Example 2. Figure 2, points out that the solution of Equation (1) holds no positive prime period two solutions on the assumption that the positive integers p,q,r and s are even. Select p = 8, q = 6, r = 4, s = 2, S_8 = 1, S_7 = 2, S-6 = 3, S-5 = 4, S-4 = 5, S_3 6, S-2 = 7, S–1 = 8, So = 9 a = = 10, b = 20, c = 15, d = 25, e = 30, f = 35. plot of S(n+1) Milnis 40 n-iteratio n 100 10Sn-6+20Sn-4+15S,-2 FIGURE 2. (Sn+1 = Sn-8 25S,-6+30Sn-4+35Sn–2 (1+u)s p uognos

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Example 2. Figure 2, points out that the solution of Equation (1) holds no positive
prime period two solutions on the assumption that the positive integers p,q,r and s
are even. Select
p = 8, q = 6, r = 4, s = 2, S_8 = 1, S_7 = 2, S_6 = 3, S_5 = 4, S-4 = 5, S_3
6, S_2 3D 7, S_1 3 8, So 3D 9 а%—
Е 10, b — 20, с — 15, d — 25, e — 30, f — 35.
plot of S(n+1)
100
n-iteratio n
FIGURE 2. ( Sn-8
10Sn-6+20Sn-4+15Sn-2
25Sn-6+30Sn-4+35Sn-2
:)
Sn+1 =
Transcribed Image Text:Example 2. Figure 2, points out that the solution of Equation (1) holds no positive prime period two solutions on the assumption that the positive integers p,q,r and s are even. Select p = 8, q = 6, r = 4, s = 2, S_8 = 1, S_7 = 2, S_6 = 3, S_5 = 4, S-4 = 5, S_3 6, S_2 3D 7, S_1 3 8, So 3D 9 а%— Е 10, b — 20, с — 15, d — 25, e — 30, f — 35. plot of S(n+1) 100 n-iteratio n FIGURE 2. ( Sn-8 10Sn-6+20Sn-4+15Sn-2 25Sn-6+30Sn-4+35Sn-2 :) Sn+1 =
The main aim of this study is to exhibit some cases on the periodic character of
the positive solutions of the rational difference equation
aSn-g + bSn-r + cSn-s
+ eSn-r + f Sn-s )
(1)
Sn+1
Sn-P
dSn-4
where a, b, c, d, e, ƒ e (0, 0). The initial conditions S-p, S-p+1,...,S-q, S-q+1,...,S-r,
S-r+1,...,S-s,...,S_s+1,...,S_1 and So are arbitrary positive real numbers such that
p > q >r > s > 0.
Transcribed Image Text:The main aim of this study is to exhibit some cases on the periodic character of the positive solutions of the rational difference equation aSn-g + bSn-r + cSn-s + eSn-r + f Sn-s ) (1) Sn+1 Sn-P dSn-4 where a, b, c, d, e, ƒ e (0, 0). The initial conditions S-p, S-p+1,...,S-q, S-q+1,...,S-r, S-r+1,...,S-s,...,S_s+1,...,S_1 and So are arbitrary positive real numbers such that p > q >r > s > 0.
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