Journal of Difference Equations and Applications


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Publications in this journal

  • Journal of Difference Equations and Applications 09/2014;
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    ABSTRACT: Infinite Leslie matrices, introduced by Demetrius 40 years ago, are mathematical models of age-structured populations defined by a countable infinite number of age classes. This article is concerned with determining solutions of the discrete dynamical system in finite time. We address this problem by appealing to the concept of kneading matrices and kneading determinants. Our analysis is applicable not only to populations models, but also to models of self-reproducing machines and self-reproducing computer programs. The dynamics of these systems can also be described in terms of infinite Leslie matrices.
    Journal of Difference Equations and Applications 05/2014;
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    ABSTRACT: This work studies stability and stochastic stabilization of numerical solutions of a class of regime-switching jump diffusion systems. These systems have a wide range of applications in communication systems, flexible manufacturing and production planning, financial engineering and economics because they involve three classes of stochastic factors: white noise, Poisson jump and Markovian switching. This paper focuses on the stability of numerical solutions of the switching jump diffusion systems and examines the conditions under which the Euler–Maruyama (EM) and the backward EM may share the stability of the exact solution. These conditions show that all these three classes of stochastic factors may serve as stabilizing factors and play positive roles for the stability property of both exact and numerical solutions.
    Journal of Difference Equations and Applications 10/2013; 19(11):,1733-1757.
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    ABSTRACT: We study a class of nonlinear discrete fourth-order Lidstone boundary value problems with dependence on two parameters. The existence, uniqueness and dependence of positive solutions on the parameters are discussed. Two sequences are constructed so that they converge uniformly to the unique solution of the problems. One example is included in the paper. Numerical computations of the example confirm our theoretical results. Recent results in the literature are extended and improved.
    Journal of Difference Equations and Applications 01/2013; 19:1133--1146.
  • Journal of Difference Equations and Applications 12/2012; 18(12):1951-1966.
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    ABSTRACT: Let X be a complex Banach space and q ≥ 2 be a fixed integer number. Let be a q-periodic discrete evolution family generated by the (X)-valued, q-periodic sequence (A n ). We prove that the solution of the following discrete problem is bounded (uniformly with respect to the parameter μ ) for each vector b X if and only if the Poincare map U(q,0) is stable.
    Journal of Difference Equations and Applications 09/2012; 18(9):1435-1441.
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    ABSTRACT: Exact finite difference schemes and non-standard finite difference schemes are constructed for the first-order differential equation , for and . In particular, we show that the central finite difference scheme is an exact scheme for the differential equation .
    Journal of Difference Equations and Applications 09/2012; 18(9):1511-1517.
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    ABSTRACT: This paper presents a proof of almost sure asymptotic stability of trivial solution of stochastic systems of linear difference equations driven by -integrable martingale-type noise. For this purpose, we exploit a convergence theorem for non-negative semi-martingale decompositions and verify a practical criteria based on non-random eigenvalues. Two 2D examples illustrate the applicability of obtained criteria.
    Journal of Difference Equations and Applications 08/2012; 18(8):1333-1343.
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    ABSTRACT: Stochastic difference equations and a stochastic partial differential equation (SPDE) are simultaneously derived for the time-dependent neutron angular density in a general three-dimensional medium where the neutron angular density is a function of position, direction, energy and time. Special cases of the equations are given, such as transport in one-dimensional plane geometry with isotropic scattering and transport in a homogeneous medium. The stochastic equations are derived from basic principles, i.e. from the changes that occur in a small time interval. Stochastic difference equations of the neutron angular density are constructed, taking into account the inherent randomness in scatters, absorptions and source neutrons. As the time interval decreases, the stochastic difference equations lead to a system of Itô stochastic differential equations. As the energy, direction, and position intervals decrease, an SPDE is derived for the neutron angular density. Comparisons between numerical solutions of the stochastic difference equations and independently formulated Monte Carlo calculations support the accuracy of the derivations.
    Journal of Difference Equations and Applications 08/2012; 18(8):1267-1285.
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    ABSTRACT: It is known that if we apply Newton's method to the complex function , with , then the immediate basin of attraction of the roots of P has finite area. In this paper, we show that under certain conditions on the polynomial P, if , then there is at least one immediate basin of attraction having infinite area.
    Journal of Difference Equations and Applications 06/2012; 18(6):1067-1076.
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    ABSTRACT: Let G be a finite connected graph. Suppose is a map homotopic to the identity that permutes the vertices. For such a map, a rotation matrix is defined and the basic properties of this matrix are given. It is shown that this matrix generalizes some of the information given by the rotation interval, which is defined when the graph is a circle, to more general graphs.
    Journal of Difference Equations and Applications 06/2012; 18(6):1033-1041.
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    ABSTRACT: We study the existence of positive solutions with respect to a cone for a nonlinear system with second-order differences, subject to some -point boundary conditions.
    Journal of Difference Equations and Applications 05/2012; 18(5):865-877.
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    ABSTRACT: The second-order non-autonomous difference equation where h>0 is a parameter and f is continuous and has three real zeros L 0 < 0 < L is investigated. The equation is a discretization of differential equations arising in hydrodynamics or in the nonlinear field theory. This paper provides conditions for f which guarantee that the equation can have four types of solutions – escape, homoclinic, damped and non-monotonous.
    Journal of Difference Equations and Applications 05/2012; 18(5):895-907.
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    ABSTRACT: We describe the sequences given by the non-autonomous second-order Lyness difference equations , where is either a 2-periodic or a 3-periodic sequence of positive values and the initial conditions are also positive. We also show an interesting phenomenon of the discrete dynamical systems associated with some of these difference equations: the existence of one oscillation of their associated rotation number functions. This behaviour does not appear for the autonomous Lyness difference equations.
    Journal of Difference Equations and Applications 05/2012; 18(5):849-864.
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    ABSTRACT: Let , where is the -th cyclotomic polynomial. Let or , depending if the leading coefficient of the polynomial is ‘+1’ or ‘ − 1’, respectively. The rational function can be written as , where , the 's are positive integers, 's are integers and is a positive integer depending on . In the present paper, we study the set where the intersection is considered over all the possible decompositions of of the type mentioned above. Here, we describe the set in terms of the arithmetic properties of the integers . We also study the question: given S a finite subset of the natural numbers, does exists a , such that ? The set is called the minimal set of Lefschetz periods associated with q(t). The motivation of these problems comes from differentiable dynamics, when we are interested in describing the minimal set of periods for a class of differentiable maps on orientable surfaces. In this class of maps, the Morse–Smale diffeomorphisms are included (cf. Llibre and Sirvent, Houston J. Math. 35 (2009), pp. 835–855).
    Journal of Difference Equations and Applications 05/2012; 18(5):763-783.

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