence of collocation solutions for linear Volterra-type functional integral and integro-differential equations with delay functions θ(t) vanishing at the initial point of the interval of integration (with θ(t) = qt (0 < q < 1,t ≥0) being an important special case),and (ii) to point,by means of a list of open problems,to areas in the numerical analysis of such Volterra functional equations where more research needs to be carried out.

  19. About one special boundary value problem for multidimensional parabolic integro-differential equation

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    Khairullin, Ermek

    2016-08-01

    In this paper we consider a special boundary value problem for multidimensional parabolic integro-differential equation with boundary conditions that contains as a boundary condition containing derivatives of order higher than the order of the equation. The solution is sought in the form of a thermal potential of a double layer. Shows lemma of finding the limits of the derivatives of the unknown function in the neighborhood of the hyperplane. Using the boundary condition and lemma obtained integral-differential equation (IDE) of parabolic operators, whĐţre an unknown function under the integral contains higher-order space variables derivatives. IDE is reduced to a singular integral equation (SIE), when an unknown function in the spatial variables satisfies the Holder. The characteristic part is solved in the class of distribution function using method of transformation of Fourier-Laplace. Found an algebraic condition for the transition to the classical generalized solution. Integral equation of the resolvent for the characteristic part of SIE is obtained. Integro-differential equation is reduced to the Volterra-Fredholm type integral equation of the second kind by method of regularization. It is shown that the solution of SIE is a solution of IDE. Obtain a theorem on the solvability of the boundary value problem of multidimensional parabolic integro-differential equation, when a known function of the spatial variables belongs to the Holder class and satisfies the solvability conditions.

  20. An oscillation criterion for inhomogeneous Stieltjes integro-differential equations

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    M. A. El-Sayed

    1994-01-01

    Full Text Available The aim of the paper is to give an oscillation theorem for inhomogeneous Stieltjes integro-differential equation of the form p(tx′+∫atx(sdσ=f(t. The paper generalizes the author's work [2].

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

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    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.

  2. Asymptotically periodic solutions of Volterra integral equations

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    Muhammad N. Islam

    2016-03-01

    Full Text Available We study the existence of asymptotically periodic solutions of a nonlinear Volterra integral equation. In the process, we obtain the existence of periodic solutions of an associated nonlinear integral equation with infinite delay. Schauder's fixed point theorem is used in the analysis.

  3. Lipschitz Regularity of Solutions for Mixed Integro-Differential Equations

    CERN Document Server

    Barles, Guy; Ciomaga, Adina; Imbert, Cyril

    2011-01-01

    We establish new Hoelder and Lipschitz estimates for viscosity solutions of a large class of elliptic and parabolic nonlinear integro-differential equations, by the classical Ishii-Lions's method. We thus extend the Hoelder regularity results recently obtained by Barles, Chasseigne and Imbert (2011). In addition, we deal with a new class of nonlocal equations that we term mixed integro-differential equations. These equations are particularly interesting, as they are degenerate both in the local and nonlocal term, but their overall behavior is driven by the local-nonlocal interaction, e.g. the fractional diffusion may give the ellipticity in one direction and the classical diffusion in the complementary one.

  4. Adomian Method for Solving Fuzzy Fredholm-Volterra Integral Equations

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    M. Barkhordari Ahmadi

    2013-09-01

    Full Text Available In this paper, Adomian method has been applied to approximate the solution of fuzzy volterra-fredholm integral equation. That, by using parametric form of fuzzy numbers, a fuzzy volterra-fredholm integral equation has been converted to a system of volterra-fredholm integral equation in crisp case. Finally, the method is explained with illustrative examples.

  5. Almost Automorphic Solutions to Nonautonomous Stochastic Functional Integrodifferential Equations

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    Li Xi-liang

    2013-01-01

    Full Text Available This paper concerns the square-mean almost automorphic solutions to a class of abstract semilinear nonautonomous functional integrodifferential stochastic evolution equations in real separable Hilbert spaces. Using the so-called “Acquistapace-Terreni” conditions and Banach contraction principle, the existence, uniqueness, and asymptotical stability results of square-mean almost automorphic mild solutions to such stochastic equations are established. As an application, square-mean almost automorphic solution to a concrete nonautonomous integro-differential stochastic evolution equation is analyzed to illustrate our abstract results.

  6. On Some Fractional Stochastic Integrodifferential Equations in Hilbert Space

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    Hamdy M. Ahmed

    2009-01-01

    Full Text Available We study a class of fractional stochastic integrodifferential equations considered in a real Hilbert space. The existence and uniqueness of the Mild solutions of the considered problem is also studied. We also give an application for stochastic integropartial differential equations of fractional order.

  7. On a Volterra Stieltjes integral equation

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    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.

  8. Nonclassical linear Volterra equations of the first kind

    CERN Document Server

    Apartsyn, Anatoly S

    2003-01-01

    This monograph deals with linear integra Volterra equations of the first kind with variable upper and lower limits of integration. Volterra operators of this type are the basic operators for integral models of dynamic systems.

  9. Existence and Uniqueness of Mild Solution for Fractional Integrodifferential Equations

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    N'Guérékata GastonM

    2010-01-01

    Full Text Available We study the existence and uniqueness of mild solution of a class of nonlinear fractional integrodifferential equations , , , in a Banach space , where . New results are obtained by fixed point theorem. An application of the abstract results is also given.

  10. Solvability of Nonautonomous Fractional Integrodifferential Equations with Infinite Delay

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    Li Fang

    2011-01-01

    Full Text Available We study the existence and uniqueness of mild solution of a class of nonlinear nonautonomous fractional integrodifferential equations with infinite delay in a Banach space . The existence of mild solution is obtained by using the theory of the measure of noncompactness and Sadovskii's fixed point theorem. An application of the abstract results is also given.

  11. Existence of solutions for neutral functional integrodifferential equations

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    R. Murugesu

    2010-06-01

    Full Text Available In this paper, by using fractional power of operators and Sadovskii's fixed point theorem, we study the existence of mild and strong solutions of nonlinear neutral functional integrodifferential equations. The results we obtained are a generalization and continuation of the recent results on this issue.

  12. ON SOLUTIONS TO SEMILINEAR INTEGRODIFFERENTIAL EQUATIONS WITH NONLOCAL CONDITIONS

    Institute of Scientific and Technical Information of China (English)

    2008-01-01

    In this paper, using the theory of resolvent operators, Banach,s contraction prin-ciple and Schauder,s fixed point theorem, we study the existence of integral solutions to semilinear integrodifferential equations under nonlocal conditions in Banach space. An example is provided to illustrate the results obtained.

  13. Stability and Boundedness of Solutions to Nonautonomous Parabolic Integrodifferential Equations

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    Michael Gil'

    2016-01-01

    Full Text Available We consider a class of linear nonautonomous parabolic integrodifferential equations. We will assume that the coefficients are slowly varying in time. Conditions for the boundedness and stability of solutions to the considered equations are suggested. Our results are based on a combined usage of the recent norm estimates for operator functions and theory of equations on the tensor product of Hilbert spaces.

  14. An approximation scheme for optimal control of Volterra integral equations

    OpenAIRE

    Belbas, S. A.

    2006-01-01

    We present and analyze a new method for solving optimal control problems for Volterra integral equations, based on approximating the controlled Volterra integral equations by a sequence of systems of controlled ordinary differential equations. The resulting approximating problems can then be solved by dynamic programming methods for ODE controlled systems. Other, straightforward versions of dynamic programming, are not applicable to Volterra integral equations. We also derive the connection b...

  15. ON THE FINITE VOLUME ELEMENT VERSION OF RITZ-VOLTERRA PROJECTION AND APPLICATIONS TO RELATED EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    Tie Zhang; Yan-ping Lin; Robert J.Tait

    2002-01-01

    In this paper, we present a general error analysis framework for the finite volume element (FVE) approximation to the Ritz-Volterra projection, the Sobolev equations and parabolic integro-differential equations. The main idea in our paper is to consider the FVE methods as perturbations of standard finite element methods which enables us to derive the optimal L2 and H1 norm error estimates, and the L∞ and W1∞ norm error estimates by means of the time dependent Green functions. Our disc ussions also include elliptic and parabolic problems as the special cases.

  16. 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.

  17. Time Reversal of Volterra Processes Driven Stochastic Differential Equations

    Directory of Open Access Journals (Sweden)

    L. Decreusefond

    2013-01-01

    Full Text Available We consider stochastic differential equations driven by some Volterra processes. Under time reversal, these equations are transformed into past-dependent stochastic differential equations driven by a standard Brownian motion. We are then in position to derive existence and uniqueness of solutions of the Volterra driven SDE considered at the beginning.

  18. Existence and Uniqueness of Mild Solution for Fractional Integrodifferential Equations

    Directory of Open Access Journals (Sweden)

    Fang Li

    2010-01-01

    Full Text Available We study the existence and uniqueness of mild solution of a class of nonlinear fractional integrodifferential equations dqu(t/dtq+Au(t=f(t,u(t+∫0ta(t−sg(s,u(sds, t∈[0,T], u(0=u0, in a Banach space X, where 0

  19. 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...

  20. On stochastic fractional Volterra equations in Hilbert space

    OpenAIRE

    Karczewska, Anna; Lizama, Carlos

    2006-01-01

    In this paper stochastic Volterra equations admitting exponentially bounded resolvents are studied. After obtaining convergence of resolvents, some properties of stochastic convolutions are given. The paper provides a sufficient condition for a stochastic convolution to be a strong solution to a stochastic Volterra equation.

  1. Analytic solution to a class of integro-differential equations

    Directory of Open Access Journals (Sweden)

    Xuming Xie

    2003-03-01

    Full Text Available In this paper, we consider the integro-differential equation $$ epsilon^2 y''(x+L(xmathcal{H}(y=N(epsilon,x,y,mathcal{H}(y, $$ where $mathcal{H}(y[x]=frac{1}{pi}(Pint_{-infty}^{infty} frac{y(t}{t-x}dt$ is the Hilbert transform. The existence and uniqueness of analytic solution in appropriately chosen space is proved. Our method consists of extending the equation to an appropriately chosen region in the complex plane, then use the Contraction Mapping Theorem.

  2. 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

  3. 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 th

  4. Piecewise weighted pseudo almost periodic solutions of impulsive integro-differential equations via fractional operators

    Directory of Open Access Journals (Sweden)

    Zhinan Xia

    2015-07-01

    Full Text Available In this article, we show sufficient conditions for the existence, uniqueness and attractivity of piecewise weighted pseudo almost periodic classical solution of nonlinear impulsive integro-differential equations. The working tools are based on the fixed point theorem and fractional powers of operators. An application to impulsive integro-differential equations is presented.

  5. POSITIVE PERIODIC SOLUTIONS OFIMPULSIVE LATKA-VOLTERRA EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    LiJianli; ShenJianhua

    2005-01-01

    By using the continuation of coincidence degree theory, we study the periodic Lotka-Volterra equations with impulses, and some sufficient onditions for the existence of positive periodic solutions are obtained.

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

    DEFF Research Database (Denmark)

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

    2016-01-01

    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......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...

  7. 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.

  8. Algebraic Integrability of Lotka-Volterra equations in three dimensions

    CERN Document Server

    Constandinides, Kyriacos

    2009-01-01

    We examine the algebraic complete integrability of Lotka-Volterra equations in three dimensions. We restrict our attention to Lotka-Volterra systems defined by a skew symmetric matrix. We obtain a complete classification of such systems. The classification is obtained using Painleve analysis and more specifically by the use of Kowalevski exponents. The imposition of certain integrality conditions on the Kowalevski exponents gives necessary conditions for the algebraic integrability of the corresponding systems. We also show that the conditions are sufficient.

  9. Construction of Canonical Polynomial Basis Functions for Solving Special Nth -Order Linear Integro-Differential Equations

    Directory of Open Access Journals (Sweden)

    1 Taiwo O. A

    2013-01-01

    Full Text Available The problem of solving special nth-order linear integro-differential equations has special importance in engineering and sciences that constitutes a good model for many systems in various fields. In this paper, we construct canonical polynomial from the differential parts of special nth-order integro-differential equations and use it as our basis function for the numerical solutions of special nth-order integro-differential equations. The results obtained by this method are compared with those obtained by Adomian Decomposition method. It is also observed that the new method is an effective method with high accuracy. Some examples are given to illustrate the method.

  10. 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.

  11. The Rothe's Method to a Parabolic Integrodifferential Equation with a Nonclassical Boundary Conditions

    Directory of Open Access Journals (Sweden)

    Abdelfatah Bouziani

    2010-01-01

    the weak solvability of parabolic integrodifferential equations with a nonclassical boundary conditions. The investigation is made by means of approximation by the Rothes method which is based on a semidiscretization of the given problem with respect to the time variable.

  12. Analytical-numerical solution of a nonlinear integrodifferential equation in econometrics

    Science.gov (United States)

    Kakhktsyan, V. M.; Khachatryan, A. Kh.

    2013-07-01

    A mixed problem for a nonlinear integrodifferential equation arising in econometrics is considered. An analytical-numerical method is proposed for solving the problem. Some numerical results are presented.

  13. Existence of Solutions of Abstract Nonlinear Mixed Functional Integrodifferential equation with nonlocal conditions

    Directory of Open Access Journals (Sweden)

    Dhakne Machindra B.

    2017-04-01

    Full Text Available In this paper we discuss the existence of mild and strong solutions of abstract nonlinear mixed functional integrodifferential equation with nonlocal condition by using Sadovskii’s fixed point theorem and theory of fractional power of operators.

  14. Stability analysis of Runge-Kutta methods for nonlinear neutral delay integro-differential equations

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    The sufficient conditions for the stability and asymptotic stability of Runge-Kutta methods for nonlinear neutral delay integro-differential equations are derived. A numerical test that confirms the theoretical results is given in the end.

  15. Existence of Solutions of Nonlinear Integrodifferential Equations of Sobolev Type with Nonlocal Condition in Banach Spaces

    Indian Academy of Sciences (India)

    K Balachandran; K Uchiyama

    2000-05-01

    In this paper we prove the existence of mild and strong solutions of a nonlinear integrodifferential equation of Sobolev type with nonlocal condition. The results are obtained by using semigroup theory and the Schauder fixed point theorem.

  16. Some stability conditions for scalar Volterra difference equations

    Directory of Open Access Journals (Sweden)

    Leonid Berezansky

    2016-01-01

    Full Text Available New explicit stability results are obtained for the following scalar linear difference equation \\[x(n+1-x(n=-a(nx(n+\\sum_{k=1}^n A(n,kx(k+f(n\\] and for some nonlinear Volterra difference equations.

  17. Controllability of semilinear integrodifferential equations with nonlocal conditions

    Directory of Open Access Journals (Sweden)

    Rahima Atmania

    2005-07-01

    Full Text Available We establish sufficient conditions for the controllability of some semilinear integrodifferential systems with nonlocal condition in a Banach space. The results are obtained using the Schaefer fixed-point theorem and semigroup theory.

  18. Hungry Volterra equation, multi boson KP hierarchy and Two Matrix Models

    CERN Document Server

    Hisakado, M

    1998-01-01

    We consider the hungry Volterra hierarchy from the view point of the multi boson KP hierarchy. We construct the hungry Volterra equation as the ``fractional '' BT. We also study the relations between the (discrete time) hungry Volterra equation and two matrix models. From this point of view we study the reduction from (discrete time) 2d Toda lattice to the (discrete time) hungry Volterra equation.

  19. The Asymptotic Behavior for Numerical Solution of a Volterra Equation

    Institute of Scientific and Technical Information of China (English)

    Da Xu

    2003-01-01

    Long-time asymptotic stability and convergence properties for the numerical solution of a Volterra equation of parabolic type are studied. The methods are based on the first-second order backward difference methods. The memory term is approximated by the convolution quadrature and the interpolant quadrature. Discretization of the spatial partial differential operators by the finite element method is also considered.

  20. Compactness for an integro-differential equation with measures

    Directory of Open Access Journals (Sweden)

    Gabriela Grosu

    2010-01-01

    Full Text Available In this paper, using some compactness arguments, we prove some local or even global existence results for the essentially bounded solution to an integro-differential Cauchy problem with distributed measures in a real Banach space. An example involving the Dirac measure concentrated at point is included.

  1. Backward stochastic Volterra integral equations- a brief survey

    Institute of Scientific and Technical Information of China (English)

    YONG Jiong-min

    2013-01-01

    In this paper, we present a brief survey on the updated theory of backward stochas-tic Volterra integral equations (BSVIEs, for short). BSVIEs are a natural generalization of backward stochastic diff erential equations (BSDEs, for short). Some interesting motivations of studying BSVIEs are recalled. With proper solution concepts, it is possible to establish the corresponding well-posedness for BSVIEs. We also survey various comparison theorems for solutions to BSVIEs.

  2. Asymptotic Behavior of Solutions for Nonlinear Volterra Discrete Equations

    Directory of Open Access Journals (Sweden)

    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.

  3. Green's functional for a higher order ordinary integro-differential equation with nonlocal conditions

    Science.gov (United States)

    Özen, Kemal

    2016-12-01

    One of the little-known techniques for ordinary integro-differential equations in literature is Green's functional method, the origin of which dates back to Azerbaijani scientist Seyidali S. Akhiev. According to this method, Green's functional concepts for some simple forms of such equations have been introduced in the several studies. In this study, we extend Green's functional concept to a higher order ordinary integro-differential equation involving generally nonlocal conditions. A novel kind of adjoint problem and Green's functional are constructed for completely nonhomogeneous problem. By means of the obtained Green's functional, the solution to the problem is identified.

  4. Lotka-Volterra type equations and their explicit integration

    CERN Document Server

    Gervais, Jean-Loup; Jean-Loup Gervais; Mikhail V Saveliev

    1994-01-01

    In the present note we give an explicit integration of some two--dimensionalised Lotka--Volterra type equations associated with simple Lie algebras, other than the familiar A_n case, possessing a representation without branching. This allows us, in particular, to treat the first fundamental representations of A_r, B_r, C_r, and G_2 on the same footing.

  5. Group analysis of evolutionary integro-differential equations describing nonlinear waves: the general model

    Energy Technology Data Exchange (ETDEWEB)

    Ibragimov, Nail H [Department of Mathematics and Science, Blekinge Institute of Technology, SE-371 79 Karlskrona (Sweden); Meleshko, Sergey V [School of Mathematics, Institute of Science, Suranaree University of Technology, Nakhon Ratchasima 30000 (Thailand); Rudenko, Oleg V, E-mail: nib@bth.se, E-mail: sergey@math.sut.ac.th, E-mail: rudenko@acs366.phys.msu.ru [Department of Physics, Moscow State University, 119991 Moscow (Russian Federation)

    2011-08-05

    The paper deals with an evolutionary integro-differential equation describing nonlinear waves. A particular choice of the kernel in the integral leads to well-known equations such as the Khokhlov-Zabolotskaya equation, the Kadomtsev-Petviashvili equation and others. Since the solutions of these equations describe many physical phenomena, the analysis of the general model studied in this paper is important. One of the methods for obtaining solutions of differential equations is provided by the Lie group analysis. However, this method is not applicable to integro-differential equations. Therefore, we discuss new approaches developed in modern group analysis and apply them to the general model considered in this paper. Reduced equations and exact solutions are also presented.

  6. A New Positive Definite Expanded Mixed Finite Element Method for Parabolic Integrodifferential Equations

    Directory of Open Access Journals (Sweden)

    Yang Liu

    2012-01-01

    Full Text Available A new positive definite expanded mixed finite element method is proposed for parabolic partial integrodifferential equations. Compared to expanded mixed scheme, the new expanded mixed element system is symmetric positive definite and both the gradient equation and the flux equation are separated from its scalar unknown equation. The existence and uniqueness for semidiscrete scheme are proved and error estimates are derived for both semidiscrete and fully discrete schemes. Finally, some numerical results are provided to confirm our theoretical analysis.

  7. THE NUMERICAL SOLUTION FOR A PARTIAL INTEGRO-DIFFERENTIAL EQUATION WITH A WEAKLY SINGULAR KERNEL

    Institute of Scientific and Technical Information of China (English)

    2006-01-01

    In this paper, a first order semi-discrete method of a partial integro-differential equation with a weakly singular kernel is considered. We apply Galerkin spectral method in one direction, and the inversion technique for the Laplace transform in another direction, the result of the numerical experiment proves the accuracy of this method.

  8. Stepanov-like weighted pseudo almost automorphic solutions to fractional order abstract integro-differential equations

    Indian Academy of Sciences (India)

    Syed Abbas; V Kavitha; R Murugesu

    2015-08-01

    In this article, we study the concept of Stepanov-like weighted pseudo almost automorphic solutions to fractional order abstract integro-differential equations. We establish the results with Lipschitz condition and without Lipschitz condition on the forcing term. An interesting example is presented to illustrate the main findings. The results proven are new and complement the existing ones.

  9. Terminal value problems of impulsive integro-differential equations in Banach spaces

    Directory of Open Access Journals (Sweden)

    Dajun Guo

    1997-01-01

    Full Text Available This paper uses cone theory and the monotone iterative technique to investigate the existence of minimal nonnegative solutions of terminal value problems for first order nonlinear impulsive integro-differential equations of mixed type in a Banach space.

  10. Nonlocal Cauchy problem for time varying delay integrodifferential equations of Sobolev type in Banach spaces

    Directory of Open Access Journals (Sweden)

    K. Balachandran

    2006-09-01

    Full Text Available In this paper we prove the existence of mild and strong solutions of nonlinear time varying delay integrodifferential equations of Sobolev type with nonlocal conditions in Banach spaces. The results are obtained by using the theory of compact semigroups and Schaefer's fixed point theorem.

  11. EXISTENCE OF MULTIPLE POSITIVE PERIODIC SOLUTIONS TO A CLASS OF INTEGRO-DIFFERENTIAL EQUATION

    Institute of Scientific and Technical Information of China (English)

    2011-01-01

    In this paper,by the Avery-Henderson fixed point theorem,we investigate the existence of multiple positive periodic solutions to a class of integro-differential equation. Some suficient conditions are obtained for the existence of multiple positive periodic solutions.

  12. PERIODIC BOUNDARY VALUE PROBLEM FOR NONLINEAR INTEGRO-DIFFERENTIAL EQUATION OF MIXED TYPE ON TIME SCALES

    Institute of Scientific and Technical Information of China (English)

    Yepeng Xing; Qiong Wang; Valery G. Romanovski

    2009-01-01

    We prove several new comparison results and develop the monotone iterative tech-nique to show the existence of extremal solutions to a kind of periodic boundary value problem (PBVP) for nonlinear integro-differential equation of mixed type on time scales.

  13. Analytical lie group approach for solving fractional integro-differential equations

    Science.gov (United States)

    Pashayi, S.; Hashemi, M. S.; Shahmorad, S.

    2017-10-01

    This study is concerned with the Lie symmetry group analysis of Fractional Integro-Differential Equations (FIDEs) with nonlocal structures based on a new development of prolongation formula. A new prolongation for FIDEs is extracted and invariant solutions are finally presented for some illustrative examples.

  14. Weighted asymptotic behavior of solutions to semilinear integro-differential equations in Banach spaces

    Directory of Open Access Journals (Sweden)

    Yan-Tao Bian

    2014-04-01

    Full Text Available In this article, we study weighted asymptotic behavior of solutions to the semilinear integro-differential equation $$ u'(t=Au(t+\\alpha\\int_{-\\infty}^{t}e^{-\\beta(t-s}Au(sds+f(t,u(t, \\quad t\\in \\mathbb{R}, $$ where $\\alpha, \\beta \\in \\mathbb{R}$, with $\\beta > 0, \\alpha \

  15. N-th order impulsive integro-differential equations in Banach spaces

    Directory of Open Access Journals (Sweden)

    Manfeng Hu

    2004-03-01

    Full Text Available We investigate the maximal and minimal solutions of initial value problem for N-th order nonlinear impulsive integro-differential equation in Banach space by establishing a comparison result and using the upper and lower solutions methods.

  16. Inverse Problems for a Parabolic Integrodifferential Equation in a Convolutional Weak Form

    Directory of Open Access Journals (Sweden)

    Kairi Kasemets

    2013-01-01

    Full Text Available We deduce formulas for the Fréchet derivatives of cost functionals of several inverse problems for a parabolic integrodifferential equation in a weak formulation. The method consists in the application of an integrated convolutional form of the weak problem and all computations are implemented in regular Sobolev spaces.

  17. New homotopy analysis transform algorithm to solve volterra integral equation

    Directory of Open Access Journals (Sweden)

    Sunil Kumar

    2014-03-01

    Full Text Available The main aim of the present work is to propose a new and simple algorithm for Volterra integral equation arising in demography, the study of viscoelastic materials, and in insurance mathematics through the renewal equation by using homotopy analysis transform method. The homotopy analysis transform method is an innovative adjustment in Laplace transform algorithm and makes the calculation much simpler. The solutions obtained by proposed method indicate that the approach is easy to implement and computationally very attractive. The beauty of the paper is coupling of two techniques. Finally, two numerical examples are given to show the accuracy and stability of this method.

  18. Aleksandrov-Bakelman-Pucci Type Estimates For Integro-Differential Equations

    CERN Document Server

    Guillen, Nestor

    2011-01-01

    In this work we provide an Aleksandrov-Bakelman-Pucci type estimate for a certain class of fully nonlinear elliptic integro-differential equations and generalizations of both the Monge-Amp\\`ere operator and the convex envelope to a nonlocal, fractional-order setting. This particular elliptic family under consideration is large enough to capture the second order theory as the order of the integro-differential equations tends to 2. Moreover, our estimate is uniform in the order of the equations, resulting in a genuine generalization of the existing ABP estimate. This result also gives a new comparison theorem for viscosity solutions of such equations which only depends on the $L^\\infty$ and $L^n$ norms of the right hand side, in contrast to previous comparison results which utilize the continuity of the right hand side for their conclusions. These results appear to be new even for the linear case of the relevant equations.

  19. A mathematical model on fractional Lotka-Volterra equations.

    Science.gov (United States)

    Das, S; Gupta, P K

    2011-05-21

    The article presents the solutions of Lotka-Volterra equations of fractional-order time derivatives with the help of analytical method of nonlinear problem called the homotopy perturbation method (HPM). By using initial values, the explicit solutions of predator and prey populations for different particular cases have been derived. The numerical solutions show that only a few iterations are needed to obtain accurate approximate solutions. The method performs extremely well in terms of efficiency and simplicity to solve this historical biological model. Copyright © 2011 Elsevier Ltd. All rights reserved.

  20. Invariant and partially invariant solutions of integro-differential equations for linear thermoviscoelastic aging materials with memory

    Science.gov (United States)

    Zhou, Long-Qiao; Meleshko, Sergey V.

    2017-01-01

    A linear thermoviscoelastic model for homogeneous, aging materials with memory is established. A system of integro-differential equations is obtained by using two motions (a one-dimensional motion and a shearing motion) for this model. Applying the group analysis method to the system of integro-differential equations, the admitted Lie group is determined. Using this admitted Lie group, invariant and partially invariant solutions are found. The present paper gives a first example of application of partially invariant solutions to integro-differential equations.

  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. Abstract fractional integro-differential equations involving nonlocal initial conditions in α-norm

    Directory of Open Access Journals (Sweden)

    Wang Rong-Nian

    2011-01-01

    Full Text Available Abstract In the present paper, we deal with the Cauchy problems of abstract fractional integro-differential equations involving nonlocal initial conditions in α-norm, where the operator A in the linear part is the generator of a compact analytic semigroup. New criterions, ensuring the existence of mild solutions, are established. The results are obtained by using the theory of operator families associated with the function of Wright type and the semigroup generated by A, Krasnoselkii's fixed point theorem and Schauder's fixed point theorem. An application to a fractional partial integro-differential equation with nonlocal initial condition is also considered. Mathematics subject classification (2000 26A33, 34G10, 34G20

  3. Nonlinear boundary value problems for first order impulsive integro-differential equations

    Directory of Open Access Journals (Sweden)

    Xinzhi Liu

    1989-01-01

    Full Text Available In this paper, we investigate a class of first order impulsive integro-differential equations subject to certain nonlinear boundary conditions and prove, with the help of upper and lower solutions, that the problem has a solution lying between the upper and lower solutions. We also develop monotone iterative technique and show the existence of multiple solutions of a class of periodic boundary value problems.

  4. A Reproducing Kernel Hilbert Space Method for Solving Systems of Fractional Integrodifferential Equations

    Directory of Open Access Journals (Sweden)

    Samia Bushnaq

    2014-01-01

    Full Text Available We present a new version of the reproducing kernel Hilbert space method (RKHSM for the solution of systems of fractional integrodifferential equations. In this approach, the solution is obtained as a convergent series with easily computable components. Several illustrative examples are given to demonstrate the effectiveness of the present method. The method described in this paper is expected to be further employed to solve similar nonlinear problems in fractional calculus.

  5. Stability Analysis of Runge-Kutta Methods for Delay Integro-Differential Equations

    Institute of Scientific and Technical Information of China (English)

    甘四清; 郑纬民

    2004-01-01

    Considering a linear system of delay integro-differential equations with a constant delay whose zero solution is asympototically stable, this paper discusses the stability of numerical methods for the system. The adaptation of Runge-Kutta methods with a Lagrange interpolation procedure was focused on inheriting the asymptotic stability of underlying linear systems. The results show that an A-stable Runge-Kutta method preserves the asympototic stability of underlying linear systems whenever an unconstrained grid is used.

  6. On a Mixed Nonlinear One Point Boundary Value Problem for an Integrodifferential Equation

    Directory of Open Access Journals (Sweden)

    Said Mesloub

    2008-03-01

    Full Text Available This paper is devoted to the study of a mixed problem for a nonlinear parabolic integro-differential equation which mainly arise from a one dimensional quasistatic contact problem. We prove the existence and uniqueness of solutions in a weighted Sobolev space. Proofs are based on some a priori estimates and on the Schauder fixed point theorem. we also give a result which helps to establish the regularity of a solution.

  7. On a Mixed Nonlinear One Point Boundary Value Problem for an Integrodifferential Equation

    Directory of Open Access Journals (Sweden)

    Mesloub Said

    2008-01-01

    Full Text Available This paper is devoted to the study of a mixed problem for a nonlinear parabolic integro-differential equation which mainly arise from a one dimensional quasistatic contact problem. We prove the existence and uniqueness of solutions in a weighted Sobolev space. Proofs are based on some a priori estimates and on the Schauder fixed point theorem. we also give a result which helps to establish the regularity of a solution.

  8. Stochastic Volterra Equation Driven by Wiener Process and Fractional Brownian Motion

    Directory of Open Access Journals (Sweden)

    Zhi Wang

    2013-01-01

    Full Text Available For a mixed stochastic Volterra equation driven by Wiener process and fractional Brownian motion with Hurst parameter H>1/2, we prove an existence and uniqueness result for this equation under suitable assumptions.

  9. Euler-Chebyshev methods for integro-differential equations

    NARCIS (Netherlands)

    Houwen, P.J. van der; Sommeijer, B.P.

    1996-01-01

    We construct and analyse explicit methods for solving initial value problems for systems of differential equations with expensive righthand side functions whose Jacobian has its stiff eigenvalues along the negative axis. Such equations arise after spatial discretization of parabolic integro-differen

  10. On Stability of Linear Barbashin Type Integrodifferential Equations

    Directory of Open Access Journals (Sweden)

    Michael Gil’

    2015-01-01

    Full Text Available We consider the Barbashin type equation ∂u(t,x/∂t=c(t,xu(t,x+∫01k(t,x,su(t,sds+f(t,x   (t>0; 0≤x≤1, where c(·, ·, k(·, ·, ·, and f(·, · are given real functions and u(·, · is unknown. Conditions for the boundedness of solutions of this equation are suggested. In addition, a new stability test is established for the corresponding homogeneous equation. These results improve the well-known ones in the case when the coefficients are differentiable in time. Our approach is based on solution estimates for operator equations. It can be considered as the extension of the freezing method for ordinary differential equations.

  11. Bi-Hamiltonian systems and Lotka-Volterra equations: A three dimensional classification

    OpenAIRE

    Plank, Manfred

    1995-01-01

    We study three dimensional bi-Hamiltonian systems in general and use the obtained results to classify all three dimensional Lotka-Volterra equations, which admit a bi-Hamiltonian representation. In der vorliegenden Arbeit studieren wir drei-dimensionale bi-Hamiltonsche Systeme und klassifizieren alle drei-dimensionalen Lotka-Volterra Gleichungen, welche eine bi-Hamiltonsche Darstellung zulassen.

  12. Solvability of some partial functional integrodifferential equations with finite delay and optimal controls in Banach spaces.

