Dynamical Properties in a Fourth-Order Nonlinear Difference Equation
نویسندگان
چکیده
The rule of trajectory structure for fourth-order nonlinear difference equation xn 1 x a n−2 xn−3 / x a n−2xn−3 1 , n 0, 1, 2, . . . , where a ∈ 0, 1 and the initial values x−3, x−2, x−1, x0 ∈ 0,∞ , 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.
منابع مشابه
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