Dynamic behavior of a nonlinear rational difference equation and generalization

Shi, Qinwei; Xiao, Qian; Yuan, Guoqiang; Liu, Xiaojun

doi:10.1186/1687-1847-2011-36

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2015

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“…attracted the attention of many researchers recently. For example, see the articles [1][2][3][4][5][6][7][8][9]. As it turns out, many models, such as population models in mathematical biology, are members of the family of rational difference equations.…”

Section: Introductionmentioning

confidence: 99%

Stability of Hyperbolic Equilibrium Solution of Second Order Nonlinear Rational Difference Equation

Atawna

Abu-Saris

Ismail

et al. 2015

Journal of Difference Equations

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Our goal in this paper is to investigate the global asymptotic stability of the hyperbolic equilibrium solution of the second order rational difference equationxn+1=α+βxn+γxn-1/A+Bxn+Cxn-1,n=0,1,2,…, where the parametersA≥0andB,C,α,β,γare positive real numbers and the initial conditionsx-1, x0are nonnegative real numbers such thatA+Bx0+Cx-1>0. In particular, we solve Conjecture 5.201.1 proposed by Camouzis and Ladas in their book (2008) which appeared previously in Conjecture 11.4.2 in Kulenović and Ladas monograph (2002).

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