    Science.gov (United States)

    Ezzinbi, Khalil; Ndambomve, Patrice

    2016-01-01

    In this work, we consider the control system governed by some partial functional integrodifferential equations with finite delay in Banach spaces. We assume that the undelayed part admits a resolvent operator in the sense of Grimmer. Firstly, some suitable conditions are established to guarantee the existence and uniqueness of mild solutions for a broad class of partial functional integrodifferential infinite dimensional control systems. Secondly, it is proved that, under generally mild conditions of cost functional, the associated Lagrange problem has an optimal solution, and that for each optimal solution there is a minimizing sequence of the problem that converges to the optimal solution with respect to the trajectory, the control, and the functional in appropriate topologies. Our results extend and complement many other important results in the literature. Finally, a concrete example of application is given to illustrate the effectiveness of our main results.

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

    DEFF Research Database (Denmark)

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

    2016-01-01

    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......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...

  14. Linear Volterra Integral Equations as the Limit of Discrete Systems

    Institute of Scientific and Technical Information of China (English)

    M. Federson; R.Bianconi; L.Barbanti

    2004-01-01

    We consider the multidimensional abstract linear integral equation of Volterra typex (t)+(*)∫Rt a (s)x (s)ds =f (t),t∈R,as the limit of discrete Stieltjes-type systems and we prove results on the existence of continuous solutions.The functions x,a and f are Banach space-valued de .ned on a compact interval R of R n ,R t is a subinterval of R depending on t∈R and (*)∫denotes either the Bochner-Lebesgue integral or the Henstock integral.The results presented here generalize those in [1]and are in the spirit of [3].As a consequence of our approach,it is possible to study the properties of (1)by transferring the properties of the discrete systems.The Henstock integral setting enables us to consider highly oscillating functions.

  15. ON SPECTRAL METHODS FOR VOLTERRA INTEGRAL EQUATIONS AND THE CONVERGENCE ANALYSIS

    Institute of Scientific and Technical Information of China (English)

    Tao Tang; Xiang Xu; Jin Cheng

    2008-01-01

    The main purpose of this work is to provide a novel numerical approach for the Volterra integral equations based on a spectral approach. A Legendre-collocation method is pro-posed to solve the Volterra integral equations of the second kind. We provide a rigorous error analysis for the proposed method, which indicates that the numerical errors decay exponentially provided that the kernel function and the source function are sufficiently smooth. Numerical results confirm the theoretical prediction of the exponential rate of convergence. The result in this work seems to be the first successful spectral approach (with theoretical justification) for the Volterra type equations.

  16. PERIODIC SOLUTIONS OF LINEAR NEUTRAL INTEGRO-DIFFERENTIAL EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    马世旺; 王志成; 许强

    2004-01-01

    Consider the linear neutral FDEd/dt[x(t)+ Ax(t -7)] =∫R[dL(8)]x(t+s)+f(t)where x and f are n-dimensional vectors;A is an n×n constant matrix and L(s) is an n×n matrix function with bounded total variation. Some necessary and sufficient conditions are given which guarantee the existence and uniqueness of periodic solutions to the above equation.

  17. Constructing conservation laws for fractional-order integro-differential equations

    Science.gov (United States)

    Lukashchuk, S. Yu.

    2015-08-01

    In a class of functions depending on linear integro-differential fractional-order variables, we prove an analogue of the fundamental operator identity relating the infinitesimal operator of a point transformation group, the Euler-Lagrange differential operator, and Noether operators. Using this identity, we prove fractional-differential analogues of the Noether theorem and its generalizations applicable to equations with fractional-order integrals and derivatives of various types that are Euler-Lagrange equations. In explicit form, we give fractional-differential generalizations of Noether operators that gives an efficient way to construct conservation laws, which we illustrate with three examples.

  18. Existence and Boundedness of Solutions for Nonlinear Volterra Difference Equations in Banach Spaces

    Directory of Open Access Journals (Sweden)

    Rigoberto Medina

    2016-01-01

    Full Text Available We consider a class of nonlinear discrete-time Volterra equations in Banach spaces. Estimates for the norm of operator-valued functions and the resolvents of quasi-nilpotent operators are used to find sufficient conditions that all solutions of such equations are elements of an appropriate Banach space. These estimates give us explicit boundedness conditions. The boundedness of solutions to Volterra equations with infinite delay is also investigated.

  19. Relativistic integro-differential form of the Lorentz-Dirac equation in 3D without runaways

    Science.gov (United States)

    Ibison, Michael; Puthoff, Harold E.

    2001-04-01

    It is well known that the third-order Lorentz-Dirac equation admits runaway solutions wherein the energy of the particle grows without limit, even when there is no external force. These solutions can be denied simply on physical grounds, and on the basis of careful analysis of the correspondence between classical and quantum theory. Nonetheless, one would prefer an equation that did not admit unphysical behavior at the outset. Such an equation - an integro-differential version of the Lorentz-Dirac equation - is currently available either in 1 dimension only, or in 3 dimensions only in the non-relativistic limit. It is shown herein how the Lorentz-Dirac equation may be integrated without approximation, and is thereby converted to a second-order integro-differential equation in 3D satisfying the above requirement. I.E., as a result, no additional constraints on the solutions are required because runaway solutions are intrinsically absent. The derivation is placed within the historical context established by standard works on classical electrodynamics by Rohrlich, and by Jackson.

  20. On a Nonlinear Partial Integro-Differential Equation

    CERN Document Server

    Abergel, Frederic

    2009-01-01

    Consistently fitting vanilla option surfaces is an important issue when it comes to modelling in finance. Local volatility models introduced by Dupire in 1994 are widely used to price and manage the risks of structured products. However, the inconsistencies observed between the dynamics of the smile in those models and in real markets motivate researches for stochastic volatility modelling. Combining both those ideas to form Local and Stochastic Volatility models is of interest for practitioners. In this paper, we study the calibration of the vanillas in those models. This problem can be written as a nonlinear and nonlocal partial differential equation, for which we prove short-time existence of solutions.

  1. [Parameter identification for systems of nonlinear differential equations by the example of Lotka-Volterra model].

    Science.gov (United States)

    Shakurov, I R; Asadullin, R M

    2014-01-01

    In this article we study the inverse problem of finding coefficients of Lotka-Volterra's equations on one given solution. The conditions of the uniqueness and existence of the inverse problem are found.

  2. Solving Fuzzy Nonlinear Volterra-Fredholm Integral Equations by Using Homotopy Analysis and Adomian Decomposition Methods

    Directory of Open Access Journals (Sweden)

    Shadan Sadigh Behzadi

    2011-12-01

    Full Text Available In this paper, Adomian decomposition method (ADM and homotopy analysis method (HAM are proposed to solving the fuzzy nonlinear Volterra-Fredholm integral equation of the second kind$(FVFIE-2$. we convert a fuzzy nonlinear Volterra-Fredholm integral equation to a nonlinear system of Volterra-Fredholm integral equation in crisp case. we use ADM , HAM and find the approximate solution of this system and hence obtain an approximation for fuzzy solution of the nonlinear fuzzy Volterra-Fredholm integral equation. Also, the existence and uniqueness of the solution and convergence of the proposed methods are proved. Examples is given and the results reveal that homotopy analysis method is very effective and simple compared with the Adomian decomposition method.

  3. Lipschitz regularity for integro-differential equations with coercive Hamiltonians and application to large time behavior

    Science.gov (United States)

    Barles, Guy; Ley, Olivier; Topp, Erwin

    2017-02-01

    In this paper, we provide suitable adaptations of the ‘weak version of Bernstein method’ introduced by the first author in 1991, in order to obtain Lipschitz regularity results and Lipschitz estimates for nonlinear integro-differential elliptic and parabolic equations set in the whole space. Our interest is to obtain such Lipschitz results to possibly degenerate equations, or to equations which are indeed ‘uniformly elliptic’ (maybe in the nonlocal sense) but which do not satisfy the usual ‘growth condition’ on the gradient term allowing to use (for example) the Ishii-Lions’ method. We treat the case of a model equation with a superlinear coercivity on the gradient term which has a leading role in the equation. This regularity result together with comparison principle provided for the problem allow to obtain the ergodic large time behavior of the evolution problem in the periodic setting.

  4. Convergence Analysis of Legendre Pseudospectral Scheme for Solving Nonlinear Systems of Volterra Integral Equations

    Directory of Open Access Journals (Sweden)

    Emran Tohidi

    2014-01-01

    Full Text Available We are concerned with the extension of a Legendre spectral method to the numerical solution of nonlinear systems of Volterra integral equations of the second kind. It is proved theoretically that the proposed method converges exponentially provided that the solution is sufficiently smooth. Also, three biological systems which are known as the systems of Lotka-Volterra equations are approximately solved by the presented method. Numerical results confirm the theoretical prediction of the exponential rate of convergence.

  5. Controllability of nonlocal second-order impulsive neutral stochastic functional integro-differential equations with delay and Poisson jumps

    Directory of Open Access Journals (Sweden)

    Diem Dang Huan

    2015-12-01

    Full Text Available The current paper is concerned with the controllability of nonlocal second-order impulsive neutral stochastic functional integro-differential equations with infinite delay and Poisson jumps in Hilbert spaces. Using the theory of a strongly continuous cosine family of bounded linear operators, stochastic analysis theory and with the help of the Banach fixed point theorem, we derive a new set of sufficient conditions for the controllability of nonlocal second-order impulsive neutral stochastic functional integro-differential equations with infinite delay and Poisson jumps. Finally, an application to the stochastic nonlinear wave equation with infinite delay and Poisson jumps is given.

  6. 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.

  7. 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.

  8. OPTIMAL ESTIMATES FOR THE SEMIDISCRETE GALERKIN METHOD APPLIED TO PARABOLIC INTEGRO-DIFFERENTIAL EQUATIONS WITH NONSMOOTH DATA

    KAUST Repository

    GOSWAMI, DEEPJYOTI

    2014-01-01

    AWe propose and analyse an alternate approach to a priori error estimates for the semidiscrete Galerkin approximation to a time-dependent parabolic integro-differential equation with nonsmooth initial data. The method is based on energy arguments combined with repeated use of time integration, but without using parabolic-type duality techniques. An optimal L2-error estimate is derived for the semidiscrete approximation when the initial data is in L2. A superconvergence result is obtained and then used to prove a maximum norm estimate for parabolic integro-differential equations defined on a two-dimensional bounded domain. © 2014 Australian Mathematical Society.

  9. Volterra Equations of the First kind with Discontinuous Kernels in the Theory of Evolving Systems Control

    CERN Document Server

    Sidorov, Denis

    2011-01-01

    The Volterra integral equations of the first kind with piecewise smooth kernel are considered. Such equations appear in the theory of optimal control of the evolving systems. The existence theorems are proved. The method for constructing approximations of parametric families of solutions of such equations is suggested. The parametric family of solutions is constructed in terms of a logarithmic-power asymptotics.

  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. A lumped mass nonconforming finite element method for nonlinear parabolic integro-differential equations on anisotropic meshes

    Institute of Scientific and Technical Information of China (English)

    SHI Dong-yang; WANG Hui-min; LI Zhi-yan

    2009-01-01

    A lumped mass approximation scheme of a low order Crouzeix-Raviart type nonconforming triangular finite element is proposed to a kind of nonlinear parabolic integro-differential equations. The L2 error estimate is derived on anisotropic meshes without referring to the traditional nonclassical elliptic projection.

  12. Integro-differential equations of fractional order with nonlocal fractional boundary conditions associated with financial asset model

    Directory of Open Access Journals (Sweden)

    Bashir Ahmad

    2013-02-01

    Full Text Available In this article, we discuss the existence of solutions for a boundary-value problem of integro-differential equations of fractional order with nonlocal fractional boundary conditions by means of some standard tools of fixed point theory. Our problem describes a more general form of fractional stochastic dynamic model for financial asset. An illustrative example is also presented.

  13. Positive Solutions for a Second-Order Nonlinear Impulsive Singular Integro-Differential Equation with Integral Conditions in Banach Spaces

    Institute of Scientific and Technical Information of China (English)

    Xingqiu ZHANG

    2012-01-01

    The existence of positive solutions to a boundary value problem of second-order impulsive singular integro-differential equation with integral boundary conditions in a Banach space is obtained by means of fixed point theory.Moreover,an application is also given to illustrate the main result.

  14. Existence of Mild Solutions for a Semilinear Integrodifferential Equation with Nonlocal Initial Conditions

    Directory of Open Access Journals (Sweden)

    Carlos Lizama

    2012-01-01

    Full Text Available Using Hausdorff measure of noncompactness and a fixed-point argument we prove the existence of mild solutions for the semilinear integrodifferential equation subject to nonlocal initial conditions u′(t=Au(t+∫0tB(t-su(sds+f(t,u(t, t∈[0,1], u(0=g(u, where A:D(A⊆X→X, and for every t∈[0,1] the maps B(t:D(B(t⊆X→X are linear closed operators defined in a Banach space X. We assume further that D(A⊆D(B(t for every t∈[0,1], and the functions f:[0,1]×X→X and g:C([0,1];X→X are X-valued functions which satisfy appropriate conditions.

  15. Highly efficient H 1-Galerkin mixed finite element method (MFEM) for parabolic integro-differential equation

    Institute of Scientific and Technical Information of China (English)

    石东洋; 廖歆; 唐启立

    2014-01-01

    A highly effcient H 1-Galerkin mixed finite element method (MFEM) is presented with linear triangular element for the parabolic integro-differential equation. Firstly, some new results about the integral estimation and asymptotic expansions are studied. Then, the superconvergence of order O(h2) for both the original variable u in H1(Ω) norm and the flux p=∇u in H(div,Ω) norm is derived through the interpolation post processing technique. Furthermore, with the help of the asymptotic expansions and a suitable auxiliary problem, the extrapolation solutions with accuracy O(h3) are obtained for the above two variables. Finally, some numerical results are provided to confirm validity of the theoretical analysis and excellent performance of the proposed method.

  16. Homogeneous Lotka-Volterra Equation Possessing a Lie Symmetry: Extension to n-Dimensional Equation and Integrability

    Science.gov (United States)

    Imai, Kenji

    2014-02-01

    In this paper, a new n-dimensional homogeneous Lotka-Volterra (HLV) equation, which possesses a Lie symmetry, is derived by the extension from a three-dimensional HLV equation. Its integrability is shown from the viewpoint of Lie symmetries. Furthermore, we derive dynamical systems of higher order, which possess the Lie symmetry, using the algebraic structure of this HLV equation.

  17. Stability and Convergence of Solutions to Volterra Integral Equations on Time Scales

    Directory of Open Access Journals (Sweden)

    Eleonora Messina

    2015-01-01

    Full Text Available We consider Volterra integral equations on time scales and present our study about the long time behavior of their solutions. We provide sufficient conditions for the stability and investigate the convergence properties when the kernel of the equations vanishes at infinity.

  18. SINGULARLY PERTURBED NONLINEAR BOUNDARY VALUE PROBLEM FOR A KIND OF VOLTERRA TYPE FUNCTIONAL DIFFERENTIAL EQUATION

    Institute of Scientific and Technical Information of China (English)

    鲁世平

    2003-01-01

    By employing the theory of differential inequality and some analysis methods, a nonlinear boundary value problem subject to a general kind of second-order Volterra functional differential equation was considered first. Then, by constructing the right-side layer function and the outer solution, a nonlinear boundary value problem subject to a kind of second- order Volterra functional differential equation with a small parameter was studied further. By using the differential mean value theorem and the technique of upper and lower solution, a new result on the existence of the solutions to the boundary value problem is obtained, and a uniformly valid asymptotic expansions of the solution is given as well.

  19. NEW NUMERICAL METHOD FOR VOLTERRA INTEGRAL EQUATION OF THE SECOND KIND IN PIEZOELASTIC DYNAMIC PROBLEMS

    Institute of Scientific and Technical Information of China (English)

    丁皓江; 王惠明; 陈伟球

    2004-01-01

    The elastodynamic problems of piezoelectric hollow cylinders and spheres under radial deformation can be transformed into a second kind Volterra integral equation about a function with respect to time, which greatly simplifies the solving procedure for such elastodynamic problems. Meanwhile, it becomes very important to find a way to solve the second kind Volterra integral equation effectively and quickly. By using an interpolation function to approximate the unknown function, two new recursive formulae were derived, based on which numerical solution can be obtained step by step. The present method can provide accurate numerical results efficiently. It is also very stable for long time calculating.

  20. A maximum principle for forward-backward stochastic Volterra integral equations and applications in finance

    CERN Document Server

    Wang, Tianxiao

    2010-01-01

    This paper formulates and studies a stochastic maximum principle for forward-backward stochastic Volterra integral equations (FBSVIEs in short), while the control area is assumed to be convex. Then a linear quadratic (LQ in short) problem for backward stochastic Volterra integral equations (BSVIEs in short) is present to illustrate the aforementioned optimal control problem. Motivated by the technical skills in solving above problem, a more convenient and briefer method for the unique solvability of M-solution for BSVIEs is proposed. At last, we will investigate a risk minimization problem by means of the maximum principle for FBSVIEs. Closed-form optimal portfolio is obtained in some special cases.

  1. Integral mean value method for solving a general nonlinear Fredholm integro-differential equation under the mixed conditions

    Directory of Open Access Journals (Sweden)

    Ahmad Molabahrami

    2013-09-01

    Full Text Available In this paper, the integral mean value method is employed to handle the general nonlinear Fredholm integro-differential equations under the mixed conditions. The application of the method is based on the integral mean value theorem for integrals. By using the integral mean value method, an integro-differential equation is transformed to an ordinary differential equation, then by solving it, the obtained solution is transformed to a system of nonlinear algebraic equations to calculate the unknown values. The efficiency of the approach will be shown by applying the procedure on some examples. In this respect, a comparison with series pattern solutions, obtained by some analytic methods, is given. For the approximate solution given by integral mean value method, the bounds of the absolute errors are given. The Mathematica program of the integral mean value method based on the procedure in this paper is designed.

  2. Exact Null Controllability for Fractional Nonlocal Integrodifferential Equations via Implicit Evolution System

    Directory of Open Access Journals (Sweden)

    Amar Debbouche

    2012-01-01

    Full Text Available We introduce a new concept called implicit evolution system to establish the existence results of mild and strong solutions of a class of fractional nonlocal nonlinear integrodifferential system, then we prove the exact null controllability result of a class of fractional evolution nonlocal integrodifferential control system in Banach space. As an application that illustrates the abstract results, two examples are provided.

  3. GLOBAL SOLUTIONS OF SYSTEMS OF NONLINEAR IMPULSIVE VOLTERRA INTEGRAL EQUATIONS IN BANACH SPACES

    Institute of Scientific and Technical Information of China (English)

    陈芳启; 陈予恕

    2001-01-01

    The existence of solutions for systems of nonlinear impulsive Volterra integral equations on the infinite interval R+ with an infinite number of moments of impulse effect in Banach spaces is studied. Some existence theorems of extremal solutions are obtained,which extend the related results for this class of equations on a finite interval with a finite number of moments of impulse effect. The results are demonstrated by means of an example of an infinite systems for impulsive integral equations.

  4. 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.

  5. STABILITY AND BOUNDEDNESS OF SOLUTIONS OF VOLTERRA INTEGRAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAY

    Institute of Scientific and Technical Information of China (English)

    Dishen; Jiabu

    2006-01-01

    This paper studies the stability and boundedness of the solutions of Volterra integral differential equations with infinite delay in the phase space (Ch, |·|h), the h-uniform stability, h-uniformly asymptotic stability and h-boundedness of solutions are obtained.

  6. 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.

  7. Positive solutions for Neumann boundary value problems of nonlinear second-order integro-differential equations in ordered Banach spaces

    OpenAIRE

    Liang Yue; Yang He

    2011-01-01

    Abstract The paper deals with the existence of positive solutions for Neumann boundary value problems of nonlinear second-order integro-differential equations - u ″ ( t ) + M u ( t ) = f ( t , u ( t ) , ( S u ) ( t ) ) , 0 < t < 1 , u ′ ( 0 ) = u ′ ( 1 ) = θ and u ″ ( t ) + M u ( t ) = f ( t , u ( t ) , ( S u ) ( t ) ) , 0 < t < 1 , u ′ ( 0 ) ...

  8. Existence and Analytic Approximation of Solutions of Duffing Type Nonlinear Integro-Differential Equation with Integral Boundary Conditions

    Directory of Open Access Journals (Sweden)

    Alsaedi Ahmed

    2009-01-01

    Full Text Available A generalized quasilinearization technique is developed to obtain a sequence of approximate solutions converging monotonically and quadratically to a unique solution of a boundary value problem involving Duffing type nonlinear integro-differential equation with integral boundary conditions. The convergence of order for the sequence of iterates is also established. It is found that the work presented in this paper not only produces new results but also yields several old results in certain limits.

  9. Repeated games for eikonal equations, integral curvature flows and non-linear parabolic integro-differential equations

    CERN Document Server

    Imbert, Cyril

    2009-01-01

    The main purpose of this paper is to approximate several non-local evolution equations by zero-sum repeated games in the spirit of the previous works of Kohn and the second author (2006 and 2009): general fully non-linear parabolic integro-differential equations on the one hand, and the integral curvature flow of an interface (Imbert, 2008) on the other hand. In order to do so, we start by constructing such a game for eikonal equations whose speed has a non-constant sign. This provides a (discrete) deterministic control interpretation of these evolution equations. In all our games, two players choose positions successively, and their final payoff is determined by their positions and additional parameters of choice. Because of the non-locality of the problems approximated, by contrast with local problems, their choices have to "collect" information far from their current position. For integral curvature flows, players choose hypersurfaces in the whole space and positions on these hypersurfaces. For parabolic i...

  10. Solution of nonlinear Volterra-Hammerstein integral equations using alternative Legendre collocation method

    Directory of Open Access Journals (Sweden)

    Sohrab Bazm

    2016-11-01

    Full Text Available Alternative Legendre polynomials (ALPs are used to approximate the solution of a class of nonlinear Volterra-Hammerstein integral equations. For this purpose, the operational matrices of integration and the product for ALPs are derived. Then, using the collocation method, the considered problem is reduced into a set of nonlinear algebraic equations. The error analysis of the method is given and the efficiency and accuracy are illustrated by applying the method to some examples.

  11. Existence and Numerical Solution of the Volterra Fractional Integral Equations of the Second Kind

    Directory of Open Access Journals (Sweden)

    Abdon Atangana

    2013-01-01

    Full Text Available This work presents the possible generalization of the Volterra integral equation second kind to the concept of fractional integral. Using the Picard method, we present the existence and the uniqueness of the solution of the generalized integral equation. The numerical solution is obtained via the Simpson 3/8 rule method. The convergence of this scheme is presented together with numerical results.

  12. Hybrid function method for solving Fredholm and Volterra integral equations of the second kind

    Science.gov (United States)

    Hsiao, Chun-Hui

    2009-08-01

    Numerical solutions of Fredholm and Volterra integral equations of the second kind via hybrid functions, are proposed in this paper. Based upon some useful properties of hybrid functions, integration of the cross product, a special product matrix and a related coefficient matrix with optimal order, are applied to solve these integral equations. The main characteristic of this technique is to convert an integral equation into an algebraic; hence, the solution procedures are either reduced or simplified accordingly. The advantages of hybrid functions are that the values of n and m are adjustable as well as being able to yield more accurate numerical solutions than the piecewise constant orthogonal function, for the solutions of integral equations. We propose that the available optimal values of n and m can minimize the relative errors of the numerical solutions. The high accuracy and the wide applicability of the hybrid function approach will be demonstrated with numerical examples. The hybrid function method is superior to other piecewise constant orthogonal functions [W.F. Blyth, R.L. May, P. Widyaningsih, Volterra integral equations solved in Fredholm form using Walsh functions, Anziam J. 45 (E) (2004) C269-C282; M.H. Reihani, Z. Abadi, Rationalized Haar functions method for solving Fredholm and Volterra integral equations, J. Comp. Appl. Math. 200 (2007) 12-20] for these problems.

  13. Local and global existence of mild solution to impulsive fractional semilinear integro-differential equation with noncompact semigroup

    Science.gov (United States)

    Gou, Haide; Li, Baolin

    2017-01-01

    In this paper, we study local and global existence of mild solution for an impulsive fractional functional integro differential equation with non-compact semi-group in Banach spaces. We establish a general framework to find the mild solutions for impulsive fractional integro-differential equations, which will provide an effective way to deal with such problems. The theorems proved in this paper improve and extend some related conclusions on this topic. Finally, two applications are given to illustrate that our results are valuable.

  14. Dissipativity of Multistep Runge-Kutta Methods for Nonlinear Volterra Delay-integro-differential Equations

    Institute of Scientific and Technical Information of China (English)

    Rui QI; Cheng-jian ZHANG; Yu-jie ZHANG

    2012-01-01

    This paper is concerned with the numerical dissipativity of multistep Runge-Kutta methods for nonlinear Volterra delay-integro-differential equations. We investigate the dissipativity properties of (k,l)-algebraically stable multistep Runge-Kutta methods with constrained grid and an uniform grid.The finitedimensional and infinite-dimensional dissipativity results of (k,l)-algebraically stable Runge-Kutta methods are obtained.

  15. Coexistence for systems governed by difference equations of Lotka-Volterra type.

    Science.gov (United States)

    Hofbauer, J; Hutson, V; Jansen, W

    1987-01-01

    The question of the long term survival of species in models governed by Lotka-Volterra difference equations is considered. The criterion used is the biologically realistic one of permanence, that is populations with all initial values positive must eventually all become greater than some fixed positive number. We show that in spite of the complex dynamics associated even with the simplest of such systems, it is possible to obtain readily applicable criteria for permanence in a wide range of cases.

  16. Controllability for the impulsive semilinear fuzzy integrodifferential equations with nonlocal conditions

    Energy Technology Data Exchange (ETDEWEB)

    Kwun, Y C; Hwang, J S; Park, J S; Park, J H [Department of Mathematics, Dong-A University, Pusan 604-714 (Korea, Republic of); Department of Math. Education, Chinju National Universuty of Education, Chinju 660-756 (Korea, Republic of); Division of Math. Sci., Pukyong National University, Pusan 608-737 (Korea, Republic of)], E-mail: jihpark@pknu.ac.kr

    2008-02-15

    In this paper. we study the controllability for the impulsive semilinear fuzzy integrodifferential control system with nonlocal conditions in E{sub N} by using the concept of fuzzy number whose values are normal, convex, upper semicontinuous and compactly supported interval in E{sub N}.

  17. Volterra equation for pricing and hedging in a regime switching market

    Directory of Open Access Journals (Sweden)

    Anindya Goswami

    2014-12-01

    Full Text Available It is known that the risk minimizing price of European options in Markov-modulated market satisfies a system of coupled PDE, known as generalized B–S–M PDE. In this paper, another system of equations, which can be categorized as a Volterra integral equations of second kind, are considered. It is shown that this system of integral equations has smooth solution and the solution solves the generalized B–S–M PDE. Apart from showing existence and uniqueness of the PDE, this IE representation helps to develop a new computational method. It enables to compute the European option price and corresponding optimal hedging strategy by using quadrature method.

  18. Analysis of multiple interfacial cracks in three-dimensional bimaterials using hypersingular integro-differential equation method

    Institute of Scientific and Technical Information of China (English)

    Chun-hui XU; Tai-yan QIN; Li YUAN; NaoAki Noda

    2009-01-01

    By using the concept of finite-part integral, a set of hypersingular integro-differential equations for multiple interracial cracks in a three-dimensional infinite hi-material subjected to arbitrary loads is derived. In the numerical analysis, unknown displacement discontinuities are approximated with the products of the fundamental den-sity functions and power series. The fundamental functions are chosen to express a two-dimensional interface crack rigorously. As illustrative examples, the stress intensity factors for two rectangular interface cracks are calculated for various spacing, crack shape and elastic constants. It is shown that the stress intensity factors decrease with the crack spacing.

  19. Comparison principles for integro-differential equations with L{\\'e}vy operators - the case of spacial depending jumps -

    CERN Document Server

    Arisawa, M

    2010-01-01

    A comparison principle for the integro-differential equation with the L{\\'e}vy operator corresponding to the spacial depending jump process is presented in this paper. The jump $\\beta(x,z)$ at a point $x$ and the L{\\'e}vy measure $dq(z)$ satisfy conditions given independently for each of them, which is a major difference from other works. Moreover, a useful form of the viscosity solution is presented, which is equivalent to more "classical" definitions, and is used to prove the comparison principle easily.

  20. On the Property of Being a Bary Basis for a System of Eigenfunctions of a Nonlinear Integro-Differential Equation

    CERN Document Server

    Zhidkov, E P

    2000-01-01

    We consider a nonlinear integro-differential equation on a segment with zero Dirichlet boundary conditions and a normalization condition, containing a spectral parameter, which can arise in the mean field approximation for a quantum-mechanical description of a solid. We prove the existence of a countable set of solutions and investigate properties of these solutions. The main result consists in proving the property of being a Bary basis for a sequence of solutions of the problem, possessing a given behavior, the existence of which is proved.

  1. Existence of Solutions to Nonlinear Impulsive Volterra Integral Equations in Banach Spaces

    Institute of Scientific and Technical Information of China (English)

    CHEN Fangqi; TIAN Ruilan

    2005-01-01

    In this paper, the existence of solutions is studied for nonlinear impulsive Volterra integral equations with infinite moments of impulse effect on the half line R+ in Banach spaces.By the use of a new comparison result and recurrence method, the new existence theorems are achieved under a weaker compactness-type condition, which generalize and improve the related results for this class of equations with finite moments of impulse effect on finite interval and infinite moments of impulse effect on infinite interval.

  2. 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.

  3. The Lotka-Volterra equation over a finite ring Z/p{sup N}Z

    Energy Technology Data Exchange (ETDEWEB)

    Matsutani, Shigeki E-mail: RXB01142@nifty.ne.jp

    2001-12-07

    The discrete Lotka-Volterra equation over p-adic space was constructed since p-adic space is a prototype of spaces with non-Archimedean valuations and the space given by taking the ultra-discrete limit studied in soliton theory should be regarded as a space with the non-Archimedean valuations given in my previous paper (Matsutani S 2001 Int. J. Math. Math. Sci.). In this paper, using the natural projection from a p-adic integer to a ring Z/p{sup n}Z, a soliton equation is defined over the ring. Numerical computations show that it behaves regularly. (author)

  4. Incremental localized boundary-domain integro-differential equations of elastic damage mechanics for inhomogeneous body

    OpenAIRE

    Mikhailov, SE

    2006-01-01

    Copyright @ 2006 Tech Science Press A quasi-static mixed boundary value problem of elastic damage mechanics for a continuously inhomogeneous body is considered. Using the two-operator Green-Betti formula and the fundamental solution of an auxiliary homogeneous linear elasticity with frozen initial, secant or tangent elastic coe±cients, a boundary-domain integro-differential formulation of the elasto-plastic problem with respect to the displacement rates and their gradients is derived. Usin...

  5. Unsteady Integrodifferential Equation of Fluid-Structure Interaction in Constricted Collapsible Tube Model of Diseased Human Coronary Artery

    Directory of Open Access Journals (Sweden)

    Eric Velaski Tuema

    2012-01-01

    Full Text Available Unsteady flow in a collapsible tube is analyzed to simulate a diseased human coronary artery. The novelty of the approach is that the set of equations governing the fluid-structure interaction is reduced to a single integrodifferential equation in the transient state. The equation is then solved using the finite difference method to obtain the flow characteristics and compliant wall behavior. Three control parameters are investigated, namely, Reynolds number, inlet transmural pressure, and the wall thickness. The predicted wall deflection is quite large at low Reynolds numbers, suggesting possible approach to breakdown in equilibrium. The transmural pressure increases with wall deflection and bulges appear at the ends of the membrane indicating critical stage of stability, consistent with previous studies. Increase in wall thickness reduces the wall deflection and ultimately results in its collapse which may indicate another breakdown in equilibrium. An increase in internal pressure is required to maintain membrane stability.

  6. Analytical solution to DGLAP integro-differential equation in a simple toy-model with a fixed gauge coupling

    CERN Document Server

    Alvarez, Gustavo; Kniehl, Bernd A; Kondrashuk, Igor; Parra-Ferrada, Ivan

    2016-01-01

    We consider a simple model for QCD dynamics in which DGLAP integro-differential equation may be solved analytically. This is a gauge model which possesses dominant evolution of gauge boson (gluon) distribution and in which the gauge coupling does not run. This may be ${\\cal N} =4$ supersymmetric gauge theory with softly broken supersymmetry, other finite supersymmetric gauge theory with lower level of supersymmetry, or topological Chern-Simons field theories. We maintain only one term in the splitting function of unintegrated gluon distribution and solve DGLAP analytically for this simplified splitting function. The solution is found by use of the Cauchy integral formula. The solution restricts form of the unintegrated gluon distribution as function of transfer momentum and of Bjorken $x$. Then we consider an almost realistic splitting function of unintegrated gluon distribution as an input to DGLAP equation and solve it by the same method which we have developed to solve DGLAP equation for the toy-model. We ...

