[PDF] Top 20 Convergence Results on a Second Order Rational Difference Equation with Quadratic Terms

... Hindawi Publishing Corporation Advances in Difference Equations Volume 2009, Article ID 985161, 7 pages doi 10 1155/2009/985161 Research Article Convergence Results on a Second Order Rational Differen[.] ... See full document

... The study of differential/difference equations has been the object of many researchers over the last decades. Different approaches and various techniques have been adopted to investigate the qualitative properties of their ... See full document

... Nowadays, a part of the scientific community seems uses only computers and symbolic algebra for getting some results on solvability of various equations, including difference ones. This causes several problems, ... See full document

... the second author and Ladas obtained both local and global stability results for ...of convergence of all solutions in this region by using Poincar´e’s theorem and an improvement of Perron’s ... See full document

... main results are stated in Section 1. Results from literature which are used here are given in Section 2 for ...difference equation is coordinatewise strictly monotonic on I × ...global ... See full document

... the convergence of a finite difference scheme to the solu- tion of a second order ordinary differential equation with the right-hand-side nonlinearly dependent on the first ... 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 ... See full document

... stability results for those equations. The obtained results will give the regions of the parametric space where the unique positive equilibrium of () is globally asymptotically ... See full document

... in order to avoid the quadratic case, which was completely studied in ...many results have been obtained; see ...a second order quadratic polynomial equation, that is, () ... See full document

... a second order difference equation with several super-linear neutral ...The results obtained here extend or complement some of the known results reported in the ...main results ... See full document

... the convergence of the sequence of second order quadratic ...of second order quadratic variations had proved in ...localized quadratic variations have been ... See full document

... erence equation. With the term integrability of a di ff erence equation, we understand the existence of an infinite hierarchy of ...first order recursion operator were given in [10] and we refer to ... See full document

... • 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 organization of this paper is as follows. In Section 2, some basic definitions and lemmas regarding difference equations are given. The boundedness and invariant intervals of 1.11 are discussed in Section 3. The ... See full document

... above equation is transformed into a new one, which is a third-order non-neutral difference ...Using results obtained for the new equation, the asymptotic properties of the neutral difference ... See full document

... of Difference Equations has been growing ...that difference equations appear as mathematical models describing real life situations in probability theory, queuing theory, statistical problems, stochastic ... See full document

... The results at Machakos experimental field indicated that the relationship between specific draft and tillage depth at different hitching length is a second-order quadratic equation of t[r] ... 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

... of second-order linear and nonlinear difference equations has attracted considerable attention, and we refer the reader to the papers of Diblik et ...of second-order differential equations are ... See full document

... below) convergence of solutions in the interval (−1 , 0) to period-five solutions, these period-five solutions can conceivably include solutions of the form {x n } ∞ n=−3 = 0 , −1 , −d − 1 , d , −1 , 0 , −1 , ... See full document