[PDF] Top 20 Qualitative behavior of a rational difference equation

... of rational difference equations has been an area of intense interest in the recent years ...the qualitative behavior of rational 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

... For some difference equations, although their forms (or expressions) look very simple, it is extremely difficult to understand thoroughly the global behaviors of their solutions. Accordingly, one is often motivated to ... See full document

... arbitrary positive real numbers. We give sufficient conditions under which the unique equilibrium x 0 of this equation is globally asymptotically stable, which extends and includes corresponding results obtained in ... See full document

... (2) For multiple delay and order, see [3] [18] [19] [20] and their references for more results of this equation. In Theorems 4.7.1-4.7.5 in [12], Kulenovic inves- tigated the asymptotic behavior of the ... See full document

... Although difference equations are sometimes very simple in their forms ,they are extremely difficult to understand thoroughly the behavior of their solutions ...global behavior of nonlinear ... See full document

... appropriate difference equation to model a situation? how does one understand the behaviour of the difference equation model once it has been formed? There is no scopes of confusion that the ... See full document

... Difference equations appear naturally as discrete analogues and in the numerical solutions of differential and delay differential equations having applications in biology, ecology, physics, and so forth 1. The study of ... See full document

... of difference equations are well established in the study of Lie ...aspect. Qualitative properties of certain class of rational difference equations was ana- lyzed in [8, ...the ... See full document

... Since m / M, we have qm M p − 1, which implies that for p ≤ 1 there are no solutions to system 4.5 which have both coordinates positive. Now assume p > 1; from 4.7, m p − 1 − Mq/q, and substitute the latter into 4.5 ... See full document

... [8] studied the global behavior of positive solution to the fourth-order rational difference equations.. Although difference equations are sometimes very simple in their forms, they are [r] ... See full document

... Thus, the solution is bounded and persists and the proof is complete. □ Conclusion 1. In this paper , we study a asymptotic behavior of solutions of a general class of difference Equation (1.1). Our ... See full document

... this equation is investigated by introducing a new sequence, which extends and includes corresponding results obtained in the references (Li in J Math Anal Appl 312:103-111, 2005; Berenhaut et ... See full document

... Although difference equations and a system of difference equations are sometimes very simple in their forms, they are extremely difficult to understand through the behavior of their solutions. On the other hand, these ... 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

... We study numerical methods for finding the maximal symmetric positive definite solution of the nonlinear matrix equation X = Q + LX −1 L T , where Q is symmetric positive definite and L is nonsingular. Such ... See full document

... Remark 2. As one can see, the established results above mainly deal with Volterra- Fredholm type discrete inequalities with four iterated sums and infinite sum upper limit, and they are different from the results ... See full document

... Abstract. We present a normal form theorem for the propagator of a splitting method ap- plied to a linear Schr¨ odinger equation. This result allows us to derive conservation properties for the numerical solutions ... See full document

... That is, we will investigate the global behavior of 1.1 including the asymptotical stability of equilibrium points, the existence of bounded solution, the existence of period two solutio[r] ... See full document

... the behavior of real experimental systems is a testament to the incredible technical advances in atomic and optical physics over the last few decades [11, 14–18], providing exquisite tools for control and ... See full document