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

    Energy Technology Data Exchange (ETDEWEB)

    Hu Xingbiao [Institute of Computational Mathematics and Scientific Engineering Computing, AMSS, Chinese Academy of Sciences, PO Box 2719, Beijing 100080 (China); Li Chunxia [Institute of Computational Mathematics and Scientific Engineering Computing, AMSS, Chinese Academy of Sciences, PO Box 2719, Beijing 100080 (China); Nimmo, Jonathan J C [Department of Mathematics, University of Glasgow, Glasgow G12 8QW (United Kingdom); Yu Guofu [Institute of Computational Mathematics and Scientific Engineering Computing, AMSS, Chinese Academy of Sciences, PO Box 2719, Beijing 100080 (China)

    2005-01-07

    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.

  8. Numerical Solution of Nonlinear Fredholm Integro-Differential Equations Using Spectral Homotopy Analysis Method

    Directory of Open Access Journals (Sweden)

    Z. Pashazadeh Atabakan

    2013-01-01

    Full Text Available Spectral homotopy analysis method (SHAM as a modification of homotopy analysis method (HAM is applied to obtain solution of high-order nonlinear Fredholm integro-differential problems. The existence and uniqueness of the solution and convergence of the proposed method are proved. Some examples are given to approve the efficiency and the accuracy of the proposed method. The SHAM results show that the proposed approach is quite reasonable when compared to homotopy analysis method, Lagrange interpolation solutions, and exact solutions.

  9. Jacobi spectral collocation method for the approximate solution of multidimensional nonlinear Volterra integral equation.

    Science.gov (United States)

    Wei, Yunxia; Chen, Yanping; Shi, Xiulian; Zhang, Yuanyuan

    2016-01-01

    We present in this paper the convergence properties of Jacobi spectral collocation method when used to approximate the solution of multidimensional nonlinear Volterra integral equation. The solution is sufficiently smooth while the source function and the kernel function are smooth. We choose the Jacobi-Gauss points associated with the multidimensional Jacobi weight function [Formula: see text] (d denotes the space dimensions) as the collocation points. The error analysis in [Formula: see text]-norm and [Formula: see text]-norm theoretically justifies the exponential convergence of spectral collocation method in multidimensional space. We give two numerical examples in order to illustrate the validity of the proposed Jacobi spectral collocation method.

  10. Optimal Parametric Iteration Method for Solving Multispecies Lotka-Volterra Equations

    Directory of Open Access Journals (Sweden)

    Vasile Marinca

    2012-01-01

    Full Text Available We apply an analytical method called the Optimal Parametric Iteration Method (OPIM to multispecies Lotka-Volterra equations. By using initial values, accurate explicit analytic solutions have been derived. The method does not depend upon small parameters and provides us with a convenient way to optimally control the convergence of the approximate solutions. An excellent agreement has been demonstrated between the obtained solutions and the numerical ones. This new approach, which can be easily applied to other strongly nonlinear problems, is very effective and yields very accurate results.

  11. 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.

  12. Direct and inverse solver for the 3D optoacoustic Volterra equation

    CERN Document Server

    Stritzel, J; Wollweber, M; Roth, B

    2016-01-01

    The direct problem of optoacoustic signal generation in biological media consists of solving the inhomogeneous optoacoustic wave equation for an initial acoustic stress profile. In contrast, the mathematically challenging inverse problem requires the reconstruction of the initial stress profile from a proper set of observed signals. In this article, we consider the particular case of a Gaussian transverse irradiation source profile in the paraxial approximation of the wave equation, for which the direct problem along the beam axis can be cast into a linear Volterra integral equation of the second kind. This integral equation can be used in two ways: as a forward solver to predict optoacoustic signals in terms of the direct problem, and as an inverse solver for which we here devise highly efficient numerical schemes used for the reconstruction of initial pressure profiles from observed signals, constituting a methodical progress of computational aspects of optoacoustics. In this regard, we explore the validity...

  13. A periodic phase soliton of the ultradiscrete hungry Lotka-Volterra equation

    Energy Technology Data Exchange (ETDEWEB)

    Nakamura, Shinya [Major in Pure and Applied Mathematics, Graduate School of Fundamental Science and Engineering, Waseda University, 3-4-1, Okubo, Shinjuku-ku, Tokyo 169-8555 (Japan)], E-mail: s-nakamura@moegi.waseda.jp

    2009-12-11

    We propose a new type of solution to the ultradiscrete hungry Lotka-Volterra (uhLV) equation. For the solution, the periodic phase is introduced into the known soliton and the extended soliton becomes a traveling wave showing a periodic variation. We call this type of wave a 'periodic phase soliton' (PPS). The solution has two forms of expression: one is the 'perturbation form' and the other is the 'ultradiscrete permanent form'. We analyze the interaction among PPSs and solitons. Moreover, we give the outline of proof to show that the solution satisfies the bilinear equation of the uhLV equation.

  14. Solving Volterra's Population Model Using New Second Derivative Multistep Methods

    Directory of Open Access Journals (Sweden)

    K. Parand

    2008-01-01

    Full Text Available In this study new second derivative multistep methods (denoted SDMM are used to solve Volterra's model for population growth of a species within a closed system. This model is a nonlinear integro-differential where the integral term represents the effect of toxin. This model is first converted to a nonlinear ordinary differential equation and then the new SDMM, which has good stability and accuracy properties, are applied to solve this equation. We compare this method with the others and show that new SDMM gives excellent results.

  15. 线性抛物Volterra差分方程的全局吸引性%Global Attractivity of Linear Parabolic Volterra Difference Equations

    Institute of Scientific and Technical Information of China (English)

    黄立

    2004-01-01

    In this paper, by constructing Liapunov Sequences, we study the golbal attractivity of linear Parabolic volterra difference equations of neutral type and obtain some sufficient conditions for the global attractivity of the zero solution of above equations.

  16. 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.

  17. The algebraic structure of discrete zero curvature equations associated with integrable couplings and application to enlarged Volterra systems

    Institute of Scientific and Technical Information of China (English)

    2009-01-01

    An algebraic structure of discrete zero curvature equations is established for integrable coupling systems associated with semi-direct sums of Lie algebras. As an application example of this algebraic structure, a τ-symmetry algebra for the Volterra lattice integrable couplings is engendered from this theory.

  18. Analytical solution to DGLAP integro-differential equation in a simple toy-model with a fixed gauge coupling

    Energy Technology Data Exchange (ETDEWEB)

    Alvarez, Gustavo [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Concepcion Univ. (Chile). Dept. de Fisica; Cvetic, Gorazd [Univ. Tecnica Federico Santa Maria, Valparaiso (Chile). Dept. de Fisica; Kniehl, Bernd A. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Kondrashuk, Igor [Univ. del Bio-Bio, Chillan (Chile). Grupo de Matematica Aplicada; Univ. del Bio-Bio, Chillan (Chile). Grupo de Fisica de Altas Energias; Parra-Ferrada, Ivan [Talca Univ. (Chile). Inst. de Matematica y Fisica

    2016-11-15

    We consider a simple model for QCD dynamics in which DGLAP integro-differential equation may be solved analytically. This is a gauge model which possesses dominant evolution of gauge boson (gluon) distribution and in which the gauge coupling does not run. This may be N=4 supersymmetric gauge theory with softly broken supersymmetry, other finite supersymmetric gauge theory with lower level of supersymmetry, or topological Chern-Simons field theories. We maintain only one term in the splitting function of unintegrated gluon distribution and solve DGLAP analytically for this simplified splitting function. The solution is found by use of the Cauchy integral formula. The solution restricts form of the unintegrated gluon distribution as function of transfer momentum and of Bjorken x. Then we consider an almost realistic splitting function of unintegrated gluon distribution as an input to DGLAP equation and solve it by the same method which we have developed to solve DGLAP equation for the toy-model. We study a result obtained for the realistic gluon distribution and find a singular Bessel-like behaviour in the vicinity of the point x=0 and a smooth behaviour in the vicinity of the point x=1.

  19. Global attractor of coupled difference equations and applications to Lotka-Volterra systems

    Directory of Open Access Journals (Sweden)

    Pao CV

    2005-01-01

    Full Text Available This paper is concerned with a coupled system of nonlinear difference equations which is a discrete approximation of a class of nonlinear differential systems with time delays. The aim of the paper is to show the existence and uniqueness of a positive solution and to investigate the asymptotic behavior of the positive solution. Sufficient conditions are given to ensure that a unique positive equilibrium solution exists and is a global attractor of the difference system. Applications are given to three basic types of Lotka-Volterra systems with time delays where some easily verifiable conditions on the reaction rate constants are obtained for ensuring the global attraction of a positive equilibrium solution.

  20. Global attractor of coupled difference equations and applications to Lotka-Volterra systems

    Directory of Open Access Journals (Sweden)

    C. V. Pao

    2005-03-01

    Full Text Available This paper is concerned with a coupled system of nonlinear difference equations which is a discrete approximation of a class of nonlinear differential systems with time delays. The aim of the paper is to show the existence and uniqueness of a positive solution and to investigate the asymptotic behavior of the positive solution. Sufficient conditions are given to ensure that a unique positive equilibrium solution exists and is a global attractor of the difference system. Applications are given to three basic types of Lotka-Volterra systems with time delays where some easily verifiable conditions on the reaction rate constants are obtained for ensuring the global attraction of a positive equilibrium solution.

  1. A Nonconforming Arbitrary Quadrilateral H1-Galerkin Mixed Finite Element Method for Hyperbolic Type Integro-differential Equation%双曲型积分微分方程的非协调任意四边形H1-Galerkin混合有限元方法

    Institute of Scientific and Technical Information of China (English)

    王海红; 郭城

    2012-01-01

    针对双曲型积分微分方程问题,研究了非协调任意四边形H1-Galerkin混合有限元方法.在半离散格式下,利用所选单元本身的特点,在不需要Ritz-Volterra投影的情况下得到了与传统协调混合有限元方法相同的误差估计.%A nonconforming arbitrary quadrilateral H1 -Galerkin mixed finite element method for hyperbolic type integro-differential equations problem was studied. By use of the characteristic of the chosen finite elements, the same error estimates as in the traditional conforming mixed finite elements methods were derived in semi-discrete formulation without using Ritz-Volterra projection.

  2. Optimal Error Estimates of Two Mixed Finite Element Methods for Parabolic Integro-Differential Equations with Nonsmooth Initial Data

    KAUST Repository

    Goswami, Deepjyoti

    2013-05-01

    In the first part of this article, a new mixed method is proposed and analyzed for parabolic integro-differential equations (PIDE) with nonsmooth initial data. Compared to the standard mixed method for PIDE, the present method does not bank on a reformulation using a resolvent operator. Based on energy arguments combined with a repeated use of an integral operator and without using parabolic type duality technique, optimal L2 L2-error estimates are derived for semidiscrete approximations, when the initial condition is in L2 L2. Due to the presence of the integral term, it is, further, observed that a negative norm estimate plays a crucial role in our error analysis. Moreover, the proposed analysis follows the spirit of the proof techniques used in deriving optimal error estimates for finite element approximations to PIDE with smooth data and therefore, it unifies both the theories, i.e., one for smooth data and other for nonsmooth data. Finally, we extend the proposed analysis to the standard mixed method for PIDE with rough initial data and provide an optimal error estimate in L2, L 2, which improves upon the results available in the literature. © 2013 Springer Science+Business Media New York.

  3. Lotka-Volterra system with Volterra multiplier.

    Science.gov (United States)

    Gürlebeck, Klaus; Ji, Xinhua

    2011-01-01

    With the aid of Volterra multiplier, we study ecological equations for both tree system and cycle system. We obtain a set of sufficient conditions for the ultimate boundedness to nonautonomous n-dimensional Lotka-Volterra tree systems with continuous time delay. The criteria are applicable to cooperative model, competition model, and predator-prey model. As to cycle system, we consider a three-dimensional predator-prey Lotka-Volterra system. In order to get a condition under which the system is globally asymptotic stable, we obtain a Volterra multiplier, so that in a parameter region the system is with the Volterra multiplier it is globally stable. We have also proved that in regions in which the condition is not satisfied, the system is unstable or at least it is not globally stable. Therefore, we say that the three-dimensional cycle system is with global bifurcation.

  4. A New Numerical Method for Fast Solution of Partial Integro-Differential Equations

    OpenAIRE

    Dourbal, Pavel; Pekker, Mikhail

    2016-01-01

    A new method of numerical solution for partial differential equations is proposed. The method is based on a fast matrix multiplication algorithm. Two-dimensional Poison equation is used for comparison of the proposed method with conventional numerical methods. It was shown that the new method allows for linear growth in the number of elementary addition and multiplication operations with the growth of grid size, as contrasted with quadratic growth necessitated by the standard numerical method...

  5. Homotopy perturbation Laplace transform solution of fractional non-linear reaction diffusion system of Lotka-Volterra type differential equation

    Directory of Open Access Journals (Sweden)

    M.H. Tiwana

    2017-04-01

    Full Text Available This work investigates the fractional non linear reaction diffusion (FNRD system of Lotka-Volterra type. The system of equations together with the boundary conditions are solved by Homotopy perturbation transform method (HPTM. The series solutions are obtained for the two cases (homogeneous and non-homogeneous of FNRD system. The effect of fractional parameter on the mass concentration of two species are shown and discussed with the help of 3D graphs.

  6. 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.

  7. Numerical approach for a system of second kind Volterra integral equations in magneto-electro-elastic dynamic problems

    Institute of Scientific and Technical Information of China (English)

    DING Hao-jiang; WANG Hui-ming

    2005-01-01

    The elastodynamic problems of magneto-electro-elastic hollow cylinders in the state ofaxisymmetric plane strain case can be transformed into two Volterra integral equations of the second kind about two functions with respect to time. Interpolation functions were introduced to approximate two unknown functions in each time subinterval and two new recursive formulae are derived. By using the recursive formulae, numerical results were obtained step by step. Under the same time step, the accuracy of the numerical results by the present method is much higher than that by the traditional quadrature method.

  8. 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.

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

    Energy Technology Data Exchange (ETDEWEB)

    Monte, Luigi [ENEA CR Casaccia, Via P. Anguillarese 301 00100 Rome (Italy)], E-mail: luigi.monte@enea.it

    2009-06-15

    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.

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

    Science.gov (United States)

    Monte, Luigi

    2009-06-01

    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.

  11. 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.

  12. A problem with inverse time for a singularly perturbed integro-differential equation with diagonal degeneration of the kernel of high order

    Science.gov (United States)

    Bobodzhanov, A. A.; Safonov, V. F.

    2016-04-01

    We consider an algorithm for constructing asymptotic solutions regularized in the sense of Lomov (see [1], [2]). We show that such problems can be reduced to integro-differential equations with inverse time. But in contrast to known papers devoted to this topic (see, for example, [3]), in this paper we study a fundamentally new case, which is characterized by the absence, in the differential part, of a linear operator that isolates, in the asymptotics of the solution, constituents described by boundary functions and by the fact that the integral operator has kernel with diagonal degeneration of high order. Furthermore, the spectrum of the regularization operator A(t) (see below) may contain purely imaginary eigenvalues, which causes difficulties in the application of the methods of construction of asymptotic solutions proposed in the monograph [3]. Based on an analysis of the principal term of the asymptotics, we isolate a class of inhomogeneities and initial data for which the exact solution of the original problem tends to the limit solution (as \\varepsilon\\to+0) on the entire time interval under consideration, also including a boundary-layer zone (that is, we solve the so-called initialization problem). The paper is of a theoretical nature and is designed to lead to a greater understanding of the problems in the theory of singular perturbations. There may be applications in various applied areas where models described by integro-differential equations are used (for example, in elasticity theory, the theory of electrical circuits, and so on).

  13. Boundary Controllability of Nonlinear Fractional Integrodifferential Systems

    Directory of Open Access Journals (Sweden)

    Ahmed HamdyM

    2010-01-01

    Full Text Available Sufficient conditions for boundary controllability of nonlinear fractional integrodifferential systems in Banach space are established. The results are obtained by using fixed point theorems. We also give an application for integropartial differential equations of fractional order.

  14. Lotka-Volterra equations with chemotaxis: walls, barriers and travelling waves.

    Science.gov (United States)

    Pettet, G J; McElwain, D L; Norbury, J

    2000-12-01

    In this paper we consider a simple two species model for the growth of new blood vessels. The model is based upon the Lotka-Volterra system of predator and prey interaction, where we identify newly developed capillary tips as the predator species and a chemoattractant which directs their motion as the prey. We extend the Lotka-Volterra system to include a one-dimensional spatial dependence, by allowing the predators to migrate in a manner modelled on the phenomenon of chemotaxis. A feature of this model is its potential to support travelling wave solutions. We emphasize that in order to determine the existence of such travelling waves it is essential that the global relationships of a number of phase plane features other than the equilibria be investigated.

  15. Series Solution of the Multispecies Lotka-Volterra Equations by Means of the Homotopy Analysis Method

    Directory of Open Access Journals (Sweden)

    A. Sami Bataineh

    2008-01-01

    Full Text Available The time evolution of the multispecies Lotka-Volterra system is investigated by the homotopy analysis method (HAM. The continuous solution for the nonlinear system is given, which provides a convenient and straightforward approach to calculate the dynamics of the system. The HAM continuous solution generated by polynomial base functions is of comparable accuracy to the purely numerical fourth-order Runge-Kutta method. The convergence theorem for the three-dimensional case is also given.

  16. Normalized RBF networks: application to a system of integral equations

    Energy Technology Data Exchange (ETDEWEB)

    Golbabai, A; Seifollahi, S; Javidi, M [Department of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16844 (Iran, Islamic Republic of)], E-mail: golbabai@iust.ac.ir, E-mail: seif@iust.ac.ir, E-mail: mojavidi@yahoo.com

    2008-07-15

    Linear integral and integro-differential equations of Fredholm and Volterra types have been successfully treated using radial basis function (RBF) networks in previous works. This paper deals with the case of a system of integral equations of Fredholm and Volterra types with a normalized radial basis function (NRBF) network. A novel learning algorithm is developed for the training of NRBF networks in which the BFGS backpropagation (BFGS-BP) least-squares optimization method as a recursive model is used. In the approach presented here, a trial solution is given by an NRBF network of incremental architecture with a set of unknown parameters. Detailed learning algorithms and concrete examples are also included.

  17. Banach空间非线性脉冲积分-微分方程终值问题的极值解%EXTREMAL SOLUTIONS OF TERMINAL VALUE PROBLEMS FOR NONLINEAR IMPULSIVE INTEGRO-DIFFERENTIAL EQUATIONS IN BANACH SPACES

    Institute of Scientific and Technical Information of China (English)

    2000-01-01

    The comparison principle is first established,and then the lower and upper solution method and the monotone iterative technique are employed to the study of terminal value problems for the first order nonlinear impulsive integro-differential equations in Banach spaces.Finally,the existence theorem on the maximal and minimal solutions is obtained.

  18. Solution to the Volterra integral equations of the first kind with piecewise continuous kernels in class of Sobolev-Schwartz distributions

    CERN Document Server

    Sidorov, Denis

    2012-01-01

    Sufficient conditions for existence and uniqueness of the solution of the Volterra integral equations of the first kind with piecewise continuous kernels are derived in framework of Sobolev-Schwartz distribution theory. The asymptotic approximation of the parametric family of generalized solutions is constructed. The method for the solution's regular part refinement is proposed using the successive approximations method.

  19. Blow Up of a Cycle in Lotka-Volterra Type Equations with Competition-Cooperation Terms and Quasi-Linear Systems

    CERN Document Server

    Bouse, E

    2010-01-01

    We consider systems where a cycle born via the Hopf bifurcation blows up to infinity as a parameter ranges over a finite interval. Two examples demonstrating this effect are presented: planar Lotka-Volterra type systems with a competition-cooperation term and quasi-linear higher order equations.

  20. 非线性抛物积分微分方程的类Wilson非协调元分析%Analysis of Quasi-Wilson Nonconforming Element for Nonlinear Parabolic Integro-differential Equation

    Institute of Scientific and Technical Information of China (English)

    王芬玲; 石东洋; 陈金环

    2012-01-01

    在半离散和全离散格式下讨论非线性抛物积分微分方程的类Wilson非协调有限元逼近.当问题的精确解u∈H3(Ω)/H4(Ω)时,利用该元的相容误差在能量模意义下可以达到O(h2 )/O(h3)比其插值误差高一阶和二阶的特殊性质,再结合协调部分的高精度分析及插值后处理技术,并借助于双线性插值代替传统有限元分析中不可缺少的Ritz-Volterra投影导出了半离散格式下的O(h2)阶超逼近和超收敛结果.同时分别得到了向后Euler全离散格式下的超逼近性和Crank-Nicolson全离散格式下的最优误差估计.%A nonconforming quasi-Wilson finite element approximation for nonlinear parabolic integro-differential equation is discussed under the semi-discrete and fully-discrete schemes. By use of the special property of the element,i. e. , the consistence error estimate in energy norm when the exact solution u of the problem belongs to H3(Ω)/ H4(Ω) can reach to O(h2)/O(h3), one/two order higher than the interpolation error, then combination it with the higher accuracy analysis of its conforming part and the interpolated postprocessing technique, the superclose and superconvergence results with order O(h2) are obtained for semi-discrete scheme through interpolation instead of the Ritz-Volterra projection which is an indispensable tool in traditional finite element analysis. The superclose property and the optimal error estimate for backward Euler and Crank-Nicolson fully-discrete schemes are derived , respectively.

  1. ADFE METHOD WITH HIGH ACCURACY FOR NONLINEAR PARABOLIC INTEGRO-DIFFERENTIAL SYSTEM WITH NONLINEAR BOUNDARY CONDITIONS

    Institute of Scientific and Technical Information of China (English)

    崔霞

    2002-01-01

    Alternating direction finite element (ADFE) scheme for d-dimensional nonlinear system of parabolic integro-differential equations is studied. By using a local approximation based on patches of finite elements to treat the capacity term qi(u), decomposition of the coefficient matrix is realized; by using alternating direction, the multi-dimensional problem is reduced to a family of single space variable problems, calculation work is simplified; by using finite element method, high accuracy for space variant is kept; by using inductive hypothesis reasoning, the difficulty coming from the nonlinearity of the coefficients and boundary conditions is treated; by introducing Ritz-Volterra projection, the difficulty coming from the memory term is solved. Finally, by using various techniques for priori estimate for differential equations, the unique resolvability and convergence properties for both FE and ADFE schemes are rigorously demonstrated, and optimal H1 and L2norm space estimates and O((△t)2) estimate for time variant are obtained.

  2. Superconvergence of Finite Element Approximations to Parabolic and Hyperbolic Integro-Differential Equations%抛物型和双曲型积分-微分方程有限元逼近的超收敛性质

    Institute of Scientific and Technical Information of China (English)

    张铁; 李长军

    2001-01-01

    The object of this paper is to investigate the superconvergence properties of finite element approximations to parabolic and hyperbolic integro-differential equations. The quasi projection technique introduced earlier by Douglas et al. is developed to derive the O(h2r) order knot superconvergence in the case of a single space variable, and to show the optimal order negative norm estimates in the case of several space variables.

  3. Periodic Solutions of Scalar Neutral Integro-Differential Equation%中立型标量积分微分方程的周期解

    Institute of Scientific and Technical Information of China (English)

    陈凤德; 孙德献; 陈晓星

    2003-01-01

    本文考虑中立型标量方程x′(t)=a(t)x(t)+∫t-∞g(t,s,x(s))ds+∫t-∞h(t,s,x′(s))ds+f(t,x(t))的周期的存在唯一性问题. 其中a是连续函数,f是R×R上的连续函数,g(t,s,x)和h(t,s,x)是R×R×R上的连续函数,以及a(t+T)=a(t), g(t+T, s+T, x)=g(t,s,x), h(t+T, s+T, x)=h(t,s,x), f(t+T, x)=f(t,x). 通过利用线性系统解的估计式和泛函分析的方法,我们得到保证上述系统周期解存在和唯一的充分性条件.%This paper deals with the existence and uniqueness of periodic solutions of scalar neutral integro-differential equation with infinite delay of the form x′(t)=a(t)x(t)+∫t-∞g(t,s,x(s))ds+∫t-∞h(t,s,x′(s))ds+f(t,x(t))where a is continuous function, f is continuous function on R×R, g(t,s,x) and h(t,s,x) are continuous functions on R×R×R, also a(t+T)=a(t), g(t+T, s+T, x)=g(t,s,x), h(t+T, s+T, x)=h(t,s,x), f(t+T, x)=f(t,x). The sufficient conditions for the existing unique periodic solution of the equation are obtained by using functional analysis method and the estimated formulas of solutions of the linear scalar system.

  4. 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.

  5. The optimal control of a new class of impulsive stochastic neutral evolution integro-differential equations with infinite delay

    Science.gov (United States)

    Yan, Zuomao; Lu, Fangxia

    2016-08-01

    In this paper, we introduce the optimal control problems governed by a new class of impulsive stochastic partial neutral evolution equations with infinite delay in Hilbert spaces. First, by using stochastic analysis, the analytic semigroup theory, fractional powers of closed operators, and suitable fixed point theorems, we prove an existence result of mild solutions for the control systems in the α-norm without the assumptions of compactness. Next, we derive the existence conditions of optimal pairs of these systems. Finally, application to a nonlinear impulsive stochastic parabolic optimal control system is considered.

  6. On collocation methods for delay differential and Volterra integral equations with proportional delay

    Institute of Scientific and Technical Information of China (English)

    Emiko ISHIWATA; Yoshiaki MUROYA

    2009-01-01

    To compute long term integrations for the pantograph differential equation with proportional delay qt,0 < q ≤1:y'(t) = ay(t) + by(qt) +f(t),y(0) = Yo,we offer two kinds of numerical methods using special mesh distributions,that is,a rational approximant with 'quasi-uniform meshes'(see E.Ishiwata and Y.Muroya [Appl.Math.Comput.,2007,187:741-747]) and a Gauss collocation method with 'quasi-constrained meshes'.If we apply these meshes to rational approximant and Gauss collocation method,respectively,then we obtain useful numerical methods of order p* = 2m for computing long term integrations. Numerical investigations for these methods are also presented.

  7. 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.

  8. The analysis of asymptotic stability on a fractional differential equation of Volterra-Lotka predator-prey%一类分数阶Volterra-Lotka捕食方程渐近稳定性分析

    Institute of Scientific and Technical Information of China (English)

    夏述

    2010-01-01

    通过对一类分数阶Volterra-Lotka捕食方程模型的研究,并利用Krasovskii方法构造出Lyapunov函数,证明了分数阶Volterra-Lotka捕食方程在一定条件下的渐近稳定性.例子仿真说明了充分条件的有效性.

  9. 平面上Volterra型随机微分程解的轨道惟一性%Pathwise Uniqueness of the Solutions to Volterra Type Stochastic Differential Equations in the Plane

    Institute of Scientific and Technical Information of China (English)

    让光林; 徐侃

    2003-01-01

    In this paper we prove the pathwise uniqueness of a kind of two-parameter Volterra type stochastic differential equations under the coefficients satisfy the nonLipschitz conditions.We use a martingale formula in stead of Ito formula,which leads to simplicity the process of proof and extends the result to unbounded coefficients case.

  10. An H1-Galerkin Nonconforming Mixed Finite Element Method for Integro-Differential Equation of Parabolic Type%抛物型积分微分方程的非协调H1-Galerkin混合有限元方法

    Institute of Scientific and Technical Information of China (English)

    石东洋; 王海红

    2009-01-01

    H1-Galerkin nonconforming mixed finite element methods are analyzed for integro-differential equation of parabolic type.By use of the typical characteristic of the elements,we obtain that the Galerkin mixed approximations have the same rates of convergence as in the classical mixed method,but without LBB stability condition.

  11. Banach空间中二阶混合型脉冲积分-微分方程初值问题解的存在性%The Existence of Solutions of Initial Value Problems for Nonlinear Second Order Impulsive Integro-Differential Equations of Mixed Type in Banach Spaces

    Institute of Scientific and Technical Information of China (English)

    俞卫琴; 陈芳启

    2008-01-01

    By the use of Monch fixed point theorem and a new comparison result, the solutions of initial value problems for nonlinear second order impulsive integro-differential equations of mixed type in Banach spaces are investigated and the existence theorem is obtained.

  12. Approximate controllability of neutral stochastic integrodifferential systems in Hilbert spaces

    Directory of Open Access Journals (Sweden)

    Krishnan Balachandran

    2008-12-01

    Full Text Available In this paper sufficient conditions are established for the controllability of a class of neutral stochastic integrodifferential equations with nonlocal conditions in abstract space. The Nussbaum fixed point theorem is used to obtain the controllability results, which extends the linear system to the stochastic settings with the help of compact semigroup. An example is provided to illustrate the theory.

  13. Approximate controllability of nonlinear stochastic impulsive integrodifferential systems in hilbert spaces

    Energy Technology Data Exchange (ETDEWEB)

    Subalakshmi, R. [Department of Mathematics, Bharathiar University, Coimbatore 641 046 (India)], E-mail: suba.ab.bu@gmail.com; Balachandran, K. [Department of Mathematics, Bharathiar University, Coimbatore 641 046 (India)], E-mail: balachandran_k@lycos.com

    2009-11-30

    Many practical systems in physical and biological sciences have impulsive dynamical behaviours during the evolution process which can be modeled by impulsive differential equations. This paper studies the approximate controllability properties of nonlinear stochastic impulsive integrodifferential and neutral functional stochastic impulsive integrodifferential equations in Hilbert spaces. Assuming the conditions for the approximate controllability of these linear systems we obtain the sufficient conditions for the approximate controllability of these associated nonlinear stochastic impulsive integrodifferential systems in Hilbert spaces. The results are obtained by using the Nussbaum fixed-point theorem. Finally, two examples are presented to illustrate the utility of the proposed result.

  14. A novel coupled system of non-local integro-differential equations modelling Young's modulus evolution, nutrients' supply and consumption during bone fracture healing

    Science.gov (United States)

    Lu, Yanfei; Lekszycki, Tomasz

    2016-10-01

    During fracture healing, a series of complex coupled biological and mechanical phenomena occurs. They include: (i) growth and remodelling of bone, whose Young's modulus varies in space and time; (ii) nutrients' diffusion and consumption by living cells. In this paper, we newly propose to model these evolution phenomena. The considered features include: (i) a new constitutive equation for growth simulation involving the number of sensor cells; (ii) an improved equation for nutrient concentration accounting for the switch between Michaelis-Menten kinetics and linear consumption regime; (iii) a new constitutive equation for Young's modulus evolution accounting for its dependence on nutrient concentration and variable number of active cells. The effectiveness of the model and its predictive capability are qualitatively verified by numerical simulations (using COMSOL) describing the healing of bone in the presence of damaged tissue between fractured parts.

  15. Integrodifferential relations in linear elasticity

    CERN Document Server

    Kostin, Georgy V

    2012-01-01

    This work treats the elasticity of deformed bodies, including the resulting interior stresses and displacements.It also takes into account that some of constitutive relations can be considered in a weak form. To discuss this problem properly, the method of integrodifferential relations is used, and an advanced numerical technique for stress-strain analysis is presented and evaluated using various discretization techniques. The methods presented in this book are of importance for almost all elasticity problems in materials science and mechanical engineering.

  16. 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.

  17. Quasipolynomial generalization of Lotka-Volterra mappings

    Energy Technology Data Exchange (ETDEWEB)

    Hernandez-Bermejo, Benito; Brenig, Leon [Service de Physique Theorique et Mathematique, Universite Libre de Bruxelles, Campus Plaine - CP 231, Brussels (Belgium)]. E-mails: bhernand@ulb.ac.be; lbrenig@ulb.ac.be

    2002-07-05

    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)

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

    Energy Technology Data Exchange (ETDEWEB)

    Cronstroem, C. [Nordisk Inst. for Teoretisk Fysik (NORDITA), Copenhagen (Denmark); Noga, M. [Department of Theoretical Physics, Comenius University, Mlynska Dolina, Bratislava (Slovakia)

    1995-07-10

    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.).

