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The Rule of Cycle Length and Global Asymptotic Stability for a Fourth-Order Nonlinear Difference Equation
並列摘要
The rule of trajectory structure for fourth-order nonlinear difference equation (The equation is abbreviated)where b ∈ [0,1) and the initial values x_(-3), x_(-2), x_(-1), x_0 ∈ (0,∞), is described clearly out in this paper. Mainly, the lengths of positive and negative semi-cycles of its nontrivial solutions are found to occur periodically with prime period 15. The rule is 4^- ,3^+ ,1^1 ,2^+ ,2^- ,1^+ ,1^- ,1^+ in a period. By utilizing this rule its positive equilibrium point is verified to be globally asymptotically stable.
延伸閱讀
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