Global attractivity in a rational recursive sequence

Yan, Xing-Xue; Li, Wan–Tong

doi:10.1016/s0096-3003(02)00433-2

Cited by 23 publications

(5 citation statements)

References 13 publications

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“…When 4α < (3β − 1)(β + 1), we have witnessed thin regions delimited by parabolic curves where every solution seems to converge to a periodic solution. Some of the periods we have observed are 11,15,19,22,23,24,26,30,32,40, 44, 52, and 60. A detailed description of the numerical experimentation and its results will be given elsewhere.…”

Section: The First Quadrant (α > 0 and β > 0)mentioning

confidence: 82%

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On a (2,2)-rational recursive sequence

2005

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We investigate the asymptotic behavior of the recursive difference equation y n+1 = (α + βy n )/(1 + y n−1 ) when the parameters α < 0 and β ∈ R. In particular, we establish the boundedness and the global stability of solutions for different ranges of the parameters α and β. We also give a summary of results and open questions on the more general recursive sequences y n+1 = (a + by n )/(A + By n−1 ), when the parameters a,b,A,B ∈ R and abAB = 0.

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Section: The First Quadrant (α > 0 and β > 0)mentioning

confidence: 82%

“…To this effect, there have been a few papers that dealt with negative parameters. See, for example, [1,2,3,4,11,12]. In [1], Aboutaleb et al studied the equation 2) where b is the only negative parameter.…”

Section: Introductionmentioning

confidence: 99%

On a (2,2)-rational recursive sequence

2005

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“…(1.4) The global asymptotic stability of the rational recursive sequence (1.1) was investigated for when the coefficients α, β, γ and γ i are non-negative (see [7,1,8,9]. For other related results see [10,11,6,[12][13][14]. For the terminology used here, we refer the reader to [15,8].…”

Section: Introductionmentioning

confidence: 99%

On the recursive sequence xn+1=(α−βxn−k
Hamza¹
2010
Computers & Mathematics with Applications
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a b s t r a c tThis paper is devoted to investigating the asymptotic behavior of the recursive sequencewhere α ≥ 0 and β > 0 and g is continuous on R k . We show that under certain conditions this equation has a unique positive (negative) equilibrium point which is a global attractor with some basin S ⊂ R k+1 . Also we establish the oscillation of all solutions with initialWe apply these results to the recursive sequencewhere α, γ , a i , b i ≥ 0, i = 0, . . . , k − 1, and β > 0.

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“…Clearly, Eq. (1.3) has a unique equilibrium For other related results on nonlinear difference equations, one can refer to [3][4][5][6][7][8][9][10][11][12][13]. Motivated by Conjecture 1.2, the purpose of this paper is to investigate the boundedness, invariant interval, semicycle and global asymptotical stability of all nonnegative solutions of Eq.…”

Section: Introductionmentioning

confidence: 99%

Global asymptotical stability of a second order rational difference equation

2007

Computers & Mathematics with Applications

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In this paper, we investigate the boundedness, invariant interval, semicycle and global attractivity of all positive solutions of the equation x n+1 = α+γ x n−1 A+Bx n +C x n−1 , n = 0, 1, . . . , where the parameters α, γ , A, B, C ∈ (0, ∞) and the initial conditions y −1 , y 0 are nonnegative real numbers. We show that if the equation has no prime period-two solutions, then the positive equilibrium of the equation is globally asymptotically stable. Our results solve partially the conjecture proposed by Kulenović and Ladas in their monograph

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Global attractivity in a rational recursive sequence

Cited by 23 publications

References 13 publications

On a (2,2)-rational recursive sequence

On a (2,2)-rational recursive sequence

On the recursive sequence xn+1=(α−βxn−k
Hamza¹
2010
Computers & Mathematics with Applications
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Global asymptotical stability of a second order rational difference equation

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Global attractivity in a rational recursive sequence

Cited by 23 publications

References 13 publications

On a (2,2)-rational recursive sequence

On a (2,2)-rational recursive sequence

On the recursive sequence xn+1=(α−βxn−kHamza1 2010Computers & Mathematics with Applications0000View full textAdd to dashboardCite

Global asymptotical stability of a second order rational difference equation

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On the recursive sequence xn+1=(α−βxn−k
Hamza¹
2010
Computers & Mathematics with Applications
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