  19. Multi-hamiltonian structure of Lotka-Volterra and quantum Volterra models

    CERN Document Server

    Cronström, C; Cronström, C; Noga, M

    1994-01-01

    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 aclassical and as aquantal system

  20. Integrable deformations of Lotka-Volterra systems

    Energy Technology Data Exchange (ETDEWEB)

    Ballesteros, Angel, E-mail: angelb@ubu.es [Departamento de Fisica, Universidad de Burgos, 09001 Burgos (Spain); Blasco, Alfonso, E-mail: ablasco@ubu.es [Departamento de Fisica, Universidad de Burgos, 09001 Burgos (Spain); Musso, Fabio, E-mail: fmusso@ubu.es [Departamento de Fisica, Universidad de Burgos, 09001 Burgos (Spain)

    2011-09-05

    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{sup (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.

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

    Science.gov (United States)

    Babalic, Corina N.; Carstea, A. S.

    2013-04-01

    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.

  2. [Analysis of seasonal fluctuations in the Lotka-Volterra model].

    Science.gov (United States)

    Lobanov, A I; Sarancha, D A; Starozhilova, T K

    2002-01-01

    A modification of the Lotka-Volterra model was proposed. The modification takes into account the factor of seasonal fluctuations in a "predator-prey" model. In this modification, interactions between species in summer are described by the Lotka-Volterra equations; in winter, individuals of both species extinct. This generalization makes the classic model unrough, which substantially extends the field of its application. The results of numerical simulation illustrate the statement formulated above.

  3. 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.

  4. Representation of neural networks as Lotka-Volterra systems

    Science.gov (United States)

    Moreau, Yves; Louiès, Stéphane; Vandewalle, Joos; Brenig, Léon

    1999-03-01

    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 sigmoïd. 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.

  5. 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.

  6. A Simple Quantum Integro-Differential Solver (SQuIDS)

    CERN Document Server

    Delgado, Carlos Alberto Arguelles; Weaver, Christopher N

    2014-01-01

    Simple Quantum Integro-Differential Solver (SQuIDS) is a C++ code designed to solve semi-analytically the evolution of a set of density matrices and scalar functions. This is done efficiently by expressing all operators in an SU(N) basis. SQuIDS provides a base class from which users can derive new classes to include new non-trivial terms from the right hand sides of density matrix equations. The code was designed in the context of solving neutrino oscillation problems, but can be applied to any problem that involves solving the quantum evolution of a collection of particles with Hilbert space of dimension up to six.

  7. 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.

  8. Competitive Lotka-Volterra Population Dynamics with Jumps

    CERN Document Server

    Bao, Jianhai; Yin, Geroge; Yuan, Chenggui

    2011-01-01

    This paper considers competitive Lotka-Volterra population dynamics with jumps. The contributions of this paper are as follows. (a) We show stochastic differential equation (SDE) with jumps associated with the model has a unique global positive solution; (b) We discuss the uniform boundedness of $p$th moment with $p>0$ and reveal the sample Lyapunov exponents; (c) Using a variation-of-constants formula for a class of SDEs with jumps, we provide explicit solution for 1-dimensional competitive Lotka-Volterra population dynamics with jumps, and investigate the sample Lyapunov exponent for each component and the extinction of our $n$-dimensional model.

  9. A Class of Volterra-Fredholm Type Weakly Singular Difference Inequalities with Power Functions and Their Applications

    Directory of Open Access Journals (Sweden)

    Yange Huang

    2014-01-01

    Full Text Available We discuss a class of Volterra-Fredholm type difference inequalities with weakly singular. The upper bounds of the embedded unknown functions are estimated explicitly by analysis techniques. An application of the obtained inequalities to the estimation of Volterra-Fredholm type difference equations is given.

  10. 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.

  11. A Finite Volume Backward Euler Difference Method for Nonlinear Parabolic Integral-differential Equation%非线性抛物型积分-微分方程的向后Euler差分有限体积元方法

    Institute of Scientific and Technical Information of China (English)

    王波; 王强

    2009-01-01

    The Finite volume backward Euler difference method is established to discuss two-dimensional parabolic integro-differential equations.These results are new for finite volume element methods for parabolic integro-differential equations.

  12. Existence Theorem for Integral and Functional Integral Equations with Discontinuous Kernels

    OpenAIRE

    2012-01-01

    Existence of extremal solutions of nonlinear discontinuous integral equations of Volterra type is proved. This result is extended herein to functional Volterra integral equations (FVIEs) and to a system of discontinuous VIEs as well.

  13. Modern nonlinear equations

    CERN Document Server

    Saaty, Thomas L

    1981-01-01

    Covers major types of classical equations: operator, functional, difference, integro-differential, and more. Suitable for graduate students as well as scientists, technologists, and mathematicians. "A welcome contribution." - Math Reviews. 1964 edition.

  14. 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 e...

  15. Optoacoustic inversion via Volterra kernel reconstruction

    CERN Document Server

    Melchert, O; Roth, B

    2016-01-01

    In this letter we address the numeric inversion of optoacoustic signals to initial stress profiles. Therefore we put under scrutiny the optoacoustic kernel reconstruction problem in the paraxial approximation of the underlying wave-equation. We apply a Fourier-series expansion of the optoacoustic Volterra kernel and obtain the respective expansion coefficients for a given "apparative" setup by performing a gauge procedure using synthetic input data. The resulting effective kernel is subsequently used to solve the optoacoustic source reconstruction problem for general signals. We verify the validity of the proposed inversion protocol for synthetic signals and explore the feasibility of our approach to also account for the diffraction transformation of signals beyond the paraxial approximation.

  16. 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.

  17. 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.

  18. Exponential Observers for Lotka-Volterra Systems

    Directory of Open Access Journals (Sweden)

    Dr. V. Sundarapandian

    2011-03-01

    Full Text Available This paper solves the exponential observer design problem for Lotka-Volterra systems. Explicitly, Sundarapandian’s theorem (2002 for observer design for exponential observer design is used to solve the nonlinear observer design problem for 2-species, 3-species and 4-species Lotka-Volterra systems. Numerical examples are provided to illustrate the effectiveness of the proposed exponential observer design for the Lotka-Volterra systems.

  19. 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.

  20. 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].

  1. Boundary Controllability of Integrodifferential Systems in Banach Spaces

    Indian Academy of Sciences (India)

    K Balachandran; E R Anandhi

    2001-02-01

    Sufficient conditions for boundary controllability of integrodifferential systems in Banach spaces are established. The results are obtained by using the strongly continuous semigroup theory and the Banach contraction principle. Examples are provided to illustrate the theory.

  2. Generalized Volterra lattices: Binary Darboux transformations and self-consistent sources

    Science.gov (United States)

    Müller-Hoissen, F.; Chvartatskyi, O.; Toda, K.

    2017-03-01

    We study two families of matrix versions of generalized Volterra (or Bogoyavlensky) lattice equations. For each family, the equations arise as reductions of a partial differential-difference equation in one continuous and two discrete variables, which is a realization of a general integrable equation in bidifferential calculus. This allows to derive a binary Darboux transformation and also self-consistent source extensions via general results of bidifferential calculus. Exact solutions are constructed from the simplest seed solutions.

  3. 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)

  4. 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.

  5. A Biological Least-Action Principle for the Ecological Model of Volterra-Lotka

    Science.gov (United States)

    Samuelson, Paul A.

    1974-01-01

    The conservative model of Volterra for more-than-two predator-prey species is shown to be generated as extremals that minimize a definable Lagrange-Hamilton integral involving half the species and their rates of change. This least-action formulation differs from that derived two generations ago by Volterra, since his involves twice the number of phase variables and it employs as variables the cumulative integrals of the numbers of each species that have ever lived. The present result extends the variational, teleological formulations found a decade ago by the author to the more-than-two species case. The present result is anything but surprising, in view of the works by Kerner, Montroll, and others which apply Gibbs' statistical mechanics to the all-but-canonical equations of the standard Volterra model. By a globally linear transformation of coordinates, the Volterra equations are here converted into a completely canonical system isomorphic with the classical mechanics models of Newton, Lagrange, Hamilton, Jacobi, Boltzmann, Gibbs, Poincaré, and G. D. Birkhoff. The conservative nature of the Lotka-Volterra model, whatever its realism, is a crucially necessary condition for the applicability of the variational formalisms, microscopically and macroscopically. PMID:4528377

  6. Differential equations inverse and direct problems

    CERN Document Server

    Favini, Angelo

    2006-01-01

    DEGENERATE FIRST ORDER IDENTIFICATION PROBLEMS IN BANACH SPACES A NONISOTHERMAL DYNAMICAL GINZBURG-LANDAU MODEL OF SUPERCONDUCTIVITY. EXISTENCE AND UNIQUENESS THEOREMSSOME GLOBAL IN TIME RESULTS FOR INTEGRODIFFERENTIAL PARABOLIC INVERSE PROBLEMSFOURTH ORDER ORDINARY DIFFERENTIAL OPERATORS WITH GENERAL WENTZELL BOUNDARY CONDITIONSTUDY OF ELLIPTIC DIFFERENTIAL EQUATIONS IN UMD SPACESDEGENERATE INTEGRODIFFERENTIAL EQUATIONS OF PARABOLIC TYPE EXPONENTIAL ATTRACTORS FOR SEMICONDUCTOR EQUATIONSCONVERGENCE TO STATIONARY STATES OF SOLUTIONS TO THE SEMILINEAR EQUATION OF VISCOELASTICITY ASYMPTOTIC BEHA

  7. Generic Properties of an Integro-Differential Equation.

    Science.gov (United States)

    1980-06-01

    Let T (t): C * C, t > 0, be the semigroup operatora,g by (1.1); that is, T a,g(t)o(e) x(o)(t+0), -1 < o < 0. 2. Nongeneric Hopf bifurcation. To prove...in a sufficiently small neigtborhood V of a0 (s) - 492(1-s). From the results in Cooperman [11 (see also Hale (14]), the semigroup T t) has aag

  8. Existence of positive almost periodic solutions for delay Lotka-Volterra cooperative systems

    Directory of Open Access Journals (Sweden)

    Kaihong Zhao

    2013-07-01

    Full Text Available In this article, we study a Lotka-Volterra cooperative system of equations with time-varying delays and distributed delays. By using Mawhin's continuation theorem of coincidence degree theory, we obtain sufficient conditions for the existence of positive almost periodic solutions. Also we present an example to illustrate our results.

  9. Sustained dynamic transience in a Lotka–Volterra competition model system for grassland species

    NARCIS (Netherlands)

    Geijzendorffer, I.R.; Werf, van der W.; Bianchi, F.J.J.A.; Schulte, R.P.O.

    2011-01-01

    Theoretical approaches, such as the Lotka–Volterra framework, enable predictions about long term species coexistence based on stability criteria, but generally assume temporal constancy of system equations and parameters. In real world systems, temporal variability may interfere with the attainment

  10. Sustained dynamic transience in a Lotka–Volterra competition model system for grassland species

    NARCIS (Netherlands)

    Geijzendorffer, I.R.; Werf, van der W.; Bianchi, F.J.J.A.; Schulte, R.P.O.

    2011-01-01

    Theoretical approaches, such as the Lotka–Volterra framework, enable predictions about long term species coexistence based on stability criteria, but generally assume temporal constancy of system equations and parameters. In real world systems, temporal variability may interfere with the attainment

  11. Ultradiscrete soliton equations derived from ultradiscrete permanent formulae

    Energy Technology Data Exchange (ETDEWEB)

    Nakamura, Shinya, E-mail: s-nakamura@moegi.waseda.jp [Major in Pure and Applied Mathematics, Graduate School of Fundamental Science and Engineering, Waseda University, 3-4-1, Okubo, Shinjuku-ku, Tokyo 169-8555 (Japan)

    2011-07-22

    We propose formulae of ultradiscrete permanent. Utilizing the formulae, ultradiscrete soliton equations and their multi-soliton solutions are obtained by a simple process. Changing variables and parameters of the formulae, we can derive the ultradiscrete Toda, KdV and hungry Lotka-Volterra equations. An extended version of the ultradiscrete hungry Lotka-Volterra equation is also proposed.

  12. Extinction dynamics of Lotka-Volterra ecosystems on evolving networks.

    Science.gov (United States)

    Coppex, F; Droz, M; Lipowski, A

    2004-06-01

    We study a model of a multispecies ecosystem described by Lotka-Volterra-like equations. Interactions among species form a network whose evolution is determined by the dynamics of the model. Numerical simulations show power-law distribution of intervals between extinctions, but only for ecosystems with sufficient variability of species and with networks of connectivity above certain threshold that is very close to the percolation threshold of the network. The effect of slow environmental changes on extinction dynamics, degree distribution of the network of interspecies interactions, and some emergent properties of our model are also examined.

  13. 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.

  14. Stability Criteria for Volterra Integrodynamic System

    Directory of Open Access Journals (Sweden)

    Nusrat Yasmin

    2015-01-01

    Full Text Available We study conditions under which the solutions of linear Volterra integrodynamic system of the form yΔt=Atyt+∫t0tKt,sysΔs are stable on certain time scales. We construct a number of Lyapunov functionals on time scales from which we obtain necessary and sufficient conditions for stability of Volterra integrodynamic system and also we prove several results concerning qualitative behavior of this system.

  15. Solutions to systems of partial differential equations with weighted self-reference and heredity

    Directory of Open Access Journals (Sweden)

    Pham Ky Anh

    2012-07-01

    Full Text Available This article studies the existence of solutions to systems of nonlinear integro-differential self-referred and heredity equations. We show the existence of a global solution and the uniqueness of a local solution to a system of integro-differential equations with given initial conditions.

  16. On solitary patterns in Lotka-Volterra chains

    Science.gov (United States)

    Zilburg, Alon; Rosenau, Philip

    2016-03-01

    We present and study a class of Lotka-Volterra chains with symmetric 2N-neighbors interactions. To identify the types of solitary waves which may propagate along the chain, we study their quasi-continuum approximations which, depending on the coupling between neighbors, reduce into a large variety of partial differential equations. Notable among the emerging equations is a bi-cubic equation {u}t={[{{bu}}2+2κ {{uu}}{xx}+{({u}{xx})}2]}x which we study in some detail. It begets remarkably stable topological and non-topological solitary compactons that interact almost elastically. They are used to identify discretons, their solitary discrete antecedents on the lattice, which decay at a doubly exponential rate. Many of the discrete modes are robust while others either decompose or evolve into breathers.

  17. A phenomenological Hamiltonian for the Lotka-Volterra problem

    Energy Technology Data Exchange (ETDEWEB)

    Georgian, T. [Corps of Engineers, Omaha, NE (United States); Findley, G.L. [Northeast Louisiana Univ., Monroe, LA (United States)

    1996-12-31

    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{sub 1},x{sub 2}) for the Lotka-Volterra problem, which leads to the rate equations x{sub 1}=ax{sub 1}-bx{sub 1}x{sub 2}, x{sub 2}=-cx{sub 2}+bx{sub 1}x{sub 2}, with a,b and c being real constants. We thereafter present a Hamiltonian function H(x,y)[y{sub 1} = x{sub 1} and y{sub 2} = x{sub 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.

  18. 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...

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

    Energy Technology Data Exchange (ETDEWEB)

    Abdusalam, H.A E-mail: hosny@operamail.com; Fahmy, E.S

    2003-10-01

    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.

  20. Individual based modeling and parameter estimation for a Lotka-Volterra system.

    Science.gov (United States)

    Waniewski, J; Jedruch, W

    1999-03-15

    Stochastic component, inevitable in biological systems, makes problematic the estimation of the model parameters from a single sequence of measurements, despite the complete knowledge of the system. We studied the problem of parameter estimation using individual-based computer simulations of a 'Lotka-Volterra world'. Two kinds (species) of particles--X (preys) and Y (predators)--moved on a sphere according to deterministic rules and at the collision (interaction) of X and Y the particle X was changed to a new particle Y. Birth of preys and death of predators were simulated by addition of X and removal of Y, respectively, according to exponential probability distributions. With this arrangement of the system, the numbers of particles of each kind might be described by the Lotka-Volterra equations. The simulations of the system with low (200-400 particles on average) number of individuals showed unstable oscillations of the population size. In some simulation runs one of the species became extinct. Nevertheless, the oscillations had some generic properties (e.g. mean, in one simulation run, oscillation period, mean ratio of the amplitudes of the consecutive maxima of X and Y numbers, etc.) characteristic for the solutions of the Lotka-Volterra equations. This observation made it possible to estimate the four parameters of the Lotka-Volterra model with high accuracy and good precision. The estimation was performed using the integral form of the Lotka-Volterra equations and two parameter linear regression for each oscillation cycle separately. We conclude that in spite of the irregular time course of the number of individuals in each population due to stochastic intraspecies component, the generic features of the simulated system evolution can provide enough information for quantitative estimation of the system parameters.

  1. Verhulst-Lotka-Volterra (VLV) model of ideological struggles

    CERN Document Server

    Ausloos, Marcel R; Dimitrova, Zlatinka I

    2011-01-01

    Let the population of e.g. a country where some opinion struggle occurs be varying in time, according to Verhulst equation. Consider next some competition between opinions such as the dynamics be described by Lotka and Volterra equations. Two kinds of influences can be used, in such a model, for describing the dynamics of an agent opinion conversion: this can occur (i) either by means of mass communication tools, under some external field influence, or (ii) by means of direct interactions between agents. It results, among other features, that change(s) in environmental conditions can prevent the extinction of populations of followers of some ideology due to different kinds of resurrection effects. The tension arising in the country population is proposed to be measured by an appropriately defined scale index.

  2. 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).

  3. Discontinuous Mixed Covolume Methods for Linear Parabolic Integrodifferential Problems

    Directory of Open Access Journals (Sweden)

    Ailing Zhu

    2014-01-01

    Full Text Available The semidiscrete and fully discrete discontinuous mixed covolume schemes for the linear parabolic integrodifferential problems on triangular meshes are proposed. The error analysis of the semidiscrete and fully discrete discontinuous mixed covolume scheme is presented and the optimal order error estimate in discontinuous H(div and first-order error estimate in L2 are obtained with the lowest order Raviart-Thomas mixed element space.

  4. Numerical solution of the Kolmogorov-Feller equation with singularities

    Science.gov (United States)

    Baranov, N. A.; Turchak, L. I.

    2010-02-01

    A method is proposed for solving the Kolmogorov-Feller integro-differential equation with kernels containing delta function singularities. The method is based on a decomposition of the solution into regular and singular parts.

  5. On the asymptotic behaviour of solutions of an asymptotically Lotka-Volterra model

    Directory of Open Access Journals (Sweden)

    Attila Dénes

    2016-09-01

    Full Text Available We make more realistic our model [Nonlinear Anal. 73(2010, 650-659] on the coexistence of fishes and plants in Lake Tanganyika. The new model is an asymptotically autonomous system whose limiting equation is a Lotka-Volterra system. We give conditions for the phenomenon that the trajectory of any solution of the original non-autonomous system "rolls up"' onto a cycle of the limiting Lotka-Volterra equation as $t\\to\\infty$, which means that the limit set of the solution of the non-autonomous system coincides with the cycle. A counterexample is constructed showing that the key integral condition on the coefficient function in the original non-autonomous model cannot be dropped. Computer simulations illustrate the results.

  6. Stability and Hopf bifurcation in a symmetric Lotka-Volterra predator-prey system with delays

    Directory of Open Access Journals (Sweden)

    Jing Xia

    2013-01-01

    Full Text Available This article concerns a symmetrical Lotka-Volterra predator-prey system with delays. By analyzing the associated characteristic equation of the original system at the positive equilibrium and choosing the delay as the bifurcation parameter, the local stability and Hopf bifurcation of the system are investigated. Using the normal form theory, we also establish the direction and stability of the Hopf bifurcation. Numerical simulations suggest an existence of Hopf bifurcation near a critical value of time delay.

  7. A maximum principle for diffusive Lotka-Volterra systems of two competing species

    Science.gov (United States)

    Chen, Chiun-Chuan; Hung, Li-Chang

    2016-10-01

    Using an elementary approach, we establish a new maximum principle for the diffusive Lotka-Volterra system of two competing species, which involves pointwise estimates of an elliptic equation consisting of the second derivative of one function, the first derivative of another function, and a quadratic nonlinearity. This maximum principle gives a priori estimates for the total mass of the two species. Moreover, applying it to the system of three competing species leads to a nonexistence theorem of traveling wave solutions.

  8. Local Integrability and Linearizability of Three-dimensional Lotka-Volterra Systems

    CERN Document Server

    Aziz, Waleed

    2011-01-01

    We investigate the local integrability and linearizability of three dimensional Lotka-Volterra equations at the origin. Necessary and sufficient conditions for both integrability and linearizability are obtained for (1,-1,1), (2,-1,1) and (1,-2,1)-resonance. To prove sufficiency, we mainly use the method of Darboux with extensions for inverse Jacobi multipliers, and the linearizability of a node in two variables with power-series arguments in the third variable.

  9. The periodic competing Lotka-Volterra model with impulsive effect.

    Science.gov (United States)

    Liu, Bing; Chen, Lansun

    2004-06-01

    In this paper, the dynamic behaviour of a classical periodic Lotka-Volterra competing system with impulsive effect is investigated. By applying the Floquet theory of linear periodic impulsive equations, some conditions are obtained for the linear stability of the trivial and semi-trivial periodic solutions. It is proved that the system can be permanent if all the trivial and semi-trivial periodic solutions are linearly unstable. We use standard bifurcation theory to show the existence of nontrivial periodic solutions which arise near the semi-trivial periodic solution. As an application, a fish harvest problem is considered. We explain how two competing species, one of which in a periodic environment without impulsive effect would be doomed to extinction, can coexist with suitably periodic impulsive harvesting.

  10. On chaos in Lotka-Volterra systems: an analytical approach

    Science.gov (United States)

    Kozlov, Vladimir; Vakulenko, Sergey

    2013-08-01

    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.

  11. THE PARALLEL RECURSIVE AP ADAPTIVE ALGORITHM BASED ON VOLTERRA SERIES

    Institute of Scientific and Technical Information of China (English)

    2005-01-01

    Aiming at the nonlinear system identification problem, a parallel recursive affine projection (AP) adaptive algorithm for the nonlinear system based on Volterra series is presented in this paper. The algorithm identifies in parallel the Volterra kernel of each order, recursively estimate the inverse of the autocorrelation matrix for the Volterra input of each order, and remarkably improve the convergence speed of the identification process compared with the NLMS and conventional AP adaptive algorithm based on Volterra series. Simulation results indicate that the proposed method in this paper is efficient.

  12. Evolutionary stability in Lotka-Volterra systems.

    Science.gov (United States)

    Cressman, Ross; Garay, József

    2003-05-21

    The Lotka-Volterra model of population ecology, which assumes all individuals in each species behave identically, is combined with the behavioral evolution model of evolutionary game theory. In the resultant monomorphic situation, conditions for the stability of the resident Lotka-Volterra system, when perturbed by a mutant phenotype in each species, are analysed. We develop an evolutionary ecology stability concept, called a monomorphic evolutionarily stable ecological equilibrium, which contains as a special case the original definition by Maynard Smith of an evolutionarily stable strategy for a single species. Heuristically, the concept asserts that the resident ecological system must be stable as well as the phenotypic evolution on the "stationary density surface". The conditions are also shown to be central to analyse stability issues in the polymorphic model that allows arbitrarily many phenotypes in each species, especially when the number of species is small. The mathematical techniques are from the theory of dynamical systems, including linearization, centre manifolds and Molchanov's Theorem.

  13. Model uncertainty in economic impacts of climate change: Bernoulli versus Lotka Volterra dynamics.

    Science.gov (United States)

    Cooke, Roger M

    2013-01-01

    The dynamic economic behavior in most integrated assessment models linking economic growth to climate change involves a differential equation solved by Jacob Bernoulli in 1695. Using the dynamic integrated climate economy (DICE) model and freezing exogenous variables at initial values, this dynamic is shown to produce implausible projections on a 60-year time frame. If world capital started at US$1, after 60 years the world economy would be indistinguishable from one starting with 10 times the current capitalization. Such behavior points to uncertainty at the level of the fundamental dynamics, and suggests that discussions of discounting, utility, damage functions, and ethics should be conducted within a more general modeling vocabulary. Lotka Volterra dynamics is proposed as an alternative with greater prime facie plausibility. With near universality, economists assume that economic growth will go on forever. Lotka Volterra dynamics alert us to the possibility of collapse.

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

    Energy Technology Data Exchange (ETDEWEB)

    Gavin, C [School of Mathematical Sciences University College Cork, Cork (Ireland); Pokrovskii, A [School of Mathematical Sciences University College Cork, Cork (Ireland); Prentice, M [Department of Microbiology University College Cork, Cork (Ireland); Sobolev, V [Department of Differential Equations and Control Theory Samara State University, Akademika Pavlova Street, 1, 443011 (Russian Federation)

    2006-12-01

    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.

  15. equations

    Directory of Open Access Journals (Sweden)

    Xinzhi Liu

    1998-01-01

    Full Text Available This paper studies a class of high order delay partial differential equations. Employing high order delay differential inequalities, several oscillation criteria are established for such equations subject to two different boundary conditions. Two examples are also given.

  16. An integrodifferential approach to modeling, control, state estimation and optimization for heat transfer systems

    Directory of Open Access Journals (Sweden)

    Rauh Andreas

    2016-03-01

    Full Text Available In this paper, control-oriented modeling approaches are presented for distributed parameter systems. These systems, which are in the focus of this contribution, are assumed to be described by suitable partial differential equations. They arise naturally during the modeling of dynamic heat transfer processes. The presented approaches aim at developing finite-dimensional system descriptions for the design of various open-loop, closed-loop, and optimal control strategies as well as state, disturbance, and parameter estimation techniques. Here, the modeling is based on the method of integrodifferential relations, which can be employed to determine accurate, finite-dimensional sets of state equations by using projection techniques. These lead to a finite element representation of the distributed parameter system. Where applicable, these finite element models are combined with finite volume representations to describe storage variables that are—with good accuracy—homogeneous over sufficiently large space domains. The advantage of this combination is keeping the computational complexity as low as possible. Under these prerequisites, real-time applicable control algorithms are derived and validated via simulation and experiment for a laboratory-scale heat transfer system at the Chair of Mechatronics at the University of Rostock. This benchmark system consists of a metallic rod that is equipped with a finite number of Peltier elements which are used either as distributed control inputs, allowing active cooling and heating, or as spatially distributed disturbance inputs.

  17. Permanence of Stochastic Lotka-Volterra Systems

    Science.gov (United States)

    Liu, Meng; Fan, Meng

    2017-04-01

    This paper proposes a new definition of permanence for stochastic population models, which overcomes some limitations and deficiency of the existing ones. Then, we explore the permanence of two-dimensional stochastic Lotka-Volterra systems in a general setting, which models several different interactions between two species such as cooperation, competition, and predation. Sharp sufficient criteria are established with the help of the Lyapunov direct method and some new techniques. This study reveals that the stochastic noises play an essential role in the permanence and characterize the systems being permanent or not.

  18. 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.

  19. 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 gamma-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.

  20. 一类积微分方程(组)的Cauchy问题%The Cauchy Problem for a Class of Intergrodifferential Equations

    Institute of Scientific and Technical Information of China (English)

    杨成荣

    2000-01-01

    The existence, uniqueness of bounded and continuous solutions of a class of integrodifferential equations and some estimates of solutions are established. Applying these results to integrodifferential systems with a small parameter ε>0, we obtain, in particular, some estimates of solutions uniform in ε.

  1. Difference equations and cluster algebras I: Poisson bracket for integrable difference equations

    CERN Document Server

    Inoue, Rei

    2010-01-01

    We introduce the cluster algebraic formulation of the integrable difference equations, the discrete Lotka-Volterra equation and the discrete Liouville equation, from the view point of the general T-system and Y-system. We also study the Poisson structure for the cluster algebra, and give the associated Poisson bracket for the two difference equations.

  2. Multivariate Moran process with Lotka-Volterra phenomenology.

    Science.gov (United States)

    Noble, Andrew E; Hastings, Alan; Fagan, William F

    2011-11-25

    For a population with any given number of types, we construct a new multivariate Moran process with frequency-dependent selection and establish, analytically, a correspondence to equilibrium Lotka-Volterra phenomenology. This correspondence, on the one hand, allows us to infer the phenomenology of our Moran process based on much simpler Lokta-Volterra phenomenology and, on the other, allows us to study Lotka-Volterra dynamics within the finite populations of a Moran process. Applications to community ecology, population genetics, and evolutionary game theory are discussed.

  3. Bifurcation Analysis of a Lotka-Volterra Mutualistic System with Multiple Delays

    Directory of Open Access Journals (Sweden)

    Xin-You Meng

    2014-01-01

    Full Text Available A class of Lotka-Volterra mutualistic system with time delays of benefit and feedback delays is introduced. By analyzing the associated characteristic equation, the local stability of the positive equilibrium and existence of Hopf bifurcation are obtained under all possible combinations of two or three delays selecting from multiple delays. Not only explicit formulas to determine the properties of the Hopf bifurcation are shown by using the normal form method and center manifold theorem, but also the global continuation of Hopf bifurcation is investigated by applying a global Hopf bifurcation result due to Wu (1998. Numerical simulations are given to support the theoretical results.

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

    Energy Technology Data Exchange (ETDEWEB)

    Inoue, Rei [Institute of Physics, Graduate School of Arts and Sciences, University of Tokyo, Komaba 3-8-1, Meguro, Tokyo 153-8902 (Japan)

    2004-01-30

    We study completely integrable Hamiltonian systems whose monodromy matrices are related to the representatives for the set of gauge equivalence classes M{sub F} of polynomial matrices. Let X be the algebraic curve given by the common characteristic equation for M{sub 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.

  5. Multistep epsilon-algorithm, Shanks' transformation, and Lotka-Volterra system by Hirota's method

    CERN Document Server

    Brezinski, Claude; Hu, Xing-Biao; Redivo-Zaglia, Michela; Sun, Jian-Qing

    2010-01-01

    In this paper, we give a multistep extension of the epsilon-algorithm of Wynn, and we show that it implements a multistep extension of the Shanks' sequence transformation which is defined by ratios of determinants. Reciprocally, the quantities defined in this transformation can be recursively computed by the multistep epsilon-algorithm. The multistep epsilon-algorithm and the multistep Shanks' transformation are related to an extended discrete Lotka-Volterra system. These results are obtained by using the Hirota's bilinear method, a procedure quite useful in the solution of nonlinear partial differential and difference equations.

  6. 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.

  7. Persistence in periodic and almost periodic Lotka-Volterra systems.

    Science.gov (United States)

    Gopalsamy, K

    1984-01-01

    It is shown that a strongly self-regulating (or resource limited) Lotka-Volterra population system can "persist" in a periodic or almost periodic environment if and only if the system tracks the environmental variations.

  8. On competitive Lotka–Volterra model in random environments

    National Research Council Canada - National Science Library

    Zhu, C; Yin, G

    2009-01-01

    Focusing on competitive Lotka-Volterra model in random environments, this paper uses regime-switching diffusions to model the dynamics of the population sizes of n different species in an ecosystem...

  9. Dynamics of a discrete Lotka-Volterra model

    National Research Council Canada - National Science Library

    Din, Qamar

    2013-01-01

    In this paper, we study the equilibrium points, local asymptotic stability of equilibrium points, and global behavior of equilibrium points of a discrete Lotka-Volterra model given by where parameters...

  10. PERMANENCE AND PERSISTENCE OF TIME VARYING LOTKA-VOLTERRA SYSTEMS

    Institute of Scientific and Technical Information of China (English)

    2006-01-01

    In this article, the permanence and persistence for three classes time varying Lotka-Volterra ecological system are investigated by using Lyapunov stability analysis and constructing the compact set of attraction. Some examples are given to illustrate the theorems.

  11. Convergence to equilibrium in competitive Lotka-Volterra equations

    CERN Document Server

    Champagnat, Nicolas; Raoul, Gael

    2010-01-01

    We study a generalized system of ODE's modeling a finite number of biological populations in a competitive interaction. We adapt the techniques in two previous articles to prove the convergence to a unique stable equilibrium.

  12. Extinction in the Lotka-Volterra model.

    Science.gov (United States)

    Parker, Matthew; Kamenev, Alex

    2009-08-01

    Birth-death processes often exhibit an oscillatory behavior. We investigate a particular case where the oscillation cycles are marginally stable on the mean-field level. An iconic example of such a system is the Lotka-Volterra model of predator-prey interaction. Fluctuation effects due to discreteness of the populations destroy the mean-field stability and eventually drive the system toward extinction of one or both species. We show that the corresponding extinction time scales as a certain power-law of the population sizes. This behavior should be contrasted with the extinction of models stable in the mean-field approximation. In the latter case the extinction time scales exponentially with size.

  13. 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.

