科研之友
微信
新浪微博
Facebook
分享链接
摘要
The rule of trajectory structure for fourth-order nonlinear difference equation x(n 1) = (x(n-2)(a) x(n-3))/(x(n-2)(a)x(n-3) 1), n = 0, 1, 2, ..., where a is an element of [0, 1) and the initial values x(-3), x(-2), x(-1), x(0) is an element of [0, infinity), is described clearly out in this paper. Mainly, the lengths of positive and negative semicycles of its nontrivial solutions are found to occur periodically with prime period 15. The rule is 4( ), 3(-), 1( ), 2(-), 2( ), 1(-), 1( ), 1(-) in a period. By utilizing this rule its positive equilibrium point is verified to be globally asymptotically stable.
