差分方程周期解的理论和应用

【作者】 傅湘陵；

【导师】 周展；

【作者基本信息】 湖南大学 ， 应用数学， 2002， 硕士

【摘要】 本论文分三章，分别讨论了几个差分系统(方程)的周期解的存在性与稳定性。 第一章，考虑具时滞反馈非线性差分系统 其中为McCulloch-Pitts型信号函数，参数ρ＞0，σ∈R。讨论了该系统的稳定的2k周期解，并得到了系统在参数(β，ρ)的某些区域内的一个稳定的2k+1周期解，所得结论推广与扩充了[29]中作者的结论，并由此推断[29]中结论为我们所得结论的特殊情形。 第二章，讨论m维具时滞反馈非线性差分系统 其中为McCulloch-Pitts型符号函数。研究了当m分别为奇、偶数时周期解的存在性与稳定性，得到了当m分别为奇、偶数时，系统的一个稳定的2k、mk周期解，所得结论推广了[28]中作者的结果。 第三章，考虑具周期系数的单物种竞争模型 其中{λ(n)}，{α(n)}都是以ω为最小正周期的周期序列，研究了该方程的正解的持久性与周期解的存在性和稳定性，所得结论拓广了[17，18，19]中的工作。更多还原

【Abstract】 This paper consists of three chapters, in which several difference systems have been investigated .In chapter 1, we study the stable periodic solution of nonlinear difference system with delayed feedbackwhere is the so-calledMcCulloch-Pitts signal transmission function, p>0,R are two parameters. Wefirst study the stable 2?periodic of (1), and our results concluded the theorems in [29] as a special case. Moreover, we get a 2k+l-periodic solution of (1) for some region of(, p). This periodic solution is also asymptotically stable.In chapter 2, we investigate the w-dimensional nonlinear difference system with delayed feedbackwhere is the McCulloch-Pitts signaltransmission function, and obtain a stable 2-period solution when m is even and a stable m/c-periodic solution when m is odd.Last, in chapter 3, we consider the discrete-time competition model with periodic coefficientswhere P>0 is constant, -periodic sequences. The persistence ofthe positive solutions of (3) and sufficient conditions for the existence and stability of the positive periodic solution of (3) are obtained, our results extended the corresponding work in [17,18,19].更多还原