  14. Global Attractivity of an Integrodifferential Model of Mutualism

    Directory of Open Access Journals (Sweden)

    Xiangdong Xie

    2014-01-01

    Full Text Available Sufficient conditions are obtained for the global attractivity of the following integrodifferential model of mutualism: dN1(t/dt=r1N1(t[((K1+α1∫0∞J2(sN2(t-sds‍/(1+∫0∞J2(sN2(t-sds‍-N1(t], dN2(t/dt=r2N2(t[((K2+α2∫0∞J1(sN1(t-sds‍/(1+∫0∞J1(sN1(t-sds‍-N2(t], where ri,Ki, and αi, i=1,2, are all positive constants. Consider αi>Ki, i=1,2. Consider   Ji∈C([0,+∞,[0,+∞ and ∫0∞‍Ji(sds=1, i=1,2. Our result shows that conditions which ensure the permanence of the system are enough to ensure the global stability of the system. The result not only improves but also complements some existing ones.

  15. 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.

  16. A solution to the accelerated-predator-satiety Lotka-Volterra predator-prey problem using Boubaker polynomial expansion scheme.

    Science.gov (United States)

    Dubey, B; Zhao, T G; Jonsson, M; Rahmanov, H

    2010-05-07

    In this study, an analytical method is introduced for the identification of predator-prey populations time-dependent evolution in a Lotka-Volterra predator-prey model which takes into account the concept of accelerated-predator-satiety. Oppositely to most of the predator-prey problem models, the actual model does not suppose that the predation is strictly proportional to the prey density. In reference to some recent experimental results and particularly to the conclusions of May (1973) about predators which are 'never not hungry', an accelerated satiety function is matched with the initial conventional equations. Solutions are plotted and compared to some relevant ones. The obtained trends are in good agreement with many standard Lotka-Volterra solutions except for the asymptotic behaviour. Copyright (c) 2010 Elsevier Ltd. All rights reserved.

  17. Population oscillations in stochastic Lotka--Volterra models: field theory and perturbational analysis

    Science.gov (United States)

    Täuber, Uwe C.

    2013-03-01

    Field theory tools are applied to analytically study fluctuation and correlation effects in spatially extended stochastic predator-prey systems. In the mean-field rate equation approximation, the classic Lotka-Volterra model is characterized by neutral cycles in phase space, describing undamped oscillations for both predator and prey populations. In contrast, Monte Carlo simulations for stochastic two-species predator-prey reaction systems on regular lattices display complex spatio-temporal structures associated with persistent erratic population oscillations. The Doi-Peliti path integral representation of the master equation for stochastic particle interaction models is utilized to arrive at a field theory action for spatial Lotka-Volterra models in the continuum limit. In the species coexistence phase, a perturbation expansion with respect to the nonlinear predation rate is employed to demonstrate that spatial degrees of freedom and stochastic noise induce instabilities toward structure formation, and to compute the fluctuation corrections for the oscillation frequency and diffusion coefficient. The drastic downward renormalization of the frequency and the enhanced diffusivity are in excellent qualitative agreement with Monte Carlo simulation data.

  18. THE CRITERIA OF ULTIMATE BOUNDEDNESS FOR NONAUTONOMOUS DIFFUSIVE LOTKA-VOLTERRA SYSTEMS IN TWO HETEROGENEOUS PATCHES

    Institute of Scientific and Technical Information of China (English)

    LI Xuezhi; GENI Gupur; ZHU Guangtian

    2001-01-01

    In this paper, a set of sufficient conditions is obtained for the ultimate boundedness of nonautonomous n-species diffusive Lotka-Volterra sub-models in two heterogeneous patches. The sub-models are the Lotka-Volterra tree systems, including the Lotka-Volterra chain systems and the Lotka-Volterra models between one and multispecies. The criteria in this paper are in explicit forms of the parameters and thus are easily verifiable.

  19. On nonlocal symmetries of some shallow water equations

    Energy Technology Data Exchange (ETDEWEB)

    Reyes, Enrique G [Departamento de Matematicas y Ciencia de la Computacion, Universidad de Santiago de Chile, Casilla 307 Correo 2 Santiago (Chile)

    2007-04-27

    A recent construction of nonlocal symmetries for the Korteweg-de Vries, Camassa-Holm and Hunter-Saxton equations is reviewed, and it is pointed out that-in the Camassa-Holm and Hunter-Saxton case-these symmetries can be considered as (nonlocal) symmetries of integro-differential equations.

  20. Monitoring in a Lotka-Volterra model.

    Science.gov (United States)

    López, I; Gámez, M; Garay, J; Varga, Z

    2007-01-01

    The problem of monitoring arises when in an ecosystem, in particular in a system of several populations, observing some components, we want to recover the state of the whole system as a function of time. Due to the difficulty to construct exactly this state process, we look for an auxiliary system called an observer. This system reproduces this process with a certain approximation. This means that the solution of the observer tends to that of the original system. An important concept for this work is observability. This means that from the observation it is possible to recover uniquely the state process, however, without determining a constructive method to obtain it. If observability holds for the original system, it guarantees the existence of an auxiliary matrix that makes it possible to construct an observer of the system. The considered system of populations is described by the classical Lotka-Volterra model with one predator and two preys and the construction of its observer is illustrated with a numerical example. Finally, it is shown how the observer can be used for the estimation of the level of an abiotic effect on the population system.

  1. Nonlinear stochastic system identification of skin using volterra kernels.

    Science.gov (United States)

    Chen, Yi; Hunter, Ian W

    2013-04-01

    Volterra kernel stochastic system identification is a technique that can be used to capture and model nonlinear dynamics in biological systems, including the nonlinear properties of skin during indentation. A high bandwidth and high stroke Lorentz force linear actuator system was developed and used to test the mechanical properties of bulk skin and underlying tissue in vivo using a non-white input force and measuring an output position. These short tests (5 s) were conducted in an indentation configuration normal to the skin surface and in an extension configuration tangent to the skin surface. Volterra kernel solution methods were used including a fast least squares procedure and an orthogonalization solution method. The practical modifications, such as frequency domain filtering, necessary for working with low-pass filtered inputs are also described. A simple linear stochastic system identification technique had a variance accounted for (VAF) of less than 75%. Representations using the first and second Volterra kernels had a much higher VAF (90-97%) as well as a lower Akaike information criteria (AICc) indicating that the Volterra kernel models were more efficient. The experimental second Volterra kernel matches well with results from a dynamic-parameter nonlinearity model with fixed mass as a function of depth as well as stiffness and damping that increase with depth into the skin. A study with 16 subjects showed that the kernel peak values have mean coefficients of variation (CV) that ranged from 3 to 8% and showed that the kernel principal components were correlated with location on the body, subject mass, body mass index (BMI), and gender. These fast and robust methods for Volterra kernel stochastic system identification can be applied to the characterization of biological tissues, diagnosis of skin diseases, and determination of consumer product efficacy.

  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. A novel identification method of Volterra series in rotor-bearing system for fault diagnosis

    Science.gov (United States)

    Xia, Xin; Zhou, Jianzhong; Xiao, Jian; Xiao, Han

    2016-01-01

    Volterra series is widely employed in the fault diagnosis of rotor-bearing system to prevent dangerous accidents and improve economic efficiency. The identification of the Volterra series involves the infinite-solution problems which is caused by the periodic characteristic of the excitation signal of rotor-bearing system. But this problem has not been considered in the current identification methods of the Volterra series. In this paper, a key kernels-PSO (KK-PSO) method is proposed for Volterra series identification. Instead of identifying the Volterra series directly, the key kernels of Volterra are found out to simply the Volterra model firstly. Then, the Volterra series with the simplest formation is identified by the PSO method. Next, simulation verification is utilized to verify the feasibility and effectiveness of the KK-PSO method by comparison to the least square (LS) method and traditional PSO method. Finally, experimental tests have been done to get the Volterra series of a rotor-bearing test rig in different states, and a fault diagnosis system is built with a neural network to classify different fault conditions by the kernels of the Volterra series. The analysis results indicate that the KK-PSO method performs good capability on the identification of Volterra series of rotor-bearing system, and the proposed method can further improve the accuracy of fault diagnosis.

  4. Study on Volterra-Laguerre behavioral model for RF power amplifier

    Institute of Scientific and Technical Information of China (English)

    Nan Jingchang; Liu Yuanan; Tang Bihua

    2007-01-01

    Volterra series behavioral model for radio frequency(RF)power amplifier(PA)has been widely used in system-level simulation,however,high computational complexity makes this kind of model limited to"weak"nonlinearity.In order to reduce the computational complexity and the number of coefficients of Volterra series kernels,a Volterra series improved behavioral model based on Lasuerre orthogonal polynomials function,namely Volterra-Laguerre behavioral model,is proposed.Mathematical expressions of Volterra-Laguerre behavioral model is derived.and accuracy of the model is verified through comparison of measured and simulation output data from a freescale PA using MRF21030 transistor.Mathematical analysis and simulation results show that Volterra-Laguerre behavioral model has a simple structure,much less coefficients and better modeling performance than general Volterra series model.The model can be used more correctly for system-level simulation of RF PA with wideband signal.

  5. Controllability of Fractional Neutral Stochastic Integro-Differential Systems with Infinite Delay

    Directory of Open Access Journals (Sweden)

    Xichao Sun

    2013-01-01

    Full Text Available This paper is concerned with the controllability of a class of fractional neutral stochastic integro-differential systems with infinite delay in an abstract space. By employing fractional calculus and Sadovskii's fixed point principle without assuming severe compactness condition on the semigroup, a set of sufficient conditions are derived for achieving the controllability result.

  6. Controllability of neutral impulsive stochastic quasilinear integrodifferential systems with nonlocal conditions

    Directory of Open Access Journals (Sweden)

    Krishnan Balachandran

    2011-06-01

    Full Text Available We establish sufficient conditions for controllability of neutral impulsive stochastic quasilinear integrodifferential systems with nonlocal conditions in Hilbert spaces. The results are obtained by using semigroup theory, evolution operator and a fixed point technique. An example is provided to illustrate the obtained results.

  7. Approximate Controllability of Semilinear Neutral Stochastic Integrodifferential Inclusions with Infinite Delay

    Directory of Open Access Journals (Sweden)

    Meili Li

    2015-01-01

    Full Text Available The approximate controllability of semilinear neutral stochastic integrodifferential inclusions with infinite delay in an abstract space is studied. Sufficient conditions are established for the approximate controllability. The results are obtained by using the theory of analytic resolvent operator, the fractional power theory, and the theorem of nonlinear alternative for Kakutani maps. Finally, an example is provided to illustrate the theory.

  8. THE NONLINEAR BOUNDARY VALUE PROBLEM FOR A CLASS OF INTEGRO-DIFFERENTIAL SYSTEM

    Institute of Scientific and Technical Information of China (English)

    Rongrong Tang

    2006-01-01

    In this paper, using the theory of differential inequalities, we study the nonlinear boundary value problem for a class of integro-differential system. Under appropriate assumptions, the existence of solution is proved and the uniformly valid asymptotic expansions for arbitrary n-th order approximation and the estimation of remainder term are obtained simply and conveniently.

  9. Nonstandard numerical integrations of a Lotka-Volterra system

    NARCIS (Netherlands)

    Bhowmik, S.K.

    2009-01-01

    In this article, we consider a three dimensional Lotka-Volterra system. We have developed some nonstandard numerical integrations of the model which preserve all properties of real solutions, and they are consistent. We have shown some numerical results to support this methods.

  10. Coexistence and exclusion of stochastic competitive Lotka-Volterra models

    Science.gov (United States)

    Nguyen, Dang H.; Yin, George

    2017-02-01

    This work derives sufficient conditions for the coexistence and exclusion of a stochastic competitive Lotka-Volterra model. The conditions obtained are close to necessary. In addition, convergence in distribution of positive solutions of the model is also established. A number of numerical examples are given to illustrate our results.

  11. Dynamic deviation Volterra predistorter designed for linearizing power amplifiers

    OpenAIRE

    2011-01-01

    Polynomial models of predistorter combined by the "black box" principle have been considered. A Volterra model using one-dimensional dynamic deviation was proposed. An adaptive predistorter was synthesized for linearizing the Wiener–Hammerstein model of power amplifiers. Estimates of the linearization accuracy and a comparative analysis of predistorter models were also presented.

  12. Integrability of Lotka-Volterra Planar Complex Cubic Systems

    Science.gov (United States)

    Dukarić, Maša; Giné, Jaume

    In this paper, we study the Lotka-Volterra complex cubic systems. We obtain necessary conditions of integrability for these systems with some restriction on the parameters. The sufficiency is proved for all conditions, except one which remains open, using different methods.

  13. 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

  14. Permanence and global attractivity for Lotka-Volterra difference systems.

    Science.gov (United States)

    Lu, Z; Wang, W

    1999-09-01

    The permanence and global attractivity for two-species difference systems of Lotka-Volterra type are considered. It is proved that a cooperative system cannot be permanent. For a permanent competitive system, the explicit expression of the permanent set E is obtained and sufficient conditions are given to guarantee the global attractivity of the positive equilibrium of the system.

  15. Nonstandard numerical integrations of a Lotka-Volterra system

    NARCIS (Netherlands)

    Bhowmik, S.K.

    2009-01-01

    In this article, we consider a three dimensional Lotka-Volterra system. We have developed some nonstandard numerical integrations of the model which preserve all properties of real solutions, and they are consistent. We have shown some numerical results to support this methods.

  16. The Lotka-Volterra Competition System with Discrete and Distributed Time Delays%具有离散和分布时滞的Lotka-Volterra竞争系统

    Institute of Scientific and Technical Information of China (English)

    张嘉防; 张志平

    2008-01-01

    In this paper.the Lotka-Volterra competition system with discrete and distributed time delays is considered.By analyzing the characteristic equation of the linearized system,the local asymptotic stability of the positive equilibrium is investigated.Moreover,we discover the delays don't effect the stability of the equilibrium in the delay system.Finally,we can conclude that the positive equilibrium is global asymptotically stable in the delay system.

  17. Numerical solution of Lotka Volterra prey predator model by using Runge–Kutta–Fehlberg method and Laplace Adomian decomposition method

    Directory of Open Access Journals (Sweden)

    Susmita Paul

    2016-03-01

    Full Text Available This paper reflects some research outcome denoting as to how Lotka–Volterra prey predator model has been solved by using the Runge–Kutta–Fehlberg method (RKF. A comparison between Runge–Kutta–Fehlberg method (RKF and the Laplace Adomian Decomposition method (LADM is carried out and exact solution is found out to verify the applicability, efficiency and accuracy of the method. The obtained approximate solution shows that the Runge–Kutta–Fehlberg method (RKF is a more powerful numerical technique for solving a system of nonlinear differential equations.

  18. Optimal control of the Lotka-Volterra system: turnpike property and numerical simulations.

    Science.gov (United States)

    Ibañez, Aitziber

    2017-12-01

    The Lotka-Volterra model is a differential system of two coupled equations representing the interaction of two species: a prey one and a predator one. We formulate an optimal control problem adding the effect of hunting both species as the control variable. We analyse the optimal hunting problem paying special attention to the nature of the optimal state and control trajectories in long time intervals. To do that, we apply recent theoretical results on the frame to show that, when the time horizon is large enough, optimal strategies are nearly steady-state. Such path is known as turnpike property. Some experiments are performed to observe such turnpike phenomenon in the hunting problem. Based on the turnpike property, we implement a variant of the single shooting method to solve the previous optimisation problem, taking the middle of the time interval as starting point.

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

    Energy Technology Data Exchange (ETDEWEB)

    Liu Bing [Department of Mathematics, Anshan Normal University, Anshan 114005, Liaoning (China) and Department of Mathematics, Xinjiang University, Urumqi 830046, Xinjiang (China)]. E-mail: liubing529@126.com; Teng Zhidong [Department of Mathematics, Xinjiang University, Urumqi 830046, Xinjiang (China); Liu Wanbo [Senior Middle School of Anshan Steel-Iron Company, Anshan 114034, Liaoning (China)

    2007-01-15

    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.

  20. 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.

  1. Turing pattern dynamics and adaptive discretization for a super-diffusive Lotka-Volterra model.

    Science.gov (United States)

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

    2016-05-01

    In this paper we analyze the effects of introducing the fractional-in-space operator into a Lotka-Volterra competitive model describing population super-diffusion. First, we study how cross super-diffusion influences the formation of spatial patterns: a linear stability analysis is carried out, showing that cross super-diffusion triggers Turing instabilities, whereas classical (self) super-diffusion does not. In addition we perform a weakly nonlinear analysis yielding a system of amplitude equations, whose study shows the stability of Turing steady states. A second goal of this contribution is to propose a fully adaptive multiresolution finite volume method that employs shifted Grünwald gradient approximations, and which is tailored for a larger class of systems involving fractional diffusion operators. The scheme is aimed at efficient dynamic mesh adaptation and substantial savings in computational burden. A numerical simulation of the model was performed near the instability boundaries, confirming the behavior predicted by our analysis.

  2. Analog integrated circuits for the Lotka-Volterra competitive neural networks.

    Science.gov (United States)

    Asai, T; Ohtani, M; Yonezu, H

    1999-01-01

    A subthreshold MOS integrated circuit (IC) is designed and fabricated for implementing a competitive neural network of the Lotka-Volterra (LV) type which is derived from conventional membrane dynamics of neurons and is used for the selection of external inputs. The steady-state solutions to the LV equation can be classified into three types, each of which represents qualitatively different selection behavior. Among the solutions, the winners-share-all (WSA) solution in which a certain number of neurons remain activated in steady states is particularly useful owing to robustness in the selection of inputs from a noisy environment. The measured results of the fabricated LV IC's agree well with the theoretical prediction as long as the influence of device mismatches is small. Furthermore, results of extensive circuit simulations prove that the large-scale LV circuit producing the WSA solution does exhibit a reliable selection compared with winner-take-all circuits, in the possible presence of device mismatches.

  3. Unlimited niche packing in a Lotka-Volterra competition game.

    Science.gov (United States)

    Cressman, Ross; Halloway, Abdel; McNickle, Gordon G; Apaloo, Joe; Brown, Joel S; Vincent, Thomas L

    2017-08-01

    A central question in the study of ecology and evolution is: "Why are there so many species?" It has been shown that certain forms of the Lotka-Volterra (L-V) competition equations lead to an unlimited number of species. Furthermore, these authors note how any change in the nature of competition (the competition kernel) leads to a finite or small number of coexisting species. Here we build upon these works by further investigating the L-V model of unlimited niche packing as a reference model and evolutionary game for understanding the environmental factors restricting biodiversity. We also examine the combined eco-evolutionary dynamics leading up to the species diversity and traits of the ESS community in both unlimited and finite niche-packing versions of the model. As an L-V game with symmetric competition, we let the strategies of individuals determine the strength of the competitive interaction (like competes most with like) and also the carrying capacity of the population. We use a mixture of analytic proofs (for one and two species systems) and numerical simulations. For the model of unlimited niche packing, we show that a finite number of species will evolve to specific convergent stable minima of the adaptive landscape (also known as species archetypes). Starting with a single species, faunal buildup can proceed either through species doubling as each diversity-specific set of minima are reached, or through the addition of species one-by-one by randomly assigning a speciation event to one of the species. Either way it is possible for an unlimited number or species to evolve and coexist. We examine two simple and biologically likely ways for breaking the unlimited niche-packing: (1) some minimum level of competition among species, and (2) constrain the fundamental niche of the trait space to a finite interval. When examined under both ecological and evolutionary dynamics, both modifications result in convergent stable ESSs with a finite number of species

  4. Fractional evolution equation nonlocal problems with noncompact semigroups

    Directory of Open Access Journals (Sweden)

    Xuping Zhang

    2016-01-01

    Full Text Available This paper is concerned with the existence results of mild solutions to the nonlocal problem of fractional semilinear integro-differential evolution equations. New existence theorems are obtained by means of the fixed point theorem for condensing maps. The results extend and improve some related results in this direction.

  5. The Volterra series as special case of artificial neural network model

    Science.gov (United States)

    Napiorkowski, J.; O Kane, J. P.

    2003-04-01

    The geophysical processes contributing to the hydrological cycle are described by theoretically sound non-linear partial differential equations of mass and energy transfer. The hydrodynamic equations describing hydrological processes were developed in non-linear form in the nineteenth century. In the case of surface runoff from a natural catchment or flow in an open channel, an accurate application of the hydraulic approach requires a detailed topographical survey and determination of roughness parameters. In order to avoid these difficulties, alternative approaches e.g. via conceptual models and black box models were developed in the second half of the last century. The conceptual model approach is to simulate the nature of the catchment response or the channel response by relatively simple non-linear model built up from simple non-linear elements, e.g. cascade of non-linear reservoirs. Each non-linear reservoir is responsible for part of the attenuation of the system response. This lumped dynamic model can be represented by a set of ordinary differential equations: begin{gathered} dot S_1 (t) = - f[S_1 (t)] + x(t) dot S_2 (t) = - f[S_2 (t)] + f[S_1 (t)] ... dot S_n (t) = - f[S_n (t)] + f[Sn - 1 (t)] y(t) = f[S_n (t)] % MathType!End!2!1! (1) where x is the input signal(rainfall or flow at the upstream end of the channel), Si is the storage in the i-th reservoir, f(.) represents the outflow-storage relation and y is the output signal (surface runoff or flow at the downstream end of the channel). Non-linear black box analysis is concerned with representing a system by a functional Volterra series in the form of a sum of convolution integrals: begin{gathered} y(t) = intlimits_0^t {h_1 (τ )x(t - τ )dτ + intlimits_0^t {intlimits_0^t {h_2 (τ _1 ,τ _2 )x(t - τ _1 )x(t - τ _2 )dτ _1 dτ _2 } } } quad quad + intlimits_0^t {intlimits_0^t {intlimits_0^t {h_3 (τ _1 ,τ _2 ,τ _3 )x(t - τ _1 )x(t - τ _2 )x(t - τ _3 )dτ _1 dτ _2 dτ _3 } + ...} } % MathType!End!2

  6. SINGULAR SOLUTIONS OF AN INTEGRO-DIFFERENTIAL EQUATION IN RADIATIVE TRANSFER

    Science.gov (United States)

    infinite for finite values of the parameter T. Some of these singular solutions first come close to the desired solution and then diverge to infinity...The nearness of approach of these singular solutions is proportional to a quantity which measures the nearness of local scattering to the conservative

  7. Qualitative analysis of an integro-differential equation model of periodic chemotherapy

    KAUST Repository

    Jain, Harsh Vardhan

    2012-12-01

    An existing model of tumor growth that accounts for cell cycle arrest and cell death induced by chemotherapy is extended to simulate the response to treatment of a tumor growing in vivo. The tumor is assumed to undergo logistic growth in the absence of therapy, and treatment is administered periodically rather than continuously. Necessary and sufficient conditions for the global stability of the cancer-free equilibrium are derived and conditions under which the system evolves to periodic solutions are determined. © 2012 Elsevier Ltd. All rights reserved.

  8. A semigroup approach to an integro-differential equation modeling slow erosion

    Science.gov (United States)

    Bressan, Alberto; Shen, Wen

    2014-10-01

    The paper is concerned with a scalar conservation law with nonlocal flux, providing a model for granular flow with slow erosion and deposition. While the solution u=u(t,x) can have jumps, the inverse function x=x(t,u) is always Lipschitz continuous; its derivative has bounded variation and satisfies a balance law with measure-valued sources. Using a backward Euler approximation scheme combined with a nonlinear projection operator, we construct a continuous semigroup whose trajectories are the unique entropy weak solutions to this balance law. Going back to the original variables, this yields the global well-posedness of the Cauchy problem for the granular flow model.

  9. Nonlinear identification of MDOF systems using Volterra series approximation

    Science.gov (United States)

    Prawin, J.; Rao, A. Rama Mohan

    2017-02-01

    Most of the practical engineering structures exhibit nonlinearity due to nonlinear dynamic characteristics of structural joints, nonlinear boundary conditions and nonlinear material properties. Meanwhile, the presence of non-linearity in the system can lead to a wide range of structural behavior, for example, jumps, limit cycles, internal resonances, modal coupling, super and sub-harmonic resonances, etc. In this paper, we present a Volterra series approximation approach based on the adaptive filter concept for nonlinear identification of multi-degree of freedom systems, without sacrificing the benefits associated with the traditional Volterra series approach. The effectiveness of the proposed approach is demonstrated using two classical single degrees of freedom systems (breathing crack problem and Duffing Holmes oscillator) and later we extend to multi-degree of freedom systems.

  10. Sparse Volterra and Polynomial Regression Models: Recoverability and Estimation

    CERN Document Server

    Kekatos, Vassilis

    2011-01-01

    Volterra and polynomial regression models play a major role in nonlinear system identification and inference tasks. Exciting applications ranging from neuroscience to genome-wide association analysis build on these models with the additional requirement of parsimony. This requirement has high interpretative value, but unfortunately cannot be met by least-squares based or kernel regression methods. To this end, compressed sampling (CS) approaches, already successful in linear regression settings, can offer a viable alternative. The viability of CS for sparse Volterra and polynomial models is the core theme of this work. A common sparse regression task is initially posed for the two models. Building on (weighted) Lasso-based schemes, an adaptive RLS-type algorithm is developed for sparse polynomial regressions. The identifiability of polynomial models is critically challenged by dimensionality. However, following the CS principle, when these models are sparse, they could be recovered by far fewer measurements. ...

  11. Lotka-Volterra systems satisfying a strong Painlevé property

    Science.gov (United States)

    Bountis, Tassos; Vanhaecke, Pol

    2016-12-01

    We use a strong version of the Painlevé property to discover and characterize a new class of n-dimensional Hamiltonian Lotka-Volterra systems, which turn out to be Liouville integrable as well as superintegrable. These systems are in fact Nambu systems, they posses Lax equations and they can be explicitly integrated in terms of elementary functions. We apply our analysis to systems containing only quadratic nonlinearities of the form aijxixj , i ≠ j, and require that all variables diverge as t-1. We also require that the leading terms depend on n - 2 free parameters. We thus discover a cocycle relation among the coefficients aij of the equations of motion and by integrating the cocycle equations we show that they are equivalent to the above strong version of the Painlevé property. We also show that these systems remain explicitly solvable even if a linear term bixi is added to the i-th equation, even though this violates the Painlevé property, as logarithmic singularities are introduced in the Laurent solutions, at the first terms following the leading order pole.

  12. New Method for Identifying Finite Degree Volterra Series

    OpenAIRE

    Suleiman, Wael; Monin, André

    2008-01-01

    International audience; In this paper, the identification of a class of nonlinear systems which admits input-output maps described by a finite degree Volterra series is considered. In actual fact, it appears that this class can model many important nonlinear multivariable processes not only in engineering, but also in biology, socio-economics, and ecology. To solve this identification problem, we propose a method based on a local gradient search in a local parameterization of the state space ...

  13. Global behavior of n-dimensional Lotka-Volterra systems.

    Science.gov (United States)

    Gouzé, J L

    1993-02-01

    The behavior of Lotka-Volterra systems is studied using as tools the results from positivity and auxiliary functions that decrease along the trajectories. One typical result is that if a decomposition of the interaction matrix into a product of a symmetric and an off-diagonal nonnegative matrix is possible, then all the trajectories either go to equilibria or cannot remain in any compact set of the interior of the positive orthant.

  14. Crosscumulants Based Approaches for the Structure Identification of Volterra Models

    Institute of Scientific and Technical Information of China (English)

    Houda Mathlouthi; Kamel Abederrahim; Faouzi Msahli; Gerard Favier

    2009-01-01

    In this paper, we address the problem of structure identification of Volterra models. It consists in estimating the model order and the memory lcngth of each kernel. Two methods based on input-output crosscumulants arc developed. The first one uses zero mean independent and identically distributed Ganssian input, and the second one concerns a symmetric input sequence. Simulations are performed on six models having different orders and kernel memory lengths to demonstrate the advantages of the proposed methods.

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

    Energy Technology Data Exchange (ETDEWEB)

    Lin Wei [Laboratory of Nonlinear Mathematics Science, Institute of Mathematics, Fudan University, Shanghai 200433 (China)]. E-mail: weilin@fudan.edu.cn; Chen Tianping [Laboratory of Nonlinear Mathematics Science, Institute of Mathematics, Fudan University, Shanghai 200433 (China)]. E-mail: tchen@fudan.edu.cn

    2005-01-17

    In this Letter, for a general class of delayed periodic Lotka-Volterra systems, we prove some new results on the existence of positive periodic solutions by Schauder's fixed point theorem. The global asymptotical stability of positive periodic solutions is discussed further, and conditions for exponential convergence are given. The conditions we obtained are weaker than the previously known ones and can be easily reduced to several special cases.

  16. Turing patterns in a modified Lotka-Volterra model

    Energy Technology Data Exchange (ETDEWEB)

    McGehee, Edward A. [Department of Chemistry, Williams College, Williamstown, MA 01267 (United States); Peacock-Lopez, Enrique [Department of Chemistry, Williams College, Williamstown, MA 01267 (United States)]. E-mail: epeacock@williams.edu

    2005-07-04

    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.

  17. A simple spatiotemporal chaotic Lotka-Volterra model

    Energy Technology Data Exchange (ETDEWEB)

    Sprott, J.C. [Department of Physics, University of Wisconsin, 1150 University Avenue, Madison, WI 53706 (United States)] e-mail: sprott@physics.wisc.edu; Wildenberg, J.C. [Department of Physics, University of Wisconsin, 1150 University Avenue, Madison, WI 53706 (United States)] e-mail: jcwildenberg@wisc.edu; Azizi, Yousef [Institute for Advanced Studies in Basic Sciences, Zanjan (Iran, Islamic Republic of)] e-mail: joseph_azizi@yahoo.com

    2005-11-01

    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.

  18. Darboux polynomials for Lotka-Volterra systems in three dimensions

    CERN Document Server

    Christodoulides, Yiannis T

    2008-01-01

    We consider Lotka-Volterra systems in three dimensions depending on three real parameters. By using elementary algebraic methods we classify the Darboux polynomials (also known as second integrals) for such systems for various values of the parameters, and give the explicit form of the corresponding cofactors. More precisely, we show that a Darboux polynomial of degree greater than one is reducible. In fact, it is a product of linear Darboux polynomials and first integrals.

  19. Stability and monotonicity of Lotka-Volterra type operators

    CERN Document Server

    Mukhamedov, Farrukh

    2009-01-01

    In the present paper, we study Lotka-Volterra (LV) type operators defined in finite dimensional simplex. We prove that any LV type operator is a surjection of the simplex. After, we introduce a new class of LV-type operators, called $M$LV type. We prove convergence of their trajectories and study certain its properties. Moreover, we show that such kind of operators have totaly different behavior than ${\\mathbf{f}}$-monotone LV type operators.

  20. A New Regularization Mechanism for the Boltzmann Equation Without Cut-Off

    Science.gov (United States)

    Silvestre, Luis

    2016-11-01

    We apply recent results on regularity for general integro-differential equations to derive a priori estimates in Hölder spaces for the space homogeneous Boltzmann equation in the non cut-off case. We also show an a priori estimate in {L^∞} which applies in the space inhomogeneous case as well, provided that the macroscopic quantities remain bounded.

  1. A DELAY-DEPENDENT STABILITY CRITERION FOR NONLINEAR STOCHASTIC DELAY-INTEGRO-DIFFERENTIAL EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    Niu Yuanling; Zhang Chengjian; Duan Jinqiao

    2011-01-01

    A type of complex systems under both random influence and memory effects is considered.The systems are modeled by a class of nonlinear stochastic delay-integrodifferential equations.A delay-dependent stability criterion for such equations is derived under the condition that the time lags are small enough.Numerical simulations are presented to illustrate the theoretical result.

  2. NONLOCAL INITIAL PROBLEM FOR NONLINEAR NONAUTONOMOUS DIFFERENTIAL EQUATIONS IN A BANACH SPACE

    Institute of Scientific and Technical Information of China (English)

    M.I.Gil'

    2004-01-01

    The nonlocal initial problem for nonlinear nonautonomous evolution equations in a Banach space is considered. It is assumed that the nonlinearities have the local Lipschitz properties. The existence and uniqueness of mild solutions are proved. Applications to integro-differential equations are discussed. The main tool in the paper is the normalizing mapping (the generalized norm).

