[PDF] Top 20 Qualitative behavior of rational difference equations of higher order

... [13] E. A. Grove and G. Ladas, Periodicities in Nonlinear Difference Equations, Chapman & Hall/CRC, 2005. [14] E. A. Grove, C. M. Kent, G. Ladas, R. Levins, and S. Valicenti, Global stability in some ... 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, ... See full document

... of rational difference equations of order greater than one is quite challen- ging and rewarding because some prototypes for the development of the basic theory of the global behavior of ... See full document

... global behavior of a system based on the knowledge of its present ...of higher-order dynamical systems, it is crucial to discuss global 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

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

... difference equations, although their forms (or expressions) look very simple, it is extremely difficult to understand thoroughly the global behaviors of their ...the qualitative behaviors of di ff erence ... See full document

... asymptotic behavior of the solutions of Poincar´e difference ...the behavior of the solutions of nonlinear difference equations in a neighborhood of a hyperbolic ...second-order rational ... See full document

... oscillation behavior of neutral difference equations has been stud- ied vigorously, for example, see [1–26] and the references cited ...difference equations find various applications in some variational ... See full document

... This implies that the equilibrium (y, z) of () is locally asymptotically stable. Lemma . Consider the system of difference equations () if p, q ∈ (, +∞) and √ pq > max {p – q, q – p}. Then every ... See full document

... asymptotic behavior of the solution of a new class of rational Difference ...these equations. Finally, we give some interesting counter examples in order to verify our strong ... See full document

... y ′ α − y ′ = p t y β − y (7) Discrete models are more suitable for understanding the problems in Economics, genetics, population dy- namics etc. In the qualitative theory of difference equations ... See full document

... Remark 3.9. Theorem 1.2 in Section 1 is a consequence of Theorem 3.7 and Corollary 2.7. Now, we present a theorem concerning the behavior of the solutions of (1.10). We will assume that the linear part of (1.10) ... See full document

... years, rational difference equations have attracted the attention of many researchers for varied ...nonlinear equations which are, in some cases, treatable but whose dynamics present some new features ... See full document

... oscillatory behavior of solutions of difference equations; see, for example papers [1 -11] and references cited there ...of difference equation with deviating argument and nonnegative ... See full document

... v, w ∈ 0, ∞. Substituting x, y, u, and g in terms of v, w, s, and t into the expression for N one obtains a rational expression N/ D with positive denominator. The numerator N has some negative coefficients. At this ... See full document

... oscillatory behavior of difference equations has been intensively studied in recent ...with equations of type ...of higher-order di ff erence equation similar to ... See full document

... Some particular cases of 1.2 had been studied previously by Li in 6, 7, by using semicycle analysis similar to that in 8. The problem concerning periodicity of semicycles of difference equations was solved in very ... 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

... Thandapani, Oscillatory and nonoscillatory behavior of second order neutral delay difference equations, Math.. Thandapani, Oscillatory and nonoscillatory behavior of second order neutral[r] ... See full document