[PDF] Top 20 DYNAMICS OF THE RATIONAL DIFFERENCE EQUATION

... • If at least one root of the characteristic equation Eq.(3.2) has absolute value greater than one, then the equilibrium point of the RDE Eq.(2.1) is unstable. • The equilibrium point of the RDE Eq.(2.1) is called ... See full document

... the rational difference equation that was investigated by Kulenovic et ...[The Dynamics of x n+1 = A+Bx α+βx n +Cx n n−1 , Facts and ... See full document

... Hindawi Publishing Corporation Advances in Difference Equations Volume 2010, Article ID 970720, 14 pages doi 10 1155/2010/970720 Research Article Dynamics of a Rational Difference Equation Xiu Mei Jia[.] ... See full document

... In this paper, we study the equilibrium points, local asymptotic stability of an equilibrium point, instability of equilibrium points, periodicity behavior of positive solutions, and global character of an equilibrium ... See full document

... The paper is organized as follows. Section  contains some necessary results on com- petitive systems in the plane. Section  provides some basic facts about the equilibrium points and injectivity of the map associated ... See full document

... population dynamics. In fact, second equation in (1) is of Leslie-Gower type, and first equation can be considered to be of Leslie-Gower type with stocking which is represented with the term a 1 , ... See full document

... In the present work, we study the qualitative behavior of two systems of higher-order rational difference equations. More precisely, we study the local asymptotic stability, instability, global asymptotic stability ... See full document

... typical dynamics of the rational difference equation ...the rational function can be thought as a response function of a biological ... See full document

... 1.1 has a variety of dynamics that depend on the value of parameters. We show that system 1.1 may have between zero and two equilibrium points, which may have different local character. If system 1.1 has one ... See full document

... nonlinear difference equations are capable of producing a complicated behavior regardless its ...nonlinear difference equations in proving that every solution of these equations conver to a period two ... See full document

... During this study, we will need to many of the basic concepts. Before anything, the concept of equilibrium point is essential in the study of the dynamics of any physical system. A point ω in the domain of the ... See full document

... In the next, we will and to many of the basic concepts. Before anything, the concept of equilibrium point is essential in the study of the dynamics of any physical system. A point ψ in the domain of the function Φ ... See full document

... of difference equations are well established in the study of Lie ...of rational difference equations was ana- lyzed in [8, ...the equation y t+1 = f(y t )g(y t−s ... See full document

... the dynamics of polynomial maps is determining the basin of attraction of the point at ∞ and in particular the boundary of that basin known as the Julia ...polynomial equation, that is, () where A +B + C + ... See full document

... But “a question ” of mathematics and biology is whether stable and sustained oscillation possible for 1.1, when αβ > 1, increases. In the present paper, we provide a detailed analysis of these questions. Regarding β ... See full document

... In this work we study various properties of (.). In Section  we study attractivity, stabil- ity and attractive region of (.) and its related equations. Further more we study bifurca- tions of (.). In Section  we ... See full document

... GLOBAL BEHAVIOR OF A HIGHER ORDER RATIONAL DIFFERENCE EQUATION HONGJIAN XI AND TAIXIANG SUN Received 17 January 2006; Revised 6 April 2006; Accepted 12 April 2006 We investigate in this paper the glob[.] ... See full document

... Rational difference equations that are the ratio of two polynomials are one of the most important and practical classes of nonlinear difference equations. Marwan Aloqeili [] investigated the stability character, ... See full document

... Difference equations are applied in the field of biology, engineer, physics, and so on [1]. The study of properties of rational difference equations has been an area of intense interest in the recent ... See full document

... Hindawi Publishing Corporation Advances in Difference Equations Volume 2009, Article ID 394635, 9 pages doi 10 1155/2009/394635 Research Article On a Conjecture for a Higher Order Rational Difference[.] ... See full document