  3. Non local Lotka-Volterra system with cross-diffusion in an heterogeneous medium.

    Science.gov (United States)

    Fontbona, Joaquin; Méléard, Sylvie

    2015-03-01

    We introduce a stochastic individual model for the spatial behavior of an animal population of dispersive and competitive species, considering various kinds of biological effects, such as heterogeneity of environmental conditions, mutual attractive or repulsive interactions between individuals or competition between them for resources. As a consequence of the study of the large population limit, global existence of a nonnegative weak solution to a multidimensional parabolic strongly coupled model of competing species is proved. The main new feature of the corresponding integro-differential equation is the nonlocal nonlinearity appearing in the diffusion terms, which may depend on the spatial densities of all population types. Moreover, the diffusion matrix is generally not strictly positive definite and the cross-diffusion effect allows for influences growing linearly with the subpopulations' sizes. We prove uniqueness of the finite measure-valued solution and give conditions under which the solution takes values in a functional space. We then make the competition kernels converge to a Dirac measure and obtain the existence of a solution to a locally competitive version of the previous equation. The techniques are essentially based on the underlying stochastic flow related to the dispersive part of the dynamics, and the use of suitable dual distances in the space of finite measures.

  4. Lectures on Cauchy's problem in linear partial differential equations

    CERN Document Server

    Hadamard, Jacques

    2003-01-01

    Would well repay study by most theoretical physicists."" - Physics Today""An overwhelming influence on subsequent work on the wave equation."" - Science Progress""One of the classical treatises on hyperbolic equations."" - Royal Naval Scientific ServiceDelivered at Columbia University and the Universities of Rome and Zürich, these lectures represent a pioneering investigation. Jacques Hadamard based his research on prior studies by Riemann, Kirchhoff, and Volterra. He extended and improved Volterra's work, applying its theories relating to spherical and cylindrical waves to all normal hyperbol

  5. On Modelling of Nonlinear Systems and Phenomena with the Use of Volterra and Wiener Series

    Directory of Open Access Journals (Sweden)

    Andrzej Borys

    2015-03-01

    Full Text Available This is a short tutorial on Volterra and Wiener series applications to modelling of nonlinear systems and phenomena, and also a survey of the recent achievements in this area. In particular, we show here how the philosophies standing behind each of the above theories differ from each other. On the other hand, we discuss also mathematical relationships between Volterra and Wiener kernels and operators. Also, the problem of a best approximation of large-scale nonlinear systems using Volterra operators in weighted Fock spaces is described. Examples of applications considered are the following: Volterra series use in description of nonlinear distortions in satellite systems and their equalization or compensation, exploiting Wiener kernels to modelling of biological systems, the use of both Volterra and Wiener theories in description of ocean waves and in magnetic resonance spectroscopy. Moreover, connections between Volterra series and neural network models, and also input-output descriptions of quantum systems by Volterra series are discussed. Finally, we consider application of Volterra series to solving some nonlinear problems occurring in hydrology, navigation, and transportation.

  6. Numerical Integration and Synchronization for the 3-Dimensional Metriplectic Volterra System

    Directory of Open Access Journals (Sweden)

    Gheorghe Ivan

    2011-01-01

    Full Text Available The main purpose of this paper is to study the metriplectic system associated to 3-dimensional Volterra model. For this system we investigate the stability problem and numerical integration via Kahan's integrator. Finally, the synchronization problem for two coupled metriplectic Volterra systems is discussed.

  7. New exact solutions to some difference differential equations

    Institute of Scientific and Technical Information of China (English)

    Wang Zhen; Zhang Hong-Qing

    2006-01-01

    In this paper, we use our method to solve the extended Lotka-Volterra equation and discrete KdV equation. With the help of Maple, we obtain a number of exact solutions to the two equations including soliton solutions presented by hyperbolic functions of sinh and cosh, periodic solutions presented by trigonometric functions of sin and cos, and rational solutions. This method can be used to solve some other nonlinear difference-differential equations.

  8. RAZUMIKHIN-TYPE THEOREM FOR NEUTRAL STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS WITH UNBOUNDED DELAY

    Institute of Scientific and Technical Information of China (English)

    Wu Fuke; Hu Shigeng; Mao Xuerong

    2011-01-01

    This paper establishes the Razumikhin-type theorem on stability for neutral stochastic functional differential equations with unbounded delay.To overcome difficulties from unbounded delay,we develop several different techniques to investigate stability.To show our idea clearly,we examine neutral stochastic delay differential equations with unbounded delay and linear neutral stochastic Volterra unbounded-delay-integro-differential equations.

  9. Global topological classification of Lotka-Volterra quadratic differential systems

    Directory of Open Access Journals (Sweden)

    Dana Schlomiuk

    2012-04-01

    Full Text Available The Lotka-Volterra planar quadratic differential systems have numerous applications but the global study of this class proved to be a challenge difficult to handle. Indeed, the four attempts to classify them (Reyn (1987, W"orz-Buserkros (1993, Georgescu (2007 and Cao and Jiang (2008 produced results which are not in agreement. The lack of adequate global classification tools for the large number of phase portraits encountered, explains this situation. All Lotka-Volterra systems possess invariant straight lines, each with its own multiplicity. In this article we use as a global classification tool for Lotka-Volterra systems the concept of configuration of invariant lines (including the line at infinity. The class splits according to the types of configurations in smaller subclasses which makes it easier to have a good control over the phase portraits in each subclass. At the same time the classification becomes more transparent and easier to grasp. We obtain a total of 112 topologically distinct phase portraits: 60 of them with exactly three invariant lines, all simple; 27 portraits with invariant lines with total multiplicity at least four; 5 with the line at infinity filled up with singularities; 20 phase portraits of degenerate systems. We also make a thorough analysis of the results in the paper of Cao and Jiang [13]. In contrast to the results on the classification in [13], done in terms of inequalities on the coefficients of normal forms, we construct invariant criteria for distinguishing these portraits in the whole parameter space $mathbb{R}^{12}$ of coefficients.

  10. Workshop on Numerical Methods for Ordinary Differential Equations

    CERN Document Server

    Gear, Charles; Russo, Elvira

    1989-01-01

    Developments in numerical initial value ode methods were the focal topic of the meeting at L'Aquila which explord the connections between the classical background and new research areas such as differental-algebraic equations, delay integral and integro-differential equations, stability properties, continuous extensions (interpolants for Runge-Kutta methods and their applications, effective stepsize control, parallel algorithms for small- and large-scale parallel architectures). The resulting proceedings address many of these topics in both research and survey papers.

  11. Controllability in hybrid kinetic equations modeling nonequilibrium multicellular systems.

    Science.gov (United States)

    Bianca, Carlo

    2013-01-01

    This paper is concerned with the derivation of hybrid kinetic partial integrodifferential equations that can be proposed for the mathematical modeling of multicellular systems subjected to external force fields and characterized by nonconservative interactions. In order to prevent an uncontrolled time evolution of the moments of the solution, a control operator is introduced which is based on the Gaussian thermostat. Specifically, the analysis shows that the moments are solution of a Riccati-type differential equation.

  12. Statistics of extinction and survival in Lotka-Volterra systems

    CERN Document Server

    Abramson, G; Abramson, Guillermo; Zanette, Damian

    1998-01-01

    We analyze purely competitive many-species Lotka-Volterra systems with random interaction matrices, focusing the attention on statistical properties of their asymptotic states. Generic features of the evolution are outlined from a semiquantitative analysis of the phase-space structure, and extensive numerical simulations are performed to study the statistics of the extinctions. We find that the number of surviving species depends strongly on the statistical properties of the interaction matrix, and that the probability of survival is weakly correlated to specific initial conditions.

  13. String networks in ZN Lotka-Volterra competition models

    Science.gov (United States)

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

    2014-01-01

    In this Letter we give specific examples of ZN 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.

  14. 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.

  15. 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.

  16. Coexistence and survival in conservative Lotka-Volterra networks.

    Science.gov (United States)

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

    2013-04-19

    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.

  17. Species clustering in competitive Lotka-Volterra models.

    Science.gov (United States)

    Pigolotti, Simone; López, Cristóbal; Hernández-García, Emilio

    2007-06-22

    We study the properties of general Lotka-Volterra models with competitive interactions. The intensity of the competition depends on the position of species in an abstract niche space through an interaction kernel. We show analytically and numerically that the properties of these models change dramatically when the Fourier transform of this kernel is not positive definite, due to a pattern-forming instability. We estimate properties of the species distributions, such as the steady number of species and their spacings, for different types of interactions, including stretched exponential and constant kernels.

  18. Free Boundary Problems for a Lotka-Volterra Competition System

    Science.gov (United States)

    Wang, Mingxin; Zhao, Jingfu

    2014-09-01

    In this paper we investigate two free boundary problems for a Lotka-Volterra type competition model in one space dimension. The main objective is to understand the asymptotic behavior of the two competing species spreading via a free boundary. We prove a spreading-vanishing dichotomy, namely the two species either successfully spread to the entire space as time t goes to infinity and survive in the new environment, or they fail to establish and die out in the long run. The long time behavior of the solutions and criteria for spreading and vanishing are also obtained. This paper is an improvement and extension of J. Guo and C. Wu.

  19. Winnerless competition in coupled Lotka-Volterra maps.

    Science.gov (United States)

    González-Díaz, L A; Gutiérrez, E D; Varona, P; Cabrera, J L

    2013-07-01

    Winnerless competition is analyzed in coupled maps with discrete temporal evolution of the Lotka-Volterra type of arbitrary dimension. Necessary and sufficient conditions for the appearance of structurally stable heteroclinic cycles as a function of the model parameters are deduced. It is shown that under such conditions winnerless competition dynamics is fully exhibited. Based on these conditions different cases characterizing low, intermediate, and high dimensions are therefore computationally recreated. An analytical expression for the residence times valid in the N-dimensional case is deduced and successfully compared with the simulations.

  20. Almost periodic solution of non-autonomous Lotka-Volterra predator-prey dispersal system with delays.

    Science.gov (United States)

    Meng, Xinzhu; Chen, Lansun

    2006-12-21

    This paper studies a non-autonomous Lotka-Volterra almost periodic predator-prey dispersal system with discrete and continuous time delays which consists of n-patches, the prey species can disperse among n-patches, but the predator species is confined to one patch and cannot disperse. By using comparison theorem and delay differential equation basic theory, we prove the system is uniformly persistent under some appropriate conditions. Further, by constructing suitable Lyapunov functional, we show that the system is globally asymptotically stable under some appropriate conditions. By using almost periodic functional hull theory, we show that the almost periodic system has a unique globally asymptotical stable strictly positive almost periodic solution. The conditions for the permanence, global stability of system and the existence, uniqueness of positive almost periodic solution depend on delays, so, time delays are "profitless". Finally, conclusions and two particular cases are given. These results are basically an extension of the known results for non-autonomous Lotka-Volterra systems.

  1. Collsionless tearing instability in a non-Maxwellian neutral sheet - An integro-differential formulation

    Science.gov (United States)

    Chen, J.; Lee, Y. C.

    1985-01-01

    In the present investigation, a general integro-differential formalism is derived for the study of the collisionless tearing mode in a highly non-Maxwellian neutral sheet in which both electrons and ions are treated kinetically. The obtained formalism is applied to a specific non-Maxwellian distribution. The dispersion relation for the considered system is determined, taking into account the fundamental harmonic of the orbital frequency. It is found that the dispersion relation is dominated by the electrons. The results are presented in a number of graphs. The growth rates of non-Maxwellian distributions are generally much greater than the growth rate of the conventional isotropic tearing instability.

  2. Existence of minimal and maximal solutions to RL fractional integro-differential initial value problems

    Directory of Open Access Journals (Sweden)

    Z. Denton

    2017-01-01

    Full Text Available In this work we investigate integro-differential initial value problems with Riemann Liouville fractional derivatives where the forcing function is a sum of an increasing function and a decreasing function. We will apply the method of lower and upper solutions and develop two monotone iterative techniques by constructing two sequences that converge uniformly and monotonically to minimal and maximal solutions. In the first theorem we will construct two natural sequences and in the second theorem we will construct two intertwined sequences. Finally, we illustrate our results with an example.

  3. A reduced-rank approach for implementing higher-order Volterra filters

    Science.gov (United States)

    O. Batista, Eduardo L.; Seara, Rui

    2016-12-01

    The use of Volterra filters in practical applications is often limited by their high computational burden. To cope with this problem, many strategies for implementing Volterra filters with reduced complexity have been proposed in the open literature. Some of these strategies are based on reduced-rank approaches obtained by defining a matrix of filter coefficients and applying the singular value decomposition to such a matrix. Then, discarding the smaller singular values, effective reduced-complexity Volterra implementations can be obtained. The application of this type of approach to higher-order Volterra filters (considering orders greater than 2) is however not straightforward, which is especially due to some difficulties encountered in the definition of higher-order coefficient matrices. In this context, the present paper is devoted to the development of a novel reduced-rank approach for implementing higher-order Volterra filters. Such an approach is based on a new form of Volterra kernel implementation that allows decomposing higher-order kernels into structures composed only of second-order kernels. Then, applying the singular value decomposition to the coefficient matrices of these second-order kernels, effective implementations for higher-order Volterra filters can be obtained. Simulation results are presented aiming to assess the effectiveness of the proposed approach.

  4. Volterra series truncation and kernel estimation of nonlinear systems in the frequency domain

    Science.gov (United States)

    Zhang, B.; Billings, S. A.

    2017-02-01

    The Volterra series model is a direct generalisation of the linear convolution integral and is capable of displaying the intrinsic features of a nonlinear system in a simple and easy to apply way. Nonlinear system analysis using Volterra series is normally based on the analysis of its frequency-domain kernels and a truncated description. But the estimation of Volterra kernels and the truncation of Volterra series are coupled with each other. In this paper, a novel complex-valued orthogonal least squares algorithm is developed. The new algorithm provides a powerful tool to determine which terms should be included in the Volterra series expansion and to estimate the kernels and thus solves the two problems all together. The estimated results are compared with those determined using the analytical expressions of the kernels to validate the method. To further evaluate the effectiveness of the method, the physical parameters of the system are also extracted from the measured kernels. Simulation studies demonstrates that the new approach not only can truncate the Volterra series expansion and estimate the kernels of a weakly nonlinear system, but also can indicate the applicability of the Volterra series analysis in a severely nonlinear system case.

  5. 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.

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

    Directory of Open Access Journals (Sweden)

    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.

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

    Energy Technology Data Exchange (ETDEWEB)

    Chu Tianguang [Intelligent Control Laboratory, Center for Systems and Control, School of Engineering, Peking University, Beijing 100871 (China)], E-mail: chutg@pku.edu.cn

    2007-08-20

    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.

  8. Generalized Bihari Type Integral Inequalities and the Corresponding Integral Equations

    OpenAIRE

    2009-01-01

    We study some special nonlinear integral inequalities and the corresponding integral equations in measure spaces. They are significant generalizations of Bihari type integral inequalities and Volterra and Fredholm type integral equations. The kernels of the integral operators are determined by concave functions. Explicit upper bounds are given for the solutions of the integral inequalities. The integral equations are investigated with regard to the existence of a minimal and a maximal soluti...

  9. An hp-adaptive strategy for the solution of the exact kernel curved wire Pocklington equation

    NARCIS (Netherlands)

    Lahaye, D.; Hemker, P.W.

    2007-01-01

    In this paper we introduce an adaptive method for the numerical solution of the Pocklington integro-differential equation with exact kernel for the current induced in a smoothly curved thin wire antenna. The hp-adaptive technique is based on the representation of the discrete solution, which is expa

  10. Multipoint problem for intehrodyferentsialnyh partial differential equations, not solvable on higher derivatives

    Directory of Open Access Journals (Sweden)

    І.С. Клюс

    2007-01-01

    Full Text Available  The correctness of a problem with multi–point conditions on temporary variable of  linear partial differential equations not solved as to the highest derivative with respect to time, perturbed by the nonlinear integro-differential operator is investigated

  11. Parallel methods for nonstiff VIDEs

    NARCIS (Netherlands)

    Houwen, P.J. van der

    1998-01-01

    We consider numerical methods for nonstiff initial-value problems for Volterra integro-differential equations. Such problems may be considered as initial-value problems for ordinary differential equations with expensive righthand side functions because each righthand side evaluation requires the app

  12. The World According to Malthus and Volterra: The Mathematical Theory of the Struggle for Existence.

    Science.gov (United States)

    Bogdanov, Constantine

    1992-01-01

    Discusses the mathematical model presented by Vito Volterra to describe the dynamics of population density. Discusses the predator prey relationship, presents an computer simulated model from marine life involving sharks and mackerels, and discusses ecological chaos. (MDH)

  13. Numerical solution of functional integral equations by using B-splines

    Directory of Open Access Journals (Sweden)

    Reza Firouzdor

    2014-05-01

    Full Text Available This paper describes an approximating solution, based on Lagrange interpolation and spline functions, to treat functional integral equations of Fredholm type and Volterra type. This method can be extended to functional dierential and integro-dierential equations. For showing eciency of the method we give some numerical examples.

  14. On kinetic Boltzmann equations and related hydrodynamic flows with dry viscosity

    Directory of Open Access Journals (Sweden)

    Nikolai N. Bogoliubov (Jr.

    2007-01-01

    Full Text Available A two-component particle model of Boltzmann-Vlasov type kinetic equations in the form of special nonlinear integro-differential hydrodynamic systems on an infinite-dimensional functional manifold is discussed. We show that such systems are naturally connected with the nonlinear kinetic Boltzmann-Vlasov equations for some one-dimensional particle flows with pointwise interaction potential between particles. A new type of hydrodynamic two-component Benney equations is constructed and their Hamiltonian structure is analyzed.

  15. 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 w(i), 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 w(i)'s turn out to exhibit a power-law distribution of the form P(w) approximately w(-1-alpha). It is shown analytically that the exponent alpha 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 alpha 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

  16. Coexistence versus extinction in the stochastic cyclic Lotka-Volterra model.

    Science.gov (United States)

    Reichenbach, Tobias; Mobilia, Mauro; Frey, Erwin

    2006-11-01

    Cyclic dominance of species has been identified as a potential mechanism to maintain biodiversity, see, e.g., B. Kerr, M. A. Riley, M. W. Feldman and B. J. M. Bohannan [Nature 418, 171 (2002)] and B. Kirkup and M. A. Riley [Nature 428, 412 (2004)]. Through analytical methods supported by numerical simulations, we address this issue by studying the properties of a paradigmatic non-spatial three-species stochastic system, namely, the "rock-paper-scissors" or cyclic Lotka-Volterra model. While the deterministic approach (rate equations) predicts the coexistence of the species resulting in regular (yet neutrally stable) oscillations of the population densities, we demonstrate that fluctuations arising in the system with a finite number of agents drastically alter this picture and are responsible for extinction: After long enough time, two of the three species die out. As main findings we provide analytic estimates and numerical computation of the extinction probability at a given time. We also discuss the implications of our results for a broad class of competing population systems.

  17. 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.

  18. Periodic Solutions for n-Species Lotka-Volterra Competitive Systems with Pure Delays

    Directory of Open Access Journals (Sweden)

    Ahmadjan Muhammadhaji

    2015-01-01

    Full Text Available We study a class of periodic general n-species competitive Lotka-Volterra systems with pure delays. Based on the continuation theorem of the coincidence degree theory and Lyapunov functional, some new sufficient conditions on the existence and global attractivity of positive periodic solutions for the n-species competitive Lotka-Volterra systems are established. As an application, we also examine some special cases of the system, which have been studied extensively in the literature.

  19. An integrable Poisson map generated from the eigenvalue problem of the Lotka-Volterra hierarchy

    Energy Technology Data Exchange (ETDEWEB)

    Wu Yongtang [Department of Computer Science, Hong Kong Baptist University, Kowloon Tong, Hong Kong (China); Wang Hongye [Department of Mathematics, Zhengzhou University, Henan (China); Du Dianlou [Department of Mathematics, Zhengzhou University, Henan (China)]. E-mail: ddl@zzu.edu.cn

    2002-05-03

    A 3x3 discrete eigenvalue problem associated with the Lotka-Volterra hierarchy is studied and the corresponding nonlinearized one, an integrable Poisson map with a Lie-Poisson structure, is also presented. Moreover, a 2x2 nonlinearized eigenvalue problem, which also begets the Lotka-Volterra hierarchy, is proved to be a reduction of the Poisson map on the leaves of the symplectic foliation. (author)

  20. Conditional symmetries and exact solutions of the diffusive Lotka-Volterra system

    CERN Document Server

    Cherniha, Roman

    2010-01-01

    Q-conditional symmetries of the classical Lotka-Volterra system in the case of one space variable are completely described and a set of such symmetries in explicit form is constructed. The relevant non-Lie ans\\"atze to reduce the classical Lotka-Volterra systems with correctly-specified coefficients to ODE systems and examples of new exact solutions are found. A possible biological interpretation of some exact solutions is presented.

  1. Computational Stability Analysis of Lotka-Volterra Systems

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    Polcz Péter

    2016-12-01

    Full Text Available This paper concerns the computational stability analysis of locally stable Lotka-Volterra (LV systems by searching for appropriate Lyapunov functions in a general quadratic form composed of higher order monomial terms. The Lyapunov conditions are ensured through the solution of linear matrix inequalities. The stability region is estimated by determining the level set of the Lyapunov function within a suitable convex domain. The paper includes interesting computational results and discussion on the stability regions of higher (3,4 dimensional LV models as well as on the monomial selection for constructing the Lyapunov functions. Finally, the stability region is estimated of an uncertain 2D LV system with an uncertain interior locally stable equilibrium point.

  2. Stochastic analysis of the Lotka-Volterra model for ecosystems.

    Science.gov (United States)

    Cai, G Q; Lin, Y K

    2004-10-01

    A stochastic Lotka-Volterra-type model for the interaction between the preys and the predators in a random environment is investigated. A self-competition mechanism within the prey population itself is also included. The effect of a random environment is modeled as random variations in the birth rate of the preys and the death rate of the predators. The stochastic averaging procedure of Stratonovich and Khasminskii is applied to obtain the probability distributions of the system state variables at the state of statistical stationarity. Asymptotic behaviors of the system variables are discussed, and the mean transition time from an initial state to a critical state is obtained. Effects on the ecosystem behaviors of the self-competition term, of the random variation in the prey birth rate, and of the random variation in the predator death rate are investigated.

  3. Nonextensivity of the cyclic lattice Lotka-Volterra model.

    Science.gov (United States)

    Tsekouras, G A; Provata, A; Tsallis, C

    2004-01-01

    We numerically show that the lattice Lotka-Volterra model, when realized on a square lattice support, gives rise to a finite production, per unit time, of the nonextensive entropy S(q)=(1- summation operator (i)p(q)(i))/(q-1) (S(1)=- summation operator (i)p(i) ln p(i)). This finiteness only occurs for q=0.5 for the d=2 growth mode (growing droplet), and for q=0 for the d=1 one (growing stripe). This strong evidence of nonextensivity is consistent with the spontaneous emergence of local domains of identical particles with fractal boundaries and competing interactions. Such direct evidence is, to our knowledge, exhibited for the first time for a many-body system which, at the mean field level, is conservative.

  4. Conditions for Eltonian Pyramids in Lotka-Volterra Food Chains.

    Science.gov (United States)

    Jonsson, Tomas

    2017-09-07

    In ecological communities consumers (excluding parasites and parasitoids) are in general larger and less numerous than their resource. This results in a well-known observation known as 'Eltonian pyramids' or the 'pyramid of numbers', and metabolic arguments suggest that this pattern is independent of the number of trophic levels in a system. At the same time, Lotka-Volterra (LV) consumer-resource models are a frequently used tool to study many questions in community ecology, but their capacity to produce Eltonian pyramids has not been formally analysed. Here, I address this knowledge gap by investigating if and when LV food chain models give rise to Eltonian pyramids. I show that Eltonian pyramids are difficult to reproduce without density-dependent mortality in the consumers, unless biologically plausible relationships between mortality rate and interaction strength are taken into account.

  5. Complex Features in Lotka-Volterra Systems with Behavioral Adaptation

    Science.gov (United States)

    Tebaldi, Claudio; Lacitignola, Deborah

    Lotka-Volterra systems have played a fundamental role for mathematical modelling in many branches of theoretical biology and proved to describe, at least qualitatively, the essential features of many phenomena, see for example Murray [Murray 2002]. Furthermore models of that kind have been considered successfully also in quite different and less mathematically formalized context: Goodwin' s model of economic growth cycles [Goodwin 1967] and urban dynamics [Dendrinos 1992] are only two of a number of examples. Such systems can certainly be defined as complex ones and in fact the aim of modelling was essentially to clarify mechanims rather than to provide actual precise simulations and predictions. With regards to complex systems, we recall that one of their main feature, no matter of the specific definition one has in mind, is adaptation, i. e. the ability to adjust.

  6. El testamento y otros documentos sobre Daniele da Volterra

    Directory of Open Access Journals (Sweden)

    Redín, Gonzalo

    2010-09-01

    Full Text Available Daniele da Volterra is better known in Spain for painting the drapery that covers some of the nudes in Michelangelo’s The Last Judgment than for his own work, which defined him as his master’s most loyal successor. Nonetheless, Daniele’s influence on Spanish art through Gaspar Becerra, a disciple of his in Rome, determined to a large extent the development of sculpture in this country in the second half of the 16th century. This article makes known and discusses Daniele’s previously unpublished last will and testament, located in the Archivio di Stato di Roma among the volumes by the notary Thomassino, who attended to the inventory of his possessions. It also provides new details on Daniele’s estate and on his direct disciples Michele Alberti, Feliciano de San Vito, and Biagio Betti along with his indirect ones such as Jacopo Rocchetti.

    Daniele da Volterra es más conocido en España por pintar los paños que cubren algunos de los desnudos del Juicio final de Miguel Ángel, que por su obra, que le define como el más fiel heredero de su maestro. Sin embargo, su influencia en el arte español a través de Gaspar Becerra, discípulo suyo en Roma, condicionó el desarrollo de la escultura en buena parte de nuestro país en la segunda mitad del siglo XVI. Publicamos y comentamos aquí su testamento inédito, localizado en el Archivio di Stato di Roma entre los volúmenes del notario Thomassino, que se encargó del inventario de sus bienes, y aportamos noticias relativas a su herencia y a sus discípulos directos, Michele Alberti, Feliciano de San Vito y Biagio Betti, e indirectos, como Jacopo Rocchetti.

  7. Equivalent HPM with ADM and Convergence of the HPM to a Class of Nonlinear Integral Equations

    Directory of Open Access Journals (Sweden)

    J. Manafian Heris

    2013-03-01

    Full Text Available The purpose of this study is to implement homotopy perturbation method, for solving nonlinear Volterra integral equations. In this work, a reliable approach for convergence of the HPM when applied to a class of nonlinear Volterra integral equations is discussed. Convergence analysis is reliable enough to estimate the maximum absolute truncated error of the series solution. The results obtained by using HPM, are compared to those obtained by using Adomian decomposition method alone. The numerical results, demonstrate that HPM technique, gives the approximate solution with faster convergence rate and higher accuracy than using the standard ADM

  8. A Discrete Equivalent of the Logistic Equation

    Directory of Open Access Journals (Sweden)

    Petropoulou EugeniaN

    2010-01-01

    Full Text Available A discrete equivalent and not analogue of the well-known logistic differential equation is proposed. This discrete equivalent logistic equation is of the Volterra convolution type, is obtained by use of a functional-analytic method, and is explicitly solved using the -transform method. The connection of the solution of the discrete equivalent logistic equation with the solution of the logistic differential equation is discussed. Also, some differences of the discrete equivalent logistic equation and the well-known discrete analogue of the logistic equation are mentioned. It is hoped that this discrete equivalent of the logistic equation could be a better choice for the modelling of various problems, where different versions of known discrete logistic equations are used until nowadays.

  9. Cross rules and non-Abelian lattice equations for the discrete and confluent non-scalar {epsilon}-algorithms

    Energy Technology Data Exchange (ETDEWEB)

    Brezinski, C, E-mail: Claude.Brezinski@univ-lille1.f [Laboratoire Paul Painleve, UMR CNRS 8524, UFR de Mathematiques Pures et Appliquees, Universite des Sciences et Technologies de Lille, 59655-Villeneuve d' Ascq cedex (France)

    2010-05-21

    In this paper, we give the cross rules of the discrete and confluent vector, topological and matrix {epsilon}-algorithms. Then, from the rules of these confluent algorithms, we derive non-Abelian lattice equations, in particular some extensions of the Lotka-Volterra system, in the style of the equation related to the confluent form of the scalar {epsilon}-algorithm.

  10. Data-driven modeling based on volterra series for multidimensional blast furnace system.

    Science.gov (United States)

    Gao, Chuanhou; Jian, Ling; Liu, Xueyi; Chen, Jiming; Sun, Youxian

    2011-12-01

    The multidimensional blast furnace system is one of the most complex industrial systems and, as such, there are still many unsolved theoretical and experimental difficulties, such as silicon prediction and blast furnace automation. For this reason, this paper is concerned with developing data-driven models based on the Volterra series for this complex system. Three kinds of different low-order Volterra filters are designed to predict the hot metal silicon content collected from a pint-sized blast furnace, in which a sliding window technique is used to update the filter kernels timely. The predictive results indicate that the linear Volterra predictor can describe the evolvement of the studied silicon sequence effectively with the high percentage of hitting the target, very low root mean square error and satisfactory confidence level about the reliability of the future prediction. These advantages and the low computational complexity reveal that the sliding-window linear Volterra filter is full of potential for multidimensional blast furnace system. Also, the lack of the constructed Volterra models is analyzed and the possible direction of future investigation is pointed out.

  11. Laguerre-Volterra identification of spike-timing-dependent plasticity from spiking activity: a simulation study.

    Science.gov (United States)

    Robinson, Brian S; Song, Dong; Berger, Theodore W

    2013-01-01

    This paper presents a Laguerre-Volterra methodology for identifying a plasticity learning rule from spiking neural data with four components: 1) By analyzing input-output spiking data, the effective contribution of an input on the output firing probability can be quantified with weighted Volterra kernels. 2) The weight of these Volterra kernels can be tracked over time using the stochastic state point processing filtering algorithm (SSPPF) 3) Plasticity system Volterra kernels can be estimated by treating the tracked change in weight over time as the plasticity system output and the spike timing data as the input. 4) Laguerre expansion of all Volterra kernels allows for minimization of open parameters during estimation steps. A single input spiking neuron with Spike-timing-dependent plasticity (STDP) and prolonged STDP induction is simulated. Using the spiking data from this simulation, the amplitude of the STDP learning rule and the time course of the induction is accurately estimated. This framework can be applied to identify plasticity for more complicated plasticity paradigms and is applicable to in vivo data.

  12. Semigroup theory and numerical approximation for equations in linear viscoelasticity

    Science.gov (United States)

    Fabiano, R. H.; Ito, K.

    1990-01-01

    A class of abstract integrodifferential equations used to model linear viscoelastic beams is investigated analytically, applying a Hilbert-space approach. The basic equation is rewritten as a Cauchy problem, and its well-posedness is demonstrated. Finite-dimensional subspaces of the state space and an estimate of the state operator are obtained; approximation schemes for the equations are constructed; and the convergence is proved using the Trotter-Kato theorem of linear semigroup theory. The actual convergence behavior of different approximations is demonstrated in numerical computations, and the results are presented in tables.

  13. NEW ALTERNATING DIRECTION FINITE ELEMENT SCHEME FOR NONLINEAR PARABOLIC EQUATION

    Institute of Scientific and Technical Information of China (English)

    崔霞

    2002-01-01

    A new alternating direction (AD) finite element (FE) scheme for 3-dimensional nonlinear parabolic equation and parabolic integro-differential equation is studied. By using AD,the 3-dimensional problem is reduced to a family of single space variable problems, calculation work is simplified; by using FE, high accuracy is kept; by using various techniques for priori estimate for differential equations such as inductive hypothesis reasoning, the difficulty arising from the nonlinearity is treated. For both FE and ADFE schemes, the convergence properties are rigorously demonstrated, the optimal H1- and L2-norm space estimates and the O((△t)2) estimate for time variable are obtained.

  14. The H sub N method for solving linear transport equation: theory and applications

    CERN Document Server

    Tezcan, C; Guelecyuez, M C

    2003-01-01

    The system of singular integral equations which is obtained from the integro-differential form of the linear transport equation using the Placzek lemma is solved. The exit distributions at the boundaries of the various media and the infinite medium Green's function are used. The process is applied to the half-space and finite slab problems. The neutron angular density in terms of singular eigenfunctions of the method of elementary solutions is also used to derive the same analytical expressions.

  15. 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.

