一类二阶有理差分方程的解的渐近稳定性  

Asymptotic Stability of Solutions for a Class of Two-order Rational Difference Equation

作　　者：王丽 全卫贞 周敬人 苏丹 黄日娣 WANG Li;QUAN Wei-zhen;ZHOU Jing-ren;SU Dan;HUANG Ri-di(Department of Mathematic,Zhanjiang Preschool Education College,Zhanjiang 524037,China;Basic Education College,Lingnan Normal University,Zhanjiang 524037,China)

机构地区：[1]湛江幼儿师范专科学校数学系,广东湛江524037 [2]岭南师范学院基础教育学院,广东湛江524037

出　　处：《长春师范大学学报》2023年第4期1-6,共6页Journal of Changchun Normal University

基　　金：广东省普通高校特色创新项目“高阶差分方程的动力学及应用”(2020KTSCX351);广东省高等职业教育教学改革研究与实践项目“小学数学人文课堂教学实践的研究”(GDJG2019460);湛江市非资助科技攻关计划项目“几类高阶有理差分方程的解的研究”(2022B01198)。

摘　　要：使用有理差分方程的动力学理论、Routh-Hurwitz判别法和Schur-Cohn判别法等研究了二阶有理差分方程x_(n+1)=ax_(n-1)+b_(xn)+cx_(n-1)+d/x^(2)_(n),n=0,1,2,…的解■的渐近稳定性,其中,a,b,c,d∈R^(+),初始值x_(-1),x_0∈R^(+).并且给出平衡解是汇点、排斥点、鞍点、非双曲点等的条件.We study the asymptotic stability of the solutions for a class of the two-order rational difference equation x_(n+1)=ax_(n-1)+b_(xn)+cx_(n-1)+d/x^(2)_(n),n=0,1,2,…(a,b,c,d∈R+,x_(-1),x_(0)∈R^(+))by the dynamic theorem of the rational difference equation,the Routh-Hurwitz discriminant method and Schur-Cohn discriminant method.And the conditions for the equilibrium solution to be a sink point,a repulsive point,a saddle point and a non-hyperbolic point are given.

关 键 词：有理差分方程 Routh-Hurwitz判别法 Schur-Cohn判别法 渐近稳定性 

分 类 号：O175.12[理学—数学]