广义Fibonacci方程的渐近稳定性  

Asymptotic stability of generalized Fibonacci equations

作　　者：陈鑫 CHEN Xin(School of Mathematics,Sichuan University,Chengdu,Sichuan 610064,China)

机构地区：[1]四川大学数学学院,四川成都610064

出　　处：《内江师范学院学报》2024年第12期27-31,共5页Journal of Neijiang Normal University

摘　　要：Fibonacci数列的递推关系是一个二阶线性差分方程.本文首先讨论了广义Fibonacci方程零解渐近稳定的参数条件,其次考虑上述广义Fibonacci方程在非线性扰动下的动力学性质,通过分析得到非线性扰动不会破坏线性近似系统的零解渐近性的参数条件,从而系统的零解的渐近稳定性可以由它的线性近似系统零解的渐近稳定性来确定,于是给出其在非线性扰动下零解渐近稳定的参数条件.The recurrence relation that represents the Fibonacci sequence is given by the second-order linear difference equation.Firstly,The parameter conditions of asymptotic stability of zero solution of generalized Fibonacci equation are discussed.Secondly,the dynamic properties of the above generalized Fibonacci equation under nonlinear perturbations are considered,the parametric conditions under which the nonlinear perturbations do not destroy the asymptotic properties of the zero solution of the linear approximate system are obtained through analysis,so that the asymptotic stability of the zero solution of the system can be determined by the asymptotic stability of the zero solution of the linear approximate system.The parameter conditions of asymptotic stability of zero solution under nonlinear disturbance are given.

关 键 词：FIBONACCI数列 差分方程 非线性扰动 渐近稳定 

分 类 号：O192[理学—数学]