[PDF] Top 20 Dynamics of a Rational System of Difference Equations in the Plane

... the dynamics of the system: the boundedness character and asymptotic behavior of its solutions, the existence of periodic orbits in particular, of prime period-two solutions, and the stability of the ... 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 ... See full document

... the plane, when one of the eigenvalues of the linearized system at an equili- brium (hyperbolic or non-hyperbolic) is by absolute value smaller than 1 while the other has an arbitrary ... See full document

... y, system () is ...difference equations or strongly competitive maps are those for which the functions f and g are coordinate-wise strictly ...the plane was given in [, , , , , , ... See full document

... whose dynamics differ significantly from other equations in this class. There are a total of 42 cases that arise from 1.1 in the manner just discussed, under the hypotheses B C > 0 and α β γ > 0. The ... See full document

... of difference operators, demonstrate their connections with Nijenhuis operators and give a criteria for the existence of weakly nonlocal inverse recursion operators for differential–difference ...of ... See full document

... are strictly increasing. For the sake of contradiction, these susequences have …nite limits. Since the subsequences are increasing, they must be bounded from above. But the system (1.1) has two equilibrium points ... 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, ... See full document

... DOI: 10.4236/am.2017.810107 1471 Applied Mathematics Conclusion 1. This work is concerned with studying a dynamics and behavior of solutions of a new class of difference Equation (1) . Our results extend ... See full document

... global dynamics of a number of cases of system () from open problem  which are neither competitive nor cooperative in any parameter region along with many additional cases that were not mentioned in [], ... See full document

... and difference equations developed ...of difference equations occupies a central position in applied sciences ...of difference equations will continue to play an important role ... See full document

... This paper presents the use of a variational iteration method for systems of nonlinear difference equations. This technique is a powerful tool for solving various difference equations and can also be applied ... 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

... various equations, including difference ...difference equations and systems can be transformed to linear ones, which are solvable (for solvability of linear difference equa- tions see, ...difference ... 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. ... See full document

... real plane ,  f g ,  : R  R , f g , are continuous function is competitive if f  x y ,  is non-decreasing in x and non-increasing in y ; and g x y  ,  is non-increasing in x and non-decreasing in y .... ... 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 study of anti-competitive systems started in [] and has advanced since then (see [, ]). The principal tool of the study of anti-competitive systems is the fact that the second iterate of the map associated with ... See full document

... is non-increasing in u for each v in I and non-decreasing in v for each u in a closed internal in R . It is rest to prove that the (2.1) does not possess any prime period two solutions. If possible let there is a prime ... 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 ... See full document