[PDF] Top 20 Dynamics of a system of rational third order difference equation

... the system of the difference equation () is the extension of the third-order equa- tion in [] in the six-dimensional ...the system of difference equation () using ...of ... See full document

... 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

... of system () either converges to the unique equilibrium point or is asymptotic to one of the points at infinity, precisely to either (, ∞) or to (∞, ...the system will substantially change the ... See full document

... population dynamics, queuing problems, statistical problems, stochastic time series, combinatorial analysis, number theory, geom- etry, electrical networks, neural networks, quanta in radiation, genetics in ... See full document

... global dynamics of the System (1). We show that System (1) may have between zero and three equilibrium points, which may have different local ...If System (1) has one equilibrium point, then ... 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

... 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

... 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

... Proof . This proof can easily done depending on theorem (3.23). Assume that p > q(qr + 1) and consider the function f (x, y) = 1+x+ry p+qx . First, note that f (x, y) on the interval [q, p−q qr ] is non increasing ... See full document

... quadratic system of difference equations in the plane with an infinite number of periodic ...second order difference equations with the cubic terms with an infinite number of a period-two solutions; see Theorem ... See full document

... this equation and some related ...this system by analysing the characteristic equation, and investigate the direction of this bifurcations by using normal form ... 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

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

... global dynamics of a special quadratic fractional case of () where A = C = D = a = c = d =  was performed in [, ...The dynamics of some related quadratic fractional difference equations was considered in ... See full document

... [1]. Difference equation and their associated operators not only play a role in their own right as direct mathematical models of physical phenomena but also provide the field of numerical analysis with ... 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

... a system of difference equations are sometimes very simple in their forms, they are extremely difficult to understand through the behavior of their ...In order to consider these uncertain factors, fuzzy set ... See full document

... Falkner-Skan equation (a third- order boundary value problem arising in boundary-layer theory) using high-order and high-order-compact finite differences ...reduced-order ... See full document

... of equation () is -periodic if a = . So, this equation is also known as Todd’s ...global dynamics of the second-order Lyness equation with a >  by the interpretation of the ... See full document

... Proof The difference equation () can be solved. We will demonstrate it by using the method of variation of constants ([, ]). Namely, based on the form of the general solu- tion to the homogeneous ... See full document