  16. Fractal properties of the lattice Lotka-Volterra model.

    Science.gov (United States)

    Tsekouras, G A; Provata, A

    2002-01-01

    The lattice Lotka-Volterra (LLV) model is studied using mean-field analysis and Monte Carlo simulations. While the mean-field phase portrait consists of a center surrounded by an infinity of closed trajectories, when the process is restricted to a two-dimensional (2D) square lattice, local inhomogeneities/fluctuations appear. Spontaneous local clustering is observed on lattice and homogeneous initial distributions turn into clustered structures. Reactions take place only at the interfaces between different species and the borders adopt locally fractal structure. Intercluster surface reactions are responsible for the formation of local fluctuations of the species concentrations. The box-counting fractal dimension of the LLV dynamics on a 2D support is found to depend on the reaction constants while the upper bound of fractality determines the size of the local oscillators. Lacunarity analysis is used to determine the degree of clustering of homologous species. Besides the spontaneous clustering that takes place on a regular 2D lattice, the effects of fractal supports on the dynamics of the LLV are studied. For supports of dimensionality D(s)<2 the lattice can, for certain domains of the reaction constants, adopt a poisoned state where only one of the species survives. By appropriately selecting the fractal dimension of the substrate, it is possible to direct the system into a poisoned or oscillatory steady state at will.

  17. 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.

  18. Journal of the Nigerian Association of Mathematical Physics - Vol 14 ...

    African Journals Online (AJOL)

    Approximate controllability of neutral volterra integrodifferential equations in abstract ... Complete controllability of perturbed infinite delay systems · EMAIL FULL TEXT ... Well test analysis of horizontal wells in a two-layered reservoir system: ... Hopf bifurcations in a fractional reaction–diffusion model for the invasion and ...

  19. Kesirli mertebeden integro-diferansiyel denklemlerin çözümü için sayısal bir yöntem

    Directory of Open Access Journals (Sweden)

    Sertan Alkan

    2017-04-01

    Full Text Available In this study, sinc-collocation method is introduced for solving Volterra integro-differential equations of fractional order. Fractional derivative is described in the Caputo sense often used in fractional calculus. Obtained results are given to literature as two new theorems. Some numerical examples are presented to demonstrate the theoretical results.

  20. Volterra dendritic stimulus processors and biophysical spike generators with intrinsic noise sources

    Directory of Open Access Journals (Sweden)

    Aurel A Lazar

    2014-09-01

    Full Text Available We consider a class of neural circuit models with internal noise sources arising in sensory systems. The basic neuron model in these circuits consists of a nonlinear dendritic stimulus processor (DSP cascaded with a biophysical spike generator (BSG. The nonlinear dendritic processor is modeled as a set of nonlinear operators that are assumed to have a Volterra series representation. Biophysical point neuron models, such as the Hodgkin-Huxley neuron, are used to model the spike generator. We address the question of how intrinsic noise sources affect the precision in encoding and decoding of sensory stimuli and the functional identification of its sensory circuits.We investigate two intrinsic noise sources arising (i in the active dendritic trees underlying the DSPs, and (ii in the ion channels of the BSGs. Noise in dendritic stimulus processing arises from a combined effect of variability in synaptic transmission and dendritic interactions. Channel noise arises in the BSGs due to the fluctuation of the number of the active ion channels. Using a stochastic differential equations formalism we show that encoding with a neuron model consisting of a nonlinear DSP cascaded with a BSG with intrinsic noise sources can be treated as generalized sampling with noisy measurements.For single-input multi-output neural circuit models with feedforward, feedback and cross-feedback DSPs cascaded with BSGs we theoretically analyze the effect of noise sources on stimulus decoding. Building on a key duality property, the effect of noise parameters on the precision of the functional identification of the complete neural circuit with DSP/BSG neuron models is given. We demonstrate through extensive simulations the effects of noise on encoding stimuli with circuits that include neuron models that are akin to those commonly seen in sensory systems, e.g., complex cells in V1.

  1. Lie symmetry analysis of the Lundgren–Monin–Novikov equations for multi-point probability density functions of turbulent flow

    Science.gov (United States)

    Wacławczyk, M.; Grebenev, V. N.; Oberlack, M.

    2017-04-01

    The problem of turbulence statistics described by the Lundgren–Monin–Novikov (LMN) hierarchy of integro-differential equations is studied in terms of its group properties. For this we perform a Lie group analysis of a truncated LMN chain which presents the first two equations in an infinite set of integro-differential equations for the multi-point probability density functions (pdf’s) of velocity. A complete set of point transformations is derived for the one-point pdf’s and the independent variables: sample space of velocity, space and time. For this purpose we use a direct method based on the canonical Lie–Bäcklund operator. Due to the one-way coupling of correlation equations, the present results are complete in the sense that no additional symmetries exist for the first leading equation, even if the full infinite hierarchy is considered.

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

    Energy Technology Data Exchange (ETDEWEB)

    Lei Min [State Key Lab of Vibration, Shock and Noise, Shanghai Jiao Tong University, Shanghai 200030 (China)] e-mail: leimin@sjtu.edu.cn; Meng Guang [State Key Lab of Vibration, Shock and Noise, Shanghai Jiao Tong University, Shanghai 200030 (China); Feng Zhengjin [Institute of Mechatronic Control System, Shanghai Jiao Tong University, Shanghai 200030 (China)

    2006-04-01

    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.

  3. Asymptotic solutions of forced nonlinear second order differential equations and their extensions

    Directory of Open Access Journals (Sweden)

    Angelo B. Mingarelli

    2007-03-01

    Full Text Available Using a modified version of Schauder's fixed point theorem, measures of non-compactness and classical techniques, we provide new general results on the asymptotic behavior and the non-oscillation of second order scalar nonlinear differential equations on a half-axis. In addition, we extend the methods and present new similar results for integral equations and Volterra-Stieltjes integral equations, a framework whose benefits include the unification of second order difference and differential equations. In so doing, we enlarge the class of nonlinearities and in some cases remove the distinction between superlinear, sublinear, and linear differential equations that is normally found in the literature. An update of papers, past and present, in the theory of Volterra-Stieltjes integral equations is also presented.

  4. Difference equations in normed spaces stability and oscillations

    CERN Document Server

    Gil, Michael

    2007-01-01

    Difference equations appear as natural descriptions of observed evolution phenomena because most measurements of time evolving variables are discrete. They also appear in the applications of discretization methods for differential, integral and integro-differential equations. The application of the theory of difference equations is rapidly increasing to various fields, such as numerical analysis, control theory, finite mathematics, and computer sciences. This book is devoted to linear and nonlinear difference equations in a normed space. The main methodology presented in this book is based on a combined use of recent norm estimates for operator-valued functions with the following methods and results: The freezing methodThe Liapunov type equationThe method of majorantsThe multiplicative representation of solutionsDeals systematically with difference equations in normed spaces Considers new classes of equations that could not be studied in the frameworks of ordinary and partial difference equationsDevelops ...

  5. 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.

  6. Boltzmann, Lotka and Volterra and spatial structural evolution: an integrated methodology for some dynamical systems.

    Science.gov (United States)

    Wilson, Alan

    2008-08-01

    It is shown that Boltzmann's methods from statistical physics can be applied to a much wider range of systems, and in a variety of disciplines, than has been commonly recognized. A similar argument can be applied to the ecological models of Lotka and Volterra. Furthermore, it is shown that the two methodologies can be applied in combination to generate the Boltzmann, Lotka and Volterra (BLV) models. These techniques enable both spatial interaction and spatial structural evolution to be modelled, and it is argued that they potentially provide a much richer modelling methodology than that currently used in the analysis of 'scale-free' networks.

  7. On the stability of nonautonomous binary dynamical systems of partial differential equations

    Directory of Open Access Journals (Sweden)

    Salvatore Rionero

    2013-01-01

    Full Text Available Nonlinear nonautonomoua binary reaction-diffusion dynamical systems of partial differential equations (PDE are considered. Stability criteria - via a nonautonomous L²-energy - are obtained. Applications to nonautonomous Lotka-volterra systems of PDEs and to “preys” struggle for the life, are furnished.

  8. On the Permanence and Extinction in Nonautonomous Lotka-Volterra Comptitive Systems with Delays%具有时滞的非自治LOtka-Volterra

    Institute of Scientific and Technical Information of China (English)

    滕志东

    2001-01-01

    In this paper, the permanence and extinction of general nonautonomous N-species Lotka-Volterra type competitive systems with pure-delays are studied. Some new criteria are established. The results obtained in [8-10] for nondelayed nonau-tonomous Lotka-Volterra type competitive systems are improved and extended.%本文研究具有纯时滞的一般N-种群非自治Lotka-Volterra竞争系统的持久性和灭绝性.一些新的判别准则被建立.文献[8-10]中得到的关于无时滞非自治Lotka-Volterra竞争系统的结果被改进和推广.

  9. Integro-differential equation analysis and radioisotope imaging systems. Research proposal. [Testing of radioisotope imaging system in phantoms

    Energy Technology Data Exchange (ETDEWEB)

    Hart, H.

    1976-03-09

    Design modifications of a five-probe focusing collimator coincidence radioisotope scanning system are described. Clinical applications of the system were tested in phantoms using radioisotopes with short biological half-lives, including /sup 75/Se, /sup 192/Ir, /sup 43/K, /sup 130/I, and /sup 82/Br. Data processing methods are also described. (CH)

  10. A New Integro-Differential Equation for Rossby Solitary Waves with Topography Effect in Deep Rotational Fluids

    Directory of Open Access Journals (Sweden)

    Hongwei Yang

    2013-01-01

    solitary waves generated by topography, especially in the resonant case; a large amplitude nonstationary disturbance is generated in the forcing region. This condition may explain the blocking phenomenon which exists in the atmosphere and ocean and generated by topographic forcing.

  11. Chaotic dynamics in the Volterra predator-prey model via linked twist maps

    Directory of Open Access Journals (Sweden)

    Marina Pireddu

    2008-01-01

    Full Text Available We prove the existence of infinitely many periodic solutions and complicated dynamics, due to the presence of a topological horseshoe, for the classical Volterra predator-prey model with a periodic harvesting. The proof relies on some recent results about chaotic planar maps combined with the study of geometric features which are typical of linked twist maps.

  12. Local time and Tanaka formula for a Volterra-type multifractional Gaussian process

    CERN Document Server

    Boufoussi, Brahim; Marty, Renaud; 10.3150/10-BEJ261

    2010-01-01

    The stochastic calculus for Gaussian processes is applied to obtain a Tanaka formula for a Volterra-type multifractional Gaussian process. The existence and regularity properties of the local time of this process are obtained by means of Berman's Fourier analytic approach.

  13. 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.

  14. Dynamics in a Lotka-Volterra Predator-Prey Model with Time-Varying Delays

    Directory of Open Access Journals (Sweden)

    Changjin Xu

    2013-01-01

    Full Text Available A Lotka-Volterra predator-prey model with time-varying delays is investigated. By using the differential inequality theory, some sufficient conditions which ensure the permanence and global asymptotic stability of the system are established. The paper ends with some interesting numerical simulations that illustrate our analytical predictions.

  15. Permanence for two-species Lotka-Volterra cooperative systems with delays.

    Science.gov (United States)

    Lu, Guichen; Lu, Zhengyi

    2008-07-01

    In this paper, a two-species Lotka-Volterra cooperative delay system is considered, and the relationships between the delays and the permanence are obtained. Some sufficient conditions for the permanence under the assumption of smallness of the delays are obtained. Two examples are given to illustrate the theorems.

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

    Energy Technology Data Exchange (ETDEWEB)

    Song Yongli E-mail: songyl@sjtu.edu.cn; Han Maoan; Peng Yahong

    2004-12-01

    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.

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

    Energy Technology Data Exchange (ETDEWEB)

    Sun Wen [School of Mathematics and Statistics, Wuhan University, Wuhan 430072 (China); Chen Shihua [School of Mathematics and Statistics, Wuhan University, Wuhan 430072 (China)]. E-mail: shcheng@whu.edu.cn; Hong Zhiming [School of Mathematics and Statistics, Wuhan University, Wuhan 430072 (China); Wang Changping [Department of Mathematics and Statistics, Dalhousie University, Halifax, NS, B3H 3J5 (Canada)

    2007-08-15

    A two-species periodic competition Lotka-Volterra system with time delay and diffusion is investigated. Some sufficient conditions of the existence of positive periodic solution are established for the system by using the continuation theorem of coincidence degree theory.

  18. Experimental analysis of a Lotka-Volterra neural network for classification

    Science.gov (United States)

    Sukhu, Christopher L.; Stanton, Joseph; Aylesworth, Marc

    2015-06-01

    An experimental study of a neural network modeled by an adaptive Lotka-Volterra system follows. With totally inhibitory connections, this system can be embedded in a simple classification network. This network is able to classify and monitor its inputs in a spontaneous nonlinear fashion without prior training. We describe a framework for leveraging this behavior through an example involving breast cancer diagnosis.

  19. Bifurcation Phenomena in a Lotka-Volterra Model with Cross-Diffusion and Delay Effect

    Science.gov (United States)

    Yan, Shuling; Guo, Shangjiang

    2017-06-01

    This paper focuses on a Lotka-Volterra model with delay and cross-diffusion. By using Lyapunov-Schmidt reduction, we investigate the existence, multiplicity, stability and Hopf bifurcation of spatially nonhomogeneous steady-state solutions. Furthermore, we obtain some criteria to determine the bifurcation direction and stability of Hopf bifurcating periodic orbits by using Lyapunov-Schmidt reduction.

  20. Convergent and divergent solutions of a discrete nonautonomous Lotka-Volterra model

    Directory of Open Access Journals (Sweden)

    Xin-yuan Liao

    2005-12-01

    Full Text Available In this paper, a discrete nonautonomous $m$-species Lotka-Volterra system is investigated. By using fixed point theorems, a set of simple and easily verifiable conditions are given for the existence of convergent or divergent positive solutions.

  1. 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...

  2. Local discrete cosine transformation domain Volterra prediction of chaotic time series

    Institute of Scientific and Technical Information of China (English)

    张家树; 李恒超; 肖先赐

    2005-01-01

    In this paper a local discrete cosine transformation (DCT) domain Volterra prediction method is proposed to predict chaotic time series, where the DCT is used to lessen the complexity of solving the coefficient matrix. Numerical simulation results show that the proposed prediction method can effectively predict chaotic time series and improve the prediction accuracy compared with the traditional local linear prediction methods.

  3. 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 discussed...

  4. Black-Scholes equation from Gauge Theory of Arbitrage

    CERN Document Server

    Ilinskii, K N; Ilinski, Kirill; Kalinin, Gleb

    1997-01-01

    We apply Gauge Theory of Arbitrage (GTA) \\cite{KI,hep-th/9710148} to derivative pricing. We show how the standard results of Black-Scholes analysis appear from GTA and derive correction to the Black-Scholes equation due to a virtual arbitrage and speculators reaction on it. The model accounts for both violation of the no-arbitrage constraint and non-Brownian price walks which resemble real financial data. The correction is nonlocal and transform the differential Black-Scholes equation to an integro-differential one.

  5. Correlation function induced by a generalized diffusion equation with the presence of a harmonic potential

    Science.gov (United States)

    Fa, Kwok Sau

    2015-02-01

    An integro-differential diffusion equation with linear force, based on the continuous time random walk model, is considered. The equation generalizes the ordinary and fractional diffusion equations, which includes short, intermediate and long-time memory effects described by the waiting time probability density function. Analytical expression for the correlation function is obtained and analyzed, which can be used to describe, for instance, internal motions of proteins. The result shows that the generalized diffusion equation has a broad application and it may be used to describe different kinds of systems.

  6. An Abraham-Lorentz-like equation for the electron from the worldline variational approach to QED

    Science.gov (United States)

    Rosenfelder, R.; Schreiber, A. W.

    2004-09-01

    The variational equation for the mean square displacement of the electron in the polaron worldline approach to quenched QED can be cast into a form which closely resembles the classical Abraham-Lorentz equation but without the conceptual and practical diseases of the latter. The connection with delay equations describing field retardation effects is also established. As applications we solve this integro-differential equation numerically for various values of the coupling constant and cut-off and re-derive the variational approximation to the anomalous mass dimension of the electron found recently.

  7. An Abraham-Lorentz-like equation for the electron from the worldline variational approach to QED

    Energy Technology Data Exchange (ETDEWEB)

    Rosenfelder, R. [Paul Scherrer Institute, Villigen PSI (Switzerland); Schreiber, A.W. [University of Adelaide, Department of Physics and Mathematical Physics, and Research Centre for the Subatomic Structure of Matter, Adelaide (Australia)

    2004-09-01

    The variational equation for the mean square displacement of the electron in the polaron worldline approach to quenched QED can be cast into a form which closely resembles the classical Abraham-Lorentz equation but without the conceptual and practical diseases of the latter. The connection with delay equations describing field retardation effects is also established. As applications we solve this integro-differential equation numerically for various values of the coupling constant and cut-off and re-derive the variational approximation to the anomalous mass dimension of the electron found recently. (orig.)

  8. Poisson brackets of mappings obtained as ( q,- p) reductions of lattice equations

    Science.gov (United States)

    Tran, Dinh T.; van der Kamp, Peter H.; Quispel, G. R. W.

    2016-11-01

    In this paper, we present Poisson brackets of certain classes of mappings obtained as general periodic reductions of integrable lattice equations. The Poisson brackets are derived from a Lagrangian, using the so-called Ostrogradsky transformation. The ( q,- p) reductions are ( p + q)-dimensional maps and explicit Poisson brackets for such reductions of the discrete KdV equation, the discrete Lotka-Volterra equation, and the discrete Liouville equation are included. Lax representations of these equations can be used to construct sufficiently many integrals for the reductions. As examples we show that the (3,-2) reductions of the integrable partial difference equations are Liouville integrable in their own right.

  9. The Survival Analysis of a Non-autonomous N-dimensional Volterra Mutualistic System in a Polluted Environment

    Institute of Scientific and Technical Information of China (English)

    Xiao-jian Li; Ke Wang

    2007-01-01

    In this paper, we extend the autonomous n-Dimensional Volterra Mutualistic System to a nonautonomous system. The condition of persistence and extinction is obtained for each population, and the threshold is established for asymptotically autonomous system.

  10. On the polynomial first integrals of the ({ital a},{ital b},{ital c}) Lotka{endash}Volterra system

    Energy Technology Data Exchange (ETDEWEB)

    Labrunie, S. [Service de physique de l`etat condense, Centre d`etudes de Saclay, 91191 Gif sur Yvette (France)

    1996-11-01

    Using elementary differential algebraic techniques, we prove that the 3D Lotka{endash}Volterra dynamical system has no other nontrivial polynomial first integrals than the previously known ones. {copyright} {ital 1996 American Institute of Physics.}

  11. 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.

  12. Secondary Bifurcations in a Lotka-Volterra Model for N Competitors with Applications to Action Selection and Compulsive Behaviors

    Science.gov (United States)

    Frank, T. D.

    A Lotka-Volterra model for an arbitrary number of competitors is studied for different ratios of self-inhibition versus cross-inhibition. It is shown that winner-takes-all fixed points (states of single surviving species) are the only stable fixed points of the model when cross-inhibition exceeds self-inhibition. Secondary bifurcations in terms of bifurcations between winner-takes-all fixed points induced by changes in the exponential growth rates of competitors are studied and the critical control parameters are identified. A selection principle is derived that states that evolution proceeds in such a way that exponential growth rates of surviving competitors are magnified in evolutionary bifurcation steps. The interacting competitor model is applied as an amplitude equation model for interacting patterns of self-organizing pattern formation systems with an eye on action selection and compulsive behaviors in humans. The possibility is discussed that human behavior is subjected to the selection principle of "faster growth rates".

  13. SOLUTIONS FOR SECOND ORDER IMPULSIVE INTEGRO- DIFFERENTIAL EQUATION ON UNBOUNDED DOMAINS IN BANACH SPACES

    Institute of Scientific and Technical Information of China (English)

    CHEN Fang-qi; TIAN Rui-lan; CHEN Yu-shu

    2006-01-01

    Under loose conditions, the existence of solutions to initial value problem are studied for second order impulsive integro-differential equation with infinite moments of impulse effect on the positive half real axis in Banach spaces. By the use of recurrence method, Tonelii sequence and the locally convex topology, the new existence theorems are achieved, which improve the related results obtained by Guo Da-jun.

  14. A Novel Method to Determine the Local Stability of the n-Species Lotka-Volterra System with Multiple Delays

    Directory of Open Access Journals (Sweden)

    Xiao-Ping Chen

    2016-01-01

    Full Text Available The n-species Lotka-Volterra system with discrete delays is considered. The local asymptotic stability of positive equilibrium is investigated based on a contour integral method. The main purpose of this paper is to propose a new and general algorithm to study the local asymptotic stability of the positive equilibrium for the n-dimensional Lotka-Volterra system. Some numerical experiments are carried out to show the effectiveness of the proposed method.

  15. Finding all multiple stable fixpoints of n-species Lotka-Volterra competition models.

    Science.gov (United States)

    Lischke, Heike; Löffler, Thomas J

    2017-06-01

    One way to explore assembly of extant and novel communities from species pools, and by that biodiversity and species ranges, is to study the equilibrium behavior of dynamic competition models such as the Lotka-Volterra competition (LVC) model. We present a novel method (COMMUSTIX) to determine all stable fixpoints of the general LVC model with abundances x from a given pool of n species. To that purpose, we split the species in potentially surviving species (xi>0) and in others going extinct (xi=0). We derived criteria for the stability of xi=0 and for the equilibrium of xi>0 to determine possible combinations of extinct and surviving species by iteratively applying a mixed binary linear optimization algorithm. We tested this new method against (a) the numerical solution at equilibrium of the LVC ordinary differential equations (ODEs) and (b) the fixpoints of all combinations of surviving and extinct species (possible only for small n), tested for stability and non-negativity. The tests revealed that COMMUSTIX is reliable, it detects all multiple stable fixpoints (SFPs), which is not guaranteed by solving the ODEs, and more efficient than the combinations method. With COMMUSTIX, we studied the dependence of the fixpoint behavior on the competition strengths relative to the intra-specific competition. If inter-specific competition was considerably lower than intra-specific competition, only globally SFPs occurred. In contrast, if all inter-specific was higher than intra-specific competition, multiple SFPs consisting of only one species occurred. If competition strengths in the species pool ranged from below to above the intra-specific competition, either global or multiple SFPs strongly differing in species composition occurred. The species richness over all SFPs was high for pools of species with similar, either weak or strong competition, and lower for species with dissimilar or close to intra-specific competition strengths. The new approach is a reliable and

  16. Integration of Volterra model with artificial neural networks for rainfall-runoff simulation in forested catchment of northern Iran

    Science.gov (United States)

    Kashani, Mahsa H.; Ghorbani, Mohammad Ali; Dinpashoh, Yagob; Shahmorad, Sedaghat

    2016-09-01

    Rainfall-runoff simulation is an important task in water resources management. In this study, an integrated Volterra model with artificial neural networks (IVANN) was presented to simulate the rainfall-runoff process. The proposed integrated model includes the semi-distributed forms of the Volterra and ANN models which can explore spatial variation in rainfall-runoff process without requiring physical characteristic parameters of the catchments, while taking advantage of the potential of Volterra and ANNs models in nonlinear mapping. The IVANN model was developed using hourly rainfall and runoff data pertaining to thirteen storms to study short-term responses of a forest catchment in northern Iran; and its performance was compared with that of semi-distributed integrated ANN (IANN) model and lumped Volterra model. The Volterra model was applied as a nonlinear model (second-order Volterra (SOV) model) and solved using the ordinary least square (OLS) method. The models performance were evaluated and compared using five performance criteria namely coefficient of efficiency, root mean square error, error of total volume, relative error of peak discharge and error of time for peak to arrive. Results showed that the IVANN model performs well than the other semi-distributed and lumped models to simulate the rainfall-runoff process. Comparing to the integrated models, the lumped SOV model has lower precision to simulate the rainfall-runoff process.

  17. A General Framework for Modeling Sub- and Ultraharmonics of Ultrasound Contrast Agent Signals with MISO Volterra Series

    Directory of Open Access Journals (Sweden)

    Fatima Sbeity

    2013-01-01

    Full Text Available Sub- and ultraharmonics generation by ultrasound contrast agents makes possible sub- and ultraharmonics imaging to enhance the contrast of ultrasound images and overcome the limitations of harmonic imaging. In order to separate different frequency components of ultrasound contrast agents signals, nonlinear models like single-input single-output (SISO Volterra model are used. One important limitation of this model is its incapacity to model sub- and ultraharmonic components. Many attempts are made to model sub- and ultraharmonics using Volterra model. It led to the design of mutiple-input singe-output (MISO Volterra model instead of SISO Volterra model. The key idea of MISO modeling was to decompose the input signal of the nonlinear system into periodic subsignals at the subharmonic frequency. In this paper, sub- and ultraharmonics modeling with MISO Volterra model is presented in a general framework that details and explains the required conditions to optimally model sub- and ultraharmonics. A new decomposition of the input signal in periodic orthogonal basis functions is presented. Results of application of different MISO Volterra methods to model simulated ultrasound contrast agents signals show its efficiency in sub- and ultraharmonics imaging.

  18. A Volterra series-based method for extracting target echoes in the seafloor mining environment.

    Science.gov (United States)

    Zhao, Haiming; Ji, Yaqian; Hong, Yujiu; Hao, Qi; Ma, Liyong

    2016-09-01

    The purpose of this research was to evaluate the applicability of the Volterra adaptive method to predict the target echo of an ultrasonic signal in an underwater seafloor mining environment. There is growing interest in mining of seafloor minerals because they offer an alternative source of rare metals. Mining the minerals cause the seafloor sediments to be stirred up and suspended in sea water. In such an environment, the target signals used for seafloor mapping are unable to be detected because of the unavoidable presence of volume reverberation induced by the suspended sediments. The detection of target signals in reverberation is currently performed using a stochastic model (for example, the autoregressive (AR) model) based on the statistical characterisation of reverberation. However, we examined a new method of signal detection in volume reverberation based on the Volterra series by confirming that the reverberation is a chaotic signal and generated by a deterministic process. The advantage of this method over the stochastic model is that attributions of the specific physical process are considered in the signal detection problem. To test the Volterra series based method and its applicability to target signal detection in the volume reverberation environment derived from the seafloor mining process, we simulated the real-life conditions of seafloor mining in a water filled tank of dimensions of 5×3×1.8m. The bottom of the tank was covered with 10cm of an irregular sand layer under which 5cm of an irregular cobalt-rich crusts layer was placed. The bottom was interrogated by an acoustic wave generated as 16μs pulses of 500kHz frequency. This frequency is demonstrated to ensure a resolution on the order of one centimetre, which is adequate in exploration practice. Echo signals were collected with a data acquisition card (PCI 1714 UL, 12-bit). Detection of the target echo in these signals was performed by both the Volterra series based model and the AR model

  19. 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...

  20. Numerical evaluation of renewal equations: applications to risk theory and financial models

    OpenAIRE

    Usábel Rodrigo, Miguel Arturo

    1997-01-01

    The so-called Renewal Theory is a frequently used methodology in applied mathematics. Renewal Theory is mainly focussed on solving a Volterra integral equation of the second kind known as Renewal Integral EquationAn interesting problem arises when choosing the appropriate numerical tool in order to approximate the solution of the former integral. The decision will be based on the degree of knowledge of function F(x) and some properties of (u). Three methods based in classical methodologies (s...

  1. 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.

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

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    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.

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

    Science.gov (United States)

    Baigent, Stephen

    2013-04-01

    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.

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

    Science.gov (United States)

    Cherniha, Roman; Davydovych, Vasyl'

    2013-05-01

    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.

  5. Express Services Market Analysis Based on the Lotka-Volterra Model – Case Study Serbia

    Directory of Open Access Journals (Sweden)

    Bojan Jovanović

    2015-04-01

    Full Text Available This paper provides a preview of the former stages through which the market of express postal services had gone and the possibilities of further development, both on the global and local level. The aim of this paper is to complete an estimation of the need for this type of express services using the competitive Lotka–Volterra model in Serbia. In order to reduce the complexity of the process, the division of competition was conducted in two segments: the public operator and the private segment (comprised of all private operators. The given model provides a description of a dynamic competition relationship by indicating the existence of the equilibrium point between the public and the private sectors, and the conditions of its stability. The obtained values indicate that the private sector affects the public operator. The existing predator-prey relationship gives preference to the private sector and can be described by the Lotka-Volterra model.

  6. Dynamic stability conditions for Lotka-Volterra recurrent neural networks with delays.

    Science.gov (United States)

    Yi, Zhang; Tan, K K

    2002-07-01

    The Lotka-Volterra model of neural networks, derived from the membrane dynamics of competing neurons, have found successful applications in many "winner-take-all" types of problems. This paper studies the dynamic stability properties of general Lotka-Volterra recurrent neural networks with delays. Conditions for nondivergence of the neural networks are derived. These conditions are based on local inhibition of networks, thereby allowing these networks to possess a multistability property. Multistability is a necessary property of a network that will enable important neural computations such as those governing the decision making process. Under these nondivergence conditions, a compact set that globally attracts all the trajectories of a network can be computed explicitly. If the connection weight matrix of a network is symmetric in some sense, and the delays of the network are in L2 space, we can prove that the network will have the property of complete stability.

  7. Z-type control of populations for Lotka-Volterra model with exponential convergence.

    Science.gov (United States)

    Zhang, Yunong; Yan, Xiaogang; Liao, Bolin; Zhang, Yinyan; Ding, Yaqiong

    2016-02-01

    The population control of the Lotka-Volterra model is one of the most important and widely investigated issues in mathematical ecology. In this study, assuming that birth rate is controllable and using the Z-type dynamic method, we develop Z-type control laws to drive the prey population and/or predator population to a desired state to keep species away from extinction and to improve ecosystem stability. A direct controller group is initially designed to control the prey and predator populations simultaneously. Two indirect controllers are then proposed for prey population control and predator population control by exerting exogenous measure on another species. All three control laws possess exponential convergence performances. Finally, the corresponding numerical simulations are performed. Results substantiate the theoretical analysis and effectiveness of such Z-type control laws for the population control of the Lotka-Volterra model. Copyright © 2015 Elsevier Inc. All rights reserved.

  8. A Modified Lotka–Volterra Model for Diffusion and Substitution of Multigeneration DRAM Processing Technologies

    Directory of Open Access Journals (Sweden)

    Hui-Chih Hung

    2017-01-01

    Full Text Available We attempt to develop an effective forecasting model for the diffusion and substitution of multigeneration Dynamic Random Access Memory (DRAM processing technologies. We consider market share data and propose a modified Lotka–Volterra model, in which an additional constraint on the summation of market share is introduced. The mean absolute error is used to measure the accuracy of our market share predictions. Market share data in DRAM industries from quarter one (Q1 of 2005 to 2013 Q4 is collected to validate the prediction accuracy. Our model significantly outperforms other benchmark forecasting models of both revenue and market share data, including the Bass and Lotka–Volterra models. Compared to prior studies on forecasting the diffusion and substitution of multigeneration technologies, our model has two new perspectives: (1 allowing undetermined number of multigeneration technologies and inconsecutive adoption of new technologies and (2 requiring less data for forecasting newborn technologies.

  9. Bifurcation Analysis in an n-Dimensional Diffusive Competitive Lotka-Volterra System with Time Delay

    Science.gov (United States)

    Chang, Xiaoyuan; Wei, Junjie

    2015-06-01

    In this paper, we investigate the stability and Hopf bifurcation of an n-dimensional competitive Lotka-Volterra diffusion system with time delay and homogeneous Dirichlet boundary condition. We first show that there exists a positive nonconstant steady state solution satisfying the given asymptotic expressions and establish the stability of the positive nonconstant steady state solution. Regarding the time delay as a bifurcation parameter, we explore the system that undergoes a Hopf bifurcation near the positive nonconstant steady state solution and derive a calculation method for determining the direction of the Hopf bifurcation. Finally, we cite the stability of a three-dimensional competitive Lotka-Volterra diffusion system with time delay to illustrate our conclusions.

  10. 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.

  11. Hadamard-type fractional differential equations, inclusions and inequalities

    CERN Document Server

    Ahmad, Bashir; Ntouyas, Sotiris K; Tariboon, Jessada

    2017-01-01

    This book focuses on the recent development of fractional differential equations, integro-differential equations, and inclusions and inequalities involving the Hadamard derivative and integral. Through a comprehensive study based in part on their recent research, the authors address the issues related to initial and boundary value problems involving Hadamard type differential equations and inclusions as well as their functional counterparts. The book covers fundamental concepts of multivalued analysis and introduces a new class of mixed initial value problems involving the Hadamard derivative and Riemann-Liouville fractional integrals. In later chapters, the authors discuss nonlinear Langevin equations as well as coupled systems of Langevin equations with fractional integral conditions. Focused and thorough, this book is a useful resource for readers and researchers interested in the area of fractional calculus.

