时间尺度上Nicholson苍蝇模型正殆周期解的存在性和指数稳定性
Existence and exponential stability of positive almost periodic solution for Nicholson's blowflies models on time scales
摘要：
本文首先给出了概周期时间尺度的一个新定义和时间尺度上殆周期函数的两个新定义，并研究了它们的一些基本性质。然后，作为应用，利用巴拿赫空间中的不动点定理和时标微积分理论，得到了一类时间尺度上Nicholson苍蝇模型正殆周期解的存在性和指数稳定性的充分条件.最后，我们提出了一个说明性的例子来显示所获得的结果的有效性。我们的结果表明，在一个简单的条件下，连续时间Nicholson的苍蝇模型和它们的离散时间模拟具有相同的动力学行为。
英文摘要：
In this paper, we first give a new definition of almost periodic time scales, two new definitions of almost periodic functions on time scales and investigate some basic properties of them. Then, as an application, by using the fixed point theorem in Banach space and the time scale calculus theory, we obtain some sufficient conditions for the existence and exponential stability of positive almost periodic solutions for a class of Nicholson's blowflies models on time scales. Finally, we present an illustrative example to show the effectiveness of obtained results. Our results show that under a simple condition the continuous-time Nicholson's blowflies models and their discrete-time analogue have the same dynamical behaviors.
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