一类高阶有理差分方程的全局渐近稳定性
The global asymptotic stability of a higher-order difference equation
云南民族大学学报:自然科学版,2015,24(1):37-42

张永玲 ZYL

摘要


研究差分方程xn+1=(xn+αxn-kAxn+Bxn-k),n=0,1,2,…,所有正解的局部稳定性、素二周期解、有界性、不变区间和全局渐近稳定性,其中α,A,B∈(0,∞),k∈{1,2,3,…},初始条件x-k,…,x0是任意的正整数.获得了此方程的唯一正平衡点是全局渐近稳定的. This paper investigates the local stability,prime period-two solutions,boundedness,invariant intervals,and the global asymptotic stability of all positive solutions of the following difference equation(xn+1=(xn+αxn-kAxn+Bxn-k),n=0,1,2,…,)where α,A,B∈(0,∞),k∈{1,2,3,…},and the initial conditions x-k,…,x(0∈0,∞).It concludes that the unique equilibrium of the equation is globally asymptotically stable under certain conditions.

参考



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