Dynamics of a non-linear difference equation

作者：Mazrooei Sebdani Reza; Dehghan Mehdi^*

来源：Applied Mathematics and Computation, 2006, 178(2): 250-261.

DOI：10.1016/j.amc.2005.11.042

• local asymptotic stability
• boundedness
• invariant interval
• semicycle behavior
• global asymptotic stability

Our aim in this paper is to investigate the dynamics of difference equation
y(n+1) = y(n) + py(n-k)/y(n) + q, n = 0, 1, 2, ...,
where the initial conditions y(-k),..., y(-1), y(0) are non-negative, k is an element of {1, 2, 3,...}, and the parameters p and q are non-negative. We study characteristics such as periodicity, invariant interval, the character of semicycles, the global stability, and the boundedness of positive solutions of the above mentioned difference equation. In particular, our results solve the open problem introduced by Kulenovic and Ladas in their monograph [Dynamics of Second Order Rational Difference Equations with Open Problems and Conjectures, Chapman and Hall/CRC, Boca Raton, 2002].

• 出版日期2006-7-15