Journal of Difference Equations The latest articles from Hindawi Publishing Corporation © 2015 , Hindawi Publishing Corporation . All rights reserved. Stability of Hyperbolic Equilibrium Solution of Second Order Nonlinear Rational Difference Equation Tue, 21 Apr 2015 08:37:02 +0000 Our goal in this paper is to investigate the global asymptotic stability of the hyperbolic equilibrium solution of the second order rational difference equation , , where the parameters and , , , , are positive real numbers and the initial conditions are nonnegative real numbers such that . In particular, we solve Conjecture 5.201.1 proposed by Camouzis and Ladas in their book (2008) which appeared previously in Conjecture 11.4.2 in Kulenović and Ladas monograph (2002). S. Atawna, R. Abu-Saris, E. S. Ismail, and I. Hashim Copyright © 2015 S. Atawna et al. All rights reserved. Some General Systems of Rational Difference Equations Thu, 05 Mar 2015 06:26:11 +0000 We investigate behavior of solutions of the following systems of rational difference equations: , where is a positive integer and the initial conditions are real numbers. We show that every solution is periodic with period, considerably improving the results in the literature. Ali Gelisken and Merve Kara Copyright © 2015 Ali Gelisken and Merve Kara. All rights reserved. A Note on a Modified Cournot-Puu Duopoly Tue, 06 Jan 2015 08:49:20 +0000 The aim of this paper is to analyze a classical duopoly model introduced by Puu in 1991 when lower bounds for productions are added to the model. In particular, we prove that the complexity of the modified model is smaller than or equal to the complexity of the seminal one by comparing their topological entropies. We also discuss whether the dynamical complexity of the new model is physically observable. Jose S. Cánovas Copyright © 2015 Jose S. Cánovas. All rights reserved. Asymptotic Behavior of the Solutions of System of Difference Equations of Exponential Form Mon, 13 Oct 2014 09:38:56 +0000 The goal of this paper is to study the boundedness, the persistence, and the asymptotic behavior of the positive solutions of the system of two difference equations of exponential form: where , and are positive constants and the initial values are positive real values. Also, we determine the rate of convergence of a solution that converges to the equilibrium of this system. Vu Van Khuong and Tran Hong Thai Copyright © 2014 Vu Van Khuong and Tran Hong Thai. All rights reserved. Application of Hybrid Functions for Solving Duffing-Harmonic Oscillator Thu, 14 Aug 2014 07:09:07 +0000 A numerical method for finding the solution of Duffing-harmonic oscillator is proposed. The approach is based on hybrid functions approximation. The properties of hybrid functions that consist of block-pulse and Chebyshev cardinal functions are discussed. The associated operational matrices of integration and product are then utilized to reduce the solution of a strongly nonlinear oscillator to the solution of a system of algebraic equations. The method is easy to implement and computationally very attractive. The results are compared with the exact solution and results from several recently published methods, and the comparisons showed proper accuracy of this method. Mohammad Heydari, Ghasem Brid Loghmani, Seyed Mohammad. Hosseini, and Seyed Mehdi Karbassi Copyright © 2014 Mohammad Heydari et al. All rights reserved. Almost Periodic Solution of a Discrete Schoener’s Competition Model with Delays Thu, 24 Jul 2014 08:40:44 +0000 We consider an almost periodic discrete Schoener’s competition model with delays. By means of an almost periodic functional hull theory and constructing a suitable Lyapunov function, sufficient conditions are obtained for the existence of a unique strictly positive almost periodic solution which is globally attractive. An example together with numerical simulation indicates the feasibility of the main result. Hui Zhang, Yingqi Li, Bin Jing, Xiaofeng Fang, and Jing Wang Copyright © 2014 Hui Zhang et al. All rights reserved. Exact Controllability of an Impulsive Semilinear System with Deviated Argument in a Banach Space Wed, 16 Jul 2014 00:00:00 +0000 A functional differential equation with deviated argument coupled with impulsive conditions is studied for the existence and uniqueness of the mild solution and exact controllability of the system. The results are obtained by using Banach contraction principle and semigroup theory without imposing additional assumptions such as analyticity and compactness conditions on the generated semigroup and the nonlinear term. An example is provided to illustrate the presented theory. Sanjukta Das, Dwijendra N. Pandey, and N. Sukavanam Copyright © 2014 Sanjukta Das et al. All rights reserved. Hermite Wavelet Method for Fractional Delay Differential Equations Wed, 02 Jul 2014 09:09:44 +0000 We proposed a method by utilizing method of steps and Hermite wavelet method, for solving the fractional delay differential equations. This technique first converts the fractional delay differential equation to a fractional nondelay differential equation and then applies the Hermite wavelet method on the obtained fractional nondelay differential equation to find the solution. Several numerical examples are solved to show the applicability of the proposed method. Umer Saeed and Mujeeb ur Rehman Copyright © 2014 Umer Saeed and Mujeeb ur Rehman. All rights reserved. Rate of Convergence of Modified Baskakov-Durrmeyer Type Operators for Functions of Bounded Variation Wed, 02 Jul 2014 00:00:00 +0000 We study a certain integral modification of well-known Baskakov operators with weight function of beta basis function. We establish rate of convergence for these operators for functions having derivative of bounded variation. Also, we discuss Stancu type generalization of these operators. Prashantkumar Patel and Vishnu Narayan Mishra Copyright © 2014 Prashantkumar Patel and Vishnu Narayan Mishra. All rights reserved. Global Asymptotic Stability for Linear Fractional Difference Equation Tue, 01 Jul 2014 07:55:35 +0000 Consider the difference equation ,  , where all parameters ,  , and the initial conditions ,   are nonnegative real numbers. We investigate the asymptotic behavior of the solutions of the considered equation. We give easy-to-check conditions for the global stability and global asymptotic stability of the zero or positive equilibrium of this equation. A. Brett, E. J. Janowski, and M. R. S. Kulenović Copyright © 2014 A. Brett et al. All rights reserved. A Remark on the Regularity Criterion for the MHD Equations via Two Components in Morrey-Campanato Spaces Wed, 25 Jun 2014 11:18:10 +0000 We consider the regularity criterion for the 3D MHD equations. It is proved that if the horizontal components of the velocity and magnetic fields satisfy with , then the solution smooth. This improves the result given by Gala (2012). Zujin Zhang, Tong Tang, and Fumin Zhang Copyright © 2014 Zujin Zhang et al. All rights reserved.