  12. DYNAMICAL CONSISTENCE IN 3-DIMENSIONAL TYPE-K COMPETITIVE LOTKA-VOLTERRA SYSTEM

    Institute of Scientific and Technical Information of China (English)

    2012-01-01

    A 3-dimensional type-K competitive Lotka-Volterra system is considered in this paper. Two discretization schemes are applied to the system with an positive interior fixed point, and two corresponding discrete systems are obtained. By analyzing the local dynamics of the corresponding discrete system near the interior fixed point, it is showed that this system is not dynamically consistent with the continuous counterpart system.

  13. Diagonal Kernel Point Estimation of th-Order Discrete Volterra-Wiener Systems

    Directory of Open Access Journals (Sweden)

    Pirani Massimiliano

    2004-01-01

    Full Text Available The estimation of diagonal elements of a Wiener model kernel is a well-known problem. The new operators and notations proposed here aim at the implementation of efficient and accurate nonparametric algorithms for the identification of diagonal points. The formulas presented here allow a direct implementation of Wiener kernel identification up to the th order. Their efficiency is demonstrated by simulations conducted on discrete Volterra systems up to fifth order.

  14. Existence of Almost-Periodic Solutions for Lotka-Volterra Cooperative Systems with Time Delay

    Directory of Open Access Journals (Sweden)

    Kaihong Zhao

    2012-01-01

    Full Text Available This paper considers the existence of positive almost-periodic solutions for almost-periodic Lotka-Volterra cooperative system with time delay. By using Mawhin’s continuation theorem of coincidence degree theory, sufficient conditions for the existence of positive almost-periodic solutions are obtained. An example and its simulation figure are given to illustrate the effectiveness of our results.

  15. Global Analysis of a Delayed Impulsive Lotka-Volterra Model with Holling III Type Functional Response

    Directory of Open Access Journals (Sweden)

    Hui Wang

    2015-01-01

    Full Text Available A delayed impulsive Lotka-Volterra model with Holing III type functional response was established. With the help of Mawhin’s Continuation Theorem in coincidence degree theory, a sufficient condition is found for the existence of positive periodic solutions of the system under consideration. By applying the comparison theorem and constructing a suitable Lyapunov functional, the permanence and global attractivity of the model are proved. Two numerical simulations are also given to illustrate our main results.

  16. PERMANENCE OF ASYMPTOTICALLY PERIODIC MULTISPECIES LOTKA-VOLTERRA COMPETITION PREDATOR-PREY SYSTEM

    Institute of Scientific and Technical Information of China (English)

    2006-01-01

    In this paper, we consider the permanence of asymptotically periodic mul-tispecies Lotka-Volterra competition predator-prey system. By means of the standard comparison theorem, we improve or extend the corresponding results given by Peng and Chen [1], Teng and Li [2], Zhao and Chen [3]. Also, we obtain the conditions which ensure the permanence and global attractivity of asymptotically periodic multispecies competition predator-prey system.

  17. Modeling of signal transmitting of avionic systems based on Volterra series

    Directory of Open Access Journals (Sweden)

    Юрий Владимирович Пепа

    2014-11-01

    Full Text Available The paper deals with mathematical modeling methods for the formation and transmission of analogue and digital avionics systems using Volterra series. A mathematical model of the modulation in the presence of various initial data is developed, the computer modeling is conducted. The processes of analog modulation is simulated using MATLAB+SIMULINK, which allows you to simulate these processes, as well as explore them.

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

    Energy Technology Data Exchange (ETDEWEB)

    Zhen Jin [Department of Mathematics, North China University of Technology, Taiyuan 030051 (China)]. E-mail: jinzhn@263.net; Han Maoan [Department of Applied Mathematics, Shanghai Jiaotong University, Shanghai 200030 (China); Li Guihua [Department of Mathematics, North China University of Technology, Taiyuan 030051 (China)

    2005-05-01

    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.

  19. 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.

  20. Stability and Bifurcation of Two Kinds of Three-Dimensional Fractional Lotka-Volterra Systems

    Directory of Open Access Journals (Sweden)

    Jinglei Tian

    2014-01-01

    Full Text Available Two kinds of three-dimensional fractional Lotka-Volterra systems are discussed. For one system, the asymptotic stability of the equilibria is analyzed by providing some sufficient conditions. And bifurcation property is investigated by choosing the fractional order as the bifurcation parameter for the other system. In particular, the critical value of the fractional order is identified at which the Hopf bifurcation may occur. Furthermore, the numerical results are presented to verify the theoretical analysis.

  1. Liouville theorems, universal estimates and periodic solutions for cooperative parabolic Lotka-Volterra systems

    Science.gov (United States)

    Quittner, Pavol

    2016-02-01

    We consider positive solutions of cooperative parabolic Lotka-Volterra systems with equal diffusion coefficients, in bounded and unbounded domains. The systems are complemented by the Dirichlet or Neumann boundary conditions. Under suitable assumptions on the coefficients of the reaction terms, these problems possess both global solutions and solutions which blow up in finite time. We show that any solution (u , v) defined on the time interval (0 , T) satisfies a universal estimate of the form

  2. 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.

  3. GLOBAL ASYMPTOTIC STABILITY IN N-SPECIES NONAUTONOMOUS LOTKA-VOLTERRA COMPETITIVE SYSTEMS WITH DELAYS

    Institute of Scientific and Technical Information of China (English)

    Xu Rui(徐瑞); Chen Lansun(陈兰荪); M.A.J. Chaplain

    2003-01-01

    A delayed n-species nonautonomous Lotka-Volterra type competitive systemwithout dominating instantaneous negative feedback is investigated. By means of a suitableLyapunov functional, sufficient conditions are derived for the global asymptotic stability ofthe positive solutions of the system. As a corollary, it is shown that the global asymptoticstability of the positive solution is maintained provided that the delayed negative feedbacksdominate other interspecific interaction effects with delays and the delays are sufficientlysmall.

  4. On the minimal speed and asymptotics of the wave solutions for the lotka volterra system

    CERN Document Server

    Hou, Xiaojie

    2010-01-01

    e study the minimal wave speed and the asymptotics of the traveling wave solutions of a competitive Lotka Volterra system. The existence of the traveling wave solutions is derived by monotone iteration. The asymptotic behaviors of the wave solutions are derived by comparison argument and the exponential dichotomy, which seems to be the key to understand the geometry and the stability of the wave solutions. Also the uniqueness and the monotonicity of the waves are investigated via a generalized sliding domain method.

  5. 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.

  6. High-Order Volterra Model Predictive Control and Its Application to a Nonlinear Polymerisation Process

    Institute of Scientific and Technical Information of China (English)

    Yun Li; Hiroshi Kashiwagi

    2005-01-01

    Model Predictive Control (MPC) has recently found wide acceptance in the process industry, but existing design and implementation methods are restricted to linear process models. A chemical process, however, involves severe nonlinearity which cannot be ignored in practice. This paper aims to solve this nonlinear control problem by extending MPC to accommodate nonlinear models. It develops an analytical framework for nonlinear model predictive control (NMPC). It also offers a third-order Volterra series based nonparametric nonlinear modelling technique for NMPC design, which relieves practising engineers from the need for deriving a physical-principles based model first. An on-line realisation technique for implementing NMPC is then developed and applied to a Mitsubishi Chemicals polymerisation reaction process. Results show that this nonlinear MPC technique is feasible and very effective. It considerably outperforms linear and low-order Volterra model based methods. The advantages of the developed approach lie not only in control performance superior to existing NMPC methods, but also in eliminating the need for converting an analytical model and then convert it to a Volterra model obtainable only up to the second order.

  7. 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.

  8. On the generality of stability-complexity relationships in Lotka-Volterra ecosystems.

    Science.gov (United States)

    Townsend, Sunny E; Haydon, Daniel T; Matthews, Louise

    2010-11-21

    Understanding how complexity persists in nature is a long-standing goal of ecologists. In theoretical ecology, local stability is a widely used measure of ecosystem persistence and has made a major contribution to the ecosystem stability-complexity debate over the last few decades. However, permanence is coming to be regarded as a more satisfactory definition of ecosystem persistence and has relatively recently become available as a tool for assessing the global stability of Lotka-Volterra communities. Here we document positive relationships between permanence and Lotka-Volterra food web complexity and report a positive correlation between the probability of local stability and permanence. We investigate further the frequency of discrepancy (attributed to fragile systems that are locally stable but not permanent or locally unstable systems that are permanent and have cyclic or chaotic dynamics), associate non-permanence with the local stability or instability of equilibria on the boundary of the state-space, and investigate how these vary with aspects of ecosystem complexity. We find that locally stable interior equilibria tend to have all locally unstable boundary equilibria. Since a locally stable boundary is inconsistent with permanent dynamics, this can explain the observed positive correlation between local interior stability and permanence. Our key finding is that, at least in Lotka-Volterra model ecosystems, local stability may be a better measure of persistence than previously thought. Copyright © 2010 Elsevier Ltd. All rights reserved.

  9. Integrable reductions of the Bogoyavlenskij-Itoh Lotka-Volterra systems

    Science.gov (United States)

    Damianou, P. A.; Evripidou, C. A.; Kassotakis, P.; Vanhaecke, P.

    2017-03-01

    Given a constant skew-symmetric matrix A, it is a difficult open problem whether the associated Lotka-Volterra system is integrable or not. We solve this problem in a special case when A is a Toeplitz matrix where all off-diagonal entries are plus or minus one. In this case, the associated Lotka-Volterra system turns out to be a reduction of Liouville integrable systems, whose integrability was shown by Bogoyavlenskij and Itoh. We prove that the reduced systems are also Liouville integrable and that they are also non-commutative integrable by constructing a set of independent first integrals, having the required involutive properties (with respect to the Poisson bracket). These first integrals fall into two categories. One set consists of polynomial functions that are restriction of the Bogoyavlenskij-Itoh integrals; their involutivity was already pointed out by Bogoyavlenskij. The other set consists of rational functions which are obtained through a Poisson map from the first integrals of some recently discovered superintegrable Lotka-Volterra systems. The fact that these polynomial and rational first integrals, combined, have the required properties for Liouville and non-commutative integrability is quite remarkable; the quite technical proof of functional independence of the first integrals is given in detail.

  10. Vito Volterra and his commemoration for the centenary of Faraday's discovery of electromagnetic induction

    CERN Document Server

    Sparavigna, Amelia Carolina

    2016-01-01

    The paper presents a memoir of 1931 written by Vito Volterra on the Italian physicists of the nineteenth century and the researches these scientists made after the discoveries of Michael Faraday on electromagnetism. Here, the memoir entitled "I fisici italiani e le ricerche di Faraday" is translated from Italian. It was written to commemorate the centenary of Faraday's discovery of the electromagnetic induction. Besides being a remarkable article on the history of science, it was also, in a certain extent, a political paper. In fact, in 1931, the same year of the publication of this article, Mussolini imposed a mandatory oath of loyalty to Italian academies. Volterra was one of the very few professors who refused to take this oath of loyalty. Because of the political situation in Italy, Volterra wanted to end his paper sending a message to the scientists of the world, telling that the feeling of admiration and gratitude that in Italy the scientists had towards "the great thinker and British experimentalist" w...

  11. A Piecewise Deterministic Markov Toy Model for Traffic/Maintenance and Associated Hamilton–Jacobi Integrodifferential Systems on Networks

    Energy Technology Data Exchange (ETDEWEB)

    Goreac, Dan, E-mail: Dan.Goreac@u-pem.fr; Kobylanski, Magdalena, E-mail: Magdalena.Kobylanski@u-pem.fr; Martinez, Miguel, E-mail: Miguel.Martinez@u-pem.fr [Université Paris-Est, LAMA (UMR 8050), UPEMLV, UPEC, CNRS (France)

    2016-10-15

    We study optimal control problems in infinite horizon whxen the dynamics belong to a specific class of piecewise deterministic Markov processes constrained to star-shaped networks (corresponding to a toy traffic model). We adapt the results in Soner (SIAM J Control Optim 24(6):1110–1122, 1986) to prove the regularity of the value function and the dynamic programming principle. Extending the networks and Krylov’s “shaking the coefficients” method, we prove that the value function can be seen as the solution to a linearized optimization problem set on a convenient set of probability measures. The approach relies entirely on viscosity arguments. As a by-product, the dual formulation guarantees that the value function is the pointwise supremum over regular subsolutions of the associated Hamilton–Jacobi integrodifferential system. This ensures that the value function satisfies Perron’s preconization for the (unique) candidate to viscosity solution.

  12. Integro-differential inequality and stability of BAM FCNNs with time delays in the leakage terms and distributed delays

    Directory of Open Access Journals (Sweden)

    Zhang Xinhua

    2011-01-01

    Full Text Available Abstract In this paper, a class of impulsive bidirectional associative memory (BAM fuzzy cellular neural networks (FCNNs with time delays in the leakage terms and distributed delays is formulated and investigated. By establishing an integro-differential inequality with impulsive initial conditions and employing M-matrix theory, some sufficient conditions ensuring the existence, uniqueness and global exponential stability of equilibrium point for impulsive BAM FCNNs with time delays in the leakage terms and distributed delays are obtained. In particular, the estimate of the exponential convergence rate is also provided, which depends on the delay kernel functions and system parameters. It is believed that these results are significant and useful for the design and applications of BAM FCNNs. An example is given to show the effectiveness of the results obtained here.

  13. 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.

  14. Numerical solution of $Q^2$ evolution equations for fragmentation functions

    CERN Document Server

    Hirai, M

    2011-01-01

    Semi-inclusive hadron-production processes are becoming important in high-energy hadron reactions. They are used for investigating properties of quark-hadron matters in heavy-ion collisions, for finding the origin of nucleon spin in polarized lepton-nucleon and nucleon-nucleon reactions, and possibly for finding exotic hadrons. In describing the hadron-production cross sections in high-energy reactions, fragmentation functions are essential quantities. A fragmentation function indicates the probability of producing a hadron from a parton. Its $Q^2$ dependence is described by the standard DGLAP (Dokshitzer-Gribov-Lipatov-Altarelli-Parisi) evolution equations, which are often used in theoretical and experimental analyses of the fragmentation functions and in calculating semi-inclusive cross sections. The DGLAP equations are complicated integro-differential equations, which cannot be solved in an analytical method. In this work, a simple method is employed for solving the evolution equations by using Gauss-Legen...

  15. Existence and Controllability Result for Nonlinear Neutral Evolution Integrodifferential Systems%非线性中立发展积微分系统解的存在性和可控性

    Institute of Scientific and Technical Information of China (English)

    吕悦; 刘明姬; 吕显瑞

    2008-01-01

    In this paper,we establish suflicient conditions for existence and control lability of nonlinear neutral evolution integrodifferential systems in Banach spaces.The result is obtained by using the resolvent operators and fixed point analysis approach.

  16. Inverse scattering theory: renormalization of the Lippmann-Schwinger equation for acoustic scattering in one dimension.

    Science.gov (United States)

    Kouri, Donald J; Vijay, Amrendra

    2003-04-01

    The most robust treatment of the inverse acoustic scattering problem is based on the reversion of the Born-Neumann series solution of the Lippmann-Schwinger equation. An important issue for this approach to inversion is the radius of convergence of the Born-Neumann series for Fredholm integral kernels, and especially for acoustic scattering for which the interaction depends on the square of the frequency. By contrast, it is well known that the Born-Neumann series for the Volterra integral equations in quantum scattering are absolutely convergent, independent of the strength of the coupling characterizing the interaction. The transformation of the Lippmann-Schwinger equation from a Fredholm to a Volterra structure by renormalization has been considered previously for quantum scattering calculations and electromagnetic scattering. In this paper, we employ the renormalization technique to obtain a Volterra equation framework for the inverse acoustic scattering series, proving that this series also converges absolutely in the entire complex plane of coupling constant and frequency values. The present results are for acoustic scattering in one dimension, but the method is general. The approach is illustrated by applications to two simple one-dimensional models for acoustic scattering.

  17. The stability of the Boubaker polynomials expansion scheme (BPES)-based solution to Lotka-Volterra problem.

    Science.gov (United States)

    Milgram, A

    2011-02-21

    This comment addresses critics on the claimed stability of solution to the accelerated-predator-satiety Lotka-Volterra predator-prey problem, proposed by Dubey al. (2010. A solution to the accelerated-predator-satiety Lotka-Volterra predator-prey problem using Boubaker polynomial expansion scheme. Journal of Theoretical Biology 264, 154-160). Critics are based on incompatibilities between the claimed asymptotic behavior and the presumed Malthusian growth of prey population in absence of predator. Copyright © 2010 Elsevier Ltd. All rights reserved.

  18. [Lotka-Volterra Model of Competition between Two Species and Gause Experiments: Is There Any Correspondence?].

    Science.gov (United States)

    Nedorezov, L V

    2015-01-01

    Analysis of deviations between trajectories of Lotka-Volterra model of competition between two species and G.F. Gause experimental time series on combined cultivation of Paramecium aurelia and Paramecium caudatum shows that with rather big probability there is no correspondence between model and experimental datasets. Testing of sets of deviations was provided on symmetry with. respect to origin (Kolmogorov-Smirnov, Lehmann-Rosenblatt, Wald-Wolfowitz, and Munn-Whitney criterions) and on existence/absence of serial correlation in sequences of residuals (Swed-Eisenhart and "jumps up-jumps down" tests).

  19. Performance Analysis of Adaptive Volterra Filters in the Finite-Alphabet Input Case

    Directory of Open Access Journals (Sweden)

    Jaïdane Mériem

    2004-01-01

    Full Text Available This paper deals with the analysis of adaptive Volterra filters, driven by the LMS algorithm, in the finite-alphabet inputs case. A tailored approach for the input context is presented and used to analyze the behavior of this nonlinear adaptive filter. Complete and rigorous mean square analysis is provided without any constraining independence assumption. Exact transient and steady-state performances expressed in terms of critical step size, rate of transient decrease, optimal step size, excess mean square error in stationary mode, and tracking nonstationarities are deduced.

  20. Population evolution in mutualistic Lotka-Volterra system with spatial diffusion

    Science.gov (United States)

    Wang, Mao-Xiang; Ma, Yu-Qiang

    2014-02-01

    We consider the population dynamics of two species described by the mutualistic Lotka-Volterra model with a +/+ interaction in the presence of spatial diffusions. The results demonstrate that diffusion does not affect the system’s stability but it brings two situations: one is a win-win situation where both species propagate with the same largest speed; in the other situation the aggressive species has two propagating wave fronts and the other species travels with a single slow wave front. Our model may help to understand the evolution of mutualism.

  1. On product cannibalization. A new Lotka-Volterra model for asymmetric competition in the ICTs

    OpenAIRE

    Guidolin, Mariangela; Guseo, Renato

    2016-01-01

    Product cannibalization is a well known phenomenon in marketing and new product development and describes the case when one product steals sales from a product pertaining to the same brand. In this paper we present a new Lotka-Volterra model with asymmetric competition, which is useful to describe cases of product cannibalization. We apply the model to the case of Apple Inc, where iPhone sales concurred to determine the crisis of the iPad. Stimulated by this applied case, we studied a dffe...

  2. Evolution of Lotka-Volterra predator-prey systems under telegraph noise.

    Science.gov (United States)

    Auger, P; Du, N H; Hieu, N T

    2009-10-01

    In this paper we study a Lotka-Volterra predator-prey system with prey logistic growth under the telegraph noise. The telegraph noise switches at random two prey-predator models. The aim of this work is to determine the subset of omega-limit set of the system and show out the existence of a stationary distribution. We also focus on persistence of the predator and thus we look for conditions that allow persistence of the predator and prey community. We show that the asymptotic behaviour highly depends on the value of some constant lambda which is useful to make suitable predictions about the persistence of the system.

  3. Models of Genetic Drift as Limiting Forms of the Lotka-Volterra Competition Model

    Science.gov (United States)

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

    2015-01-01

    The relationship between the Moran model and stochastic Lotka-Volterra competition (SLVC) model is explored via time scale separation arguments. For neutral systems the two are found to be equivalent at long times. For systems with selective pressure, their behavior differs. It is argued that the SLVC is preferable to the Moran model since in the SLVC population size is regulated by competition, rather than arbitrarily fixed as in the Moran model. As a consequence, ambiguities found in the Moran model associated with the introduction of more complex processes, such as selection, are avoided.

  4. 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.

  5. The Stationary Distribution of Competitive Lotka-Volterra Population Systems with Jumps

    Directory of Open Access Journals (Sweden)

    Zhenzhong Zhang

    2014-01-01

    Full Text Available Dynamics of Lotka-Volterra population with jumps (LVWJ have recently been established (see Bao et al., 2011, and Bao and Yuan, 2012. They provided some useful criteria on the existence of stationary distribution and some asymptotic properties for LVWJ. However, the uniqueness of stationary distribution for n≥2 and asymptotic pathwise estimation limt→+∞⁡(1/t∫0t‍|X(s|pds (p>0 are still unknown for LVWJ. One of our aims in this paper is to show the uniqueness of stationary distribution and asymptotic pathwise estimation for LVWJ. Moreover, some characterizations for stationary distribution are provided.

  6. Stability, delay, and chaotic behavior in a lotka-volterra predator-prey system.

    Science.gov (United States)

    Nakaoka, S; Saito, Y; Takeuchi, Y

    2006-01-01

    We consider the following Lotka-Volterra predator-prey system with two delays: x '( t ) = x ( t ) [ r(1) - ax ( t - tau(1) ) - by( t ) ] y '( t ) = y ( t ) [ - r(1) + cx ( t ) - dy( t - tau(2) ) ] ( E ) We show that a positive equilibrium of system ( E ) is globally asymptotically stable for small delays. Critical values of time delay through which system ( E ) undergoes a Hopf bifurcation are analytically determined. Some numerical simulations suggest an existence of subcritical Hopf bifurcation near the critical values of time delay. Further system (E) exhibits some chaotic behavior when tau(2) becomes large.

  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. Influence of predator mutual interference and prey refuge on Lotka-Volterra predator-prey dynamics

    Science.gov (United States)

    Chen, Liujuan; Chen, Fengde; Wang, Yiqin

    2013-11-01

    A Lotka-Volterra predator-prey model incorporating a constant number of prey using refuges and mutual interference for predator species is presented. By applying the divergency criterion and theories on exceptional directions and normal sectors, we show that the interior equilibrium is always globally asymptotically stable and two boundary equilibria are both saddle points. Our results indicate that prey refuge has no influence on the coexistence of predator and prey species of the considered model under the effects of mutual interference for predator species, which differently from the conclusion without predator mutual interference, thus improving some known ones. Numerical simulations are performed to illustrate the validity of our results.

  9. Controllability of Neutral Fractional Functional Equations with Impulses and Infinite Delay

    Directory of Open Access Journals (Sweden)

    R. Ganesh

    2013-01-01

    Full Text Available We examine the controllability problem for a class of neutral fractional integrodifferential equations with impulses and infinite delay. More precisely, a set of sufficient conditions are derived for the exact controllability of nonlinear neutral impulsive fractional functional equation with infinite delay. Further, as a corollary, approximate controllability result is discussed by assuming compactness conditions on solution operator. The results are established by using solution operator, fractional calculations, and fixed point techniques. In particular, the controllability of nonlinear fractional control systems is established under the assumption that the corresponding linear control system is controllable. Finally, an example is given to illustrate the obtained theory.

  10. 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.

  11. 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.

  12. Dirac mass dynamics in a multidimensional nonlocal parabolic equation

    CERN Document Server

    Lorz, Alexander; Perthame, Benoit

    2010-01-01

    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 co-exist? 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 structure of gradient flow. 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.

  13. Asymptotic and spectral analysis of the gyrokinetic-waterbag integro-differential operator in toroidal geometry

    Energy Technology Data Exchange (ETDEWEB)

    Besse, Nicolas, E-mail: Nicolas.Besse@oca.eu [Laboratoire J.-L. Lagrange, UMR CNRS/OCA/UCA 7293, Université Côte d’Azur, Observatoire de la Côte d’Azur, Bd de l’Observatoire CS 34229, 06304 Nice Cedex 4 (France); Institut Jean Lamour, UMR CNRS/UL 7198, Université de Lorraine, BP 70239 54506 Vandoeuvre-lès-Nancy Cedex (France); Coulette, David, E-mail: David.Coulette@ipcms.unistra.fr [Institut Jean Lamour, UMR CNRS/UL 7198, Université de Lorraine, BP 70239 54506 Vandoeuvre-lès-Nancy Cedex (France); Institut de Physique et Chimie des Matériaux de Strasbourg, UMR CNRS/US 7504, Université de Strasbourg, 23 Rue du Loess, 67034 Strasbourg (France)

    2016-08-15

    Achieving plasmas with good stability and confinement properties is a key research goal for magnetic fusion devices. The underlying equations are the Vlasov–Poisson and Vlasov–Maxwell (VPM) equations in three space variables, three velocity variables, and one time variable. Even in those somewhat academic cases where global equilibrium solutions are known, studying their stability requires the analysis of the spectral properties of the linearized operator, a daunting task. We have identified a model, for which not only equilibrium solutions can be constructed, but many of their stability properties are amenable to rigorous analysis. It uses a class of solution to the VPM equations (or to their gyrokinetic approximations) known as waterbag solutions which, in particular, are piecewise constant in phase-space. It also uses, not only the gyrokinetic approximation of fast cyclotronic motion around magnetic field lines, but also an asymptotic approximation regarding the magnetic-field-induced anisotropy: the spatial variation along the field lines is taken much slower than across them. Together, these assumptions result in a drastic reduction in the dimensionality of the linearized problem, which becomes a set of two nested one-dimensional problems: an integral equation in the poloidal variable, followed by a one-dimensional complex Schrödinger equation in the radial variable. We show here that the operator associated to the poloidal variable is meromorphic in the eigenparameter, the pulsation frequency. We also prove that, for all but a countable set of real pulsation frequencies, the operator is compact and thus behaves mostly as a finite-dimensional one. The numerical algorithms based on such ideas have been implemented in a companion paper [D. Coulette and N. Besse, “Numerical resolution of the global eigenvalue problem for gyrokinetic-waterbag model in toroidal geometry” (submitted)] and were found to be surprisingly close to those for the original

  14. Asymptotic and spectral analysis of the gyrokinetic-waterbag integro-differential operator in toroidal geometry

    Science.gov (United States)

    Besse, Nicolas; Coulette, David

    2016-08-01

    Achieving plasmas with good stability and confinement properties is a key research goal for magnetic fusion devices. The underlying equations are the Vlasov-Poisson and Vlasov-Maxwell (VPM) equations in three space variables, three velocity variables, and one time variable. Even in those somewhat academic cases where global equilibrium solutions are known, studying their stability requires the analysis of the spectral properties of the linearized operator, a daunting task. We have identified a model, for which not only equilibrium solutions can be constructed, but many of their stability properties are amenable to rigorous analysis. It uses a class of solution to the VPM equations (or to their gyrokinetic approximations) known as waterbag solutions which, in particular, are piecewise constant in phase-space. It also uses, not only the gyrokinetic approximation of fast cyclotronic motion around magnetic field lines, but also an asymptotic approximation regarding the magnetic-field-induced anisotropy: the spatial variation along the field lines is taken much slower than across them. Together, these assumptions result in a drastic reduction in the dimensionality of the linearized problem, which becomes a set of two nested one-dimensional problems: an integral equation in the poloidal variable, followed by a one-dimensional complex Schrödinger equation in the radial variable. We show here that the operator associated to the poloidal variable is meromorphic in the eigenparameter, the pulsation frequency. We also prove that, for all but a countable set of real pulsation frequencies, the operator is compact and thus behaves mostly as a finite-dimensional one. The numerical algorithms based on such ideas have been implemented in a companion paper [D. Coulette and N. Besse, "Numerical resolution of the global eigenvalue problem for gyrokinetic-waterbag model in toroidal geometry" (submitted)] and were found to be surprisingly close to those for the original gyrokinetic

  15. 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.

  16. An integrodifferential model for phase transitions: stationary solutions in higher dimensions

    Science.gov (United States)

    Cortazar, Carmen; Elgueta, Manuel; Rossi, Julio D.; Wolanski, Noemi

    2008-01-01

    We present a model for nonlocal diffusion with Neumann boundary conditions in a bounded smooth domain prescribing the flux through the boundary. We study the limit of this family of nonlocal diffusion operators when a rescaling parameter related to the kernel of the nonlocal operator goes to zero. We prove that the solutions of this family of problems converge to a solution of the heat equation with Neumann boundary conditions.

  17. Solving the Coagulation Equation by the Moments Method

    CERN Document Server

    Estrada, Paul R

    2008-01-01

    We demonstrate an approach to solving the coagulation equation that involves using a finite number of moments of the particle size distribution. This approach is particularly useful when only general properties of the distribution, and their time evolution, are needed. The numerical solution to the integro-differential Smoluchowski coagulation equation at every time step, for every particle size, and at every spatial location is computationally expensive, and serves as the primary bottleneck in running evolutionary models over long periods of time. The advantage of using the moments method comes in the computational time savings gained from only tracking the time rate of change of the moments, as opposed to tracking the entire mass histogram which can contain hundreds or thousands of bins depending on the desired accuracy. The collision kernels of the coagulation equation contain all the necessary information about particle relative velocities, cross-sections, and sticking coefficients. We show how arbitrary ...

  18. The Lotka-Volterra predator-prey model with foraging-predation risk trade-offs.

    Science.gov (United States)

    Krivan, Vlastimil

    2007-11-01

    This article studies the effects of adaptive changes in predator and/or prey activities on the Lotka-Volterra predator-prey population dynamics. The model assumes the classical foraging-predation risk trade-offs: increased activity increases population growth rate, but it also increases mortality rate. The model considers three scenarios: prey only are adaptive, predators only are adaptive, and both species are adaptive. Under all these scenarios, the neutral stability of the classical Lotka-Volterra model is partially lost because the amplitude of maximum oscillation in species numbers is bounded, and the bound is independent of the initial population numbers. Moreover, if both prey and predators behave adaptively, the neutral stability can be completely lost, and a globally stable equilibrium would appear. This is because prey and/or predator switching leads to a piecewise constant prey (predator) isocline with a vertical (horizontal) part that limits the amplitude of oscillations in prey and predator numbers, exactly as suggested by Rosenzweig and MacArthur in their seminal work on graphical stability analysis of predator-prey systems. Prey and predator activities in a long-term run are calculated explicitly. This article shows that predictions based on short-term behavioral experiments may not correspond to long-term predictions when population dynamics are considered.

  19. Semiotic Interpretation of Lotka–Volterra Model and its Usage in Knowledge Management

    Directory of Open Access Journals (Sweden)

    Evdokimov Kirill E.

    2016-01-01

    Full Text Available Convergence of NBICS-technologies makes relevant the exact definition of objective goals’ spectrum, which pursued this self-organizing system of technologies. Authors consider the objective goals of this system of technologies as “semiotic attractors” and the tasks related to knowledge management at the NBICS-technologies niche as management of competition between the goals, which cause processes of creation, transmission, reception, usage and duplication of the new knowledge. Competitive interaction of these goals (and their symbolizations were researched on the grounds of Lotka–Volterra model. The original interpretation of Lotka–Volterra model is posed on the basis of stated interconnection between the stages of complex systems’ non-linear dynamics, this self-organization’s information mechanisms and the semiotic results of information processes’ stages. This synthesis of synergetic, cybernetic and semiotic paradigms is implemented on the grounds of A. N. Whitehead process philosophy. Semiotic interpretation of the model allowed determining the order of goals’ conversion and defining the stages of dynamics at which this transformation by means of knowledge management is constructive.

  20. The adaptive dynamics of Lotka-Volterra systems with trade-offs.

    Science.gov (United States)

    Bowers, Roger G; White, Andrew

    2002-02-01

    We analyse the adaptive dynamics of a generalised type of Lotka-Volterra model subject to an explicit trade-off between two parameters. A simple expression for the fitness of a mutant strategy in an environment determined by the established, resident strategy is obtained leading to general results for the position of the evolutionary singular strategy and the associated second-order partial derivatives of the mutant fitness with respect to the mutant and resident strategies. Combinations of these results can be used to determine the evolutionary behaviour of the system. The theory is motivated by an example of prey evolution in a predator-prey system in which results show that only (non-EUS) evolutionary repellor dynamics, where evolution is directed away from a singular strategy, or dynamics where the singular strategy is an evolutionary attractor, are possible. Moreover, the general theory can be used to show that these results are the only possibility for all Lotka-Volterra systems in which aside from the trade-offs all parameters are independent and in which the interaction terms are of quadratic order or less. The applicability of the theory is highlighted by examining the evolution of an intermediate predator in a tri-trophic model.