On the behavior of solutions of the system of rational difference equations x n + 1 = x n - 1 y n x n - 1 - 1 , y n + 1 = y n - 1 x n y n - 1 - 1 , z n + 1 = 1 y n z n

On the nature of solutions of the difference equation $mathbf{x_{n+1}=x_{n}x_{n-3}-1}$

We investigate the long-term behavior of solutions of the difference equation[ x_{n+1}=x_{n}x_{n-3}-1 ,, n=0 ,, 1 ,, ldots ,, ]noindent where the initial conditions $x_{-3} ,, x_{-2} ,, x_{-1} ,, x_{0}$ are real numbers.  In particular, we look at the periodicity and asymptotic periodicity of solutions, as well as the existence of unbounded solutions.

Dynamics of higher order rational difference equation $x_{n+1}=(alpha+beta x_{n})/(A + Bx_{n}+ Cx_{n-k})$

The main goal of this paper is to investigate the periodic character, invariant intervals, oscillation and global stability and other new results of all positive solutions of the equation$$x_{n+1}=frac{alpha+beta x_{n}}{A + Bx_{n}+ Cx_{n-k}},~~ n=0,1,2,ldots,$$where the parameters $alpha$, $beta$, $A$, $B$ and $C$ are positive, and the initial conditions $x_{-k},x_{-k+1},ldots,x_{-1},x_{0}$ are...

On the Rational Recursive Sequence X_{N+1}=ƔX_{N-K}+(AX_N+BX_{N-K})⁄(CX_N-DX_{N-K})

on the nature of solutions of the difference equation $mathbf{x_{n+1}=x_{n}x_{n-3}-1}$

we investigate the long-term behavior of solutions of the difference equation[ x_{n+1}=x_{n}x_{n-3}-1 ,, n=0 ,, 1 ,, ldots ,, ]noindent where the initial conditions $x_{-3} ,, x_{-2} ,, x_{-1} ,, x_{0}$ are real numbers.  in particular, we look at the periodicity and asymptotic periodicity of solutions, as well as the existence of unbounded solutions.

A L M N B X . Y . Z X 1 . Y 1 . Z 1 Source Dest . Regional Regional NSFnet backbone Fig 1 : Routing Information Flow

The Internet is a complex mesh of networks that use a common suite (TCP/IP) of networking protocols. A key feature of the Internet is that all of these constituent networks are interconnected, thereby providing system wide communication. The magnitude and pattern of the ow of routing information directly represents the con-nectivity stability of the Internet. The NSFNET backbone network provide...