Example 1. Figure 1, shows that Eq.(1) has no prime period two solutions if k = 2, 1= 4, o = 6, x_6 = 1, х-5 3D2, х-4 %3D 3, х-з 3 4, х-2 %3D 5, х-1 %3D 6, хо —D 7, A = 300, B = 200, C= 100, D= 75, b = 50, d = 30, е%3D 20. || || plot of y(7=(A*y(n)+B*y(n-2)+C*y(n-4)+D*y(n-6))+((b*y(n-2))/(d'y(n-2)-e*y(n-4))) 14.0005 7.0003 50 100 150 200 n-iteration The objective of this article is to investigate some qualitative behavior of the solutions of the nonlinear difference equation bxn-k Xn+1 = Axn+ Bxn-k+Cxr-1+Dxn-o + [dxn-k- exn-1] (1) n = 0,1,2,.. where the coefficients A, B, C, D, b, d, e E (0,0), while k, 1 and o are positive integers. The initial conditions X-o.….,X_1,..., X_k) ….., X–1, X0 are arbitrary positive real numbers such that k <1< 0. Note that the special cases of Eq. (1) have been studied in [1] when B= C=D=0, and k= 0,1=1, b is replaced by – b and in [27] when B=C= D=0, and k= 0, b is replaced by – b and in [33] when B = C = D = 0, 1= 0 and in [32] when A=C=D=0, 1=0, b is replaced by – b. - 6. solution of y(n+1)

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Example 1. Figure 1, shows that Eq.(1) has no prime
period two solutions if k = 2, 1= 4, o = 6, x_6 =
1, х-5 3D 2, х-4 3D 3, х-з 3 4, х-2 3D 5, х-1 — 6, хо — 7,
A = 300, B = 200, C= 100, D= 75, b = 50, d =
30, е — 20.
plot of y(=(A*y(n)+B*y(n-2)+C*y(n-4)+D*y(n-6))+((b'y(n-2))(d*y(n-2)-e*y(n-4)))
14.0005
7.0003
50
100
n-iteration
150
200
The objective of this article is to investigate some
qualitative behavior of the solutions of the nonlinear
difference equation
bxn-k
[dxn-k- exn-1)
Xn+1
Axn+ Bxn-k+ CXp-1+DXp-o +
n= 0,1,2,..
(1)
where the coefficients A, B, C, D, b, d, e e (0,0), while
k, 1 and o are positive integers. The initial conditions
X-o,..., X_1,..., X_k, ..., X_1, X0 are arbitrary positive real
numbers such that k <1< o. Note that the special cases
of Eq. (1) have been studied in [1] when B=C = D=0,
and k = 0,1= 1, b is replaced by
B= C= D=0, and k = 0, b is replaced by – b and in
[33] when B
A=C= D=0, 1=0, b is replaced by – b.
%3D
– b and in [27] when
= C = D = 0,
1
0 and in [32] when
solution of y(n+1)
Transcribed Image Text:Example 1. Figure 1, shows that Eq.(1) has no prime period two solutions if k = 2, 1= 4, o = 6, x_6 = 1, х-5 3D 2, х-4 3D 3, х-з 3 4, х-2 3D 5, х-1 — 6, хо — 7, A = 300, B = 200, C= 100, D= 75, b = 50, d = 30, е — 20. plot of y(=(A*y(n)+B*y(n-2)+C*y(n-4)+D*y(n-6))+((b'y(n-2))(d*y(n-2)-e*y(n-4))) 14.0005 7.0003 50 100 n-iteration 150 200 The objective of this article is to investigate some qualitative behavior of the solutions of the nonlinear difference equation bxn-k [dxn-k- exn-1) Xn+1 Axn+ Bxn-k+ CXp-1+DXp-o + n= 0,1,2,.. (1) where the coefficients A, B, C, D, b, d, e e (0,0), while k, 1 and o are positive integers. The initial conditions X-o,..., X_1,..., X_k, ..., X_1, X0 are arbitrary positive real numbers such that k <1< o. Note that the special cases of Eq. (1) have been studied in [1] when B=C = D=0, and k = 0,1= 1, b is replaced by B= C= D=0, and k = 0, b is replaced by – b and in [33] when B A=C= D=0, 1=0, b is replaced by – b. %3D – b and in [27] when = C = D = 0, 1 0 and in [32] when solution of y(n+1)
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