混沌阈值确定.doc

混沌阈值确定.doc基于Melnikov方法的混沌阈值确定
学院：通信工程学院 学生姓名：程远林 指导教师：李月教授
中文摘要:本文介绍了混沌理论及其研究历史。混沌系统对噪声免疫，对小信号敏感的特 性，这使得混沌系统在微弱信号检测领域具有很大的应有潜力。 混沌振子检测微弱信号具有
传统检测方法无法比拟的优越性，取得了很大的成就。如何准确的确定混沌系统的阈值成为 混沌振子检测微弱信号的关键问题。 在众多的混沌系统中，本文主要研究的是 Duffing方程
所描述的混沌系统。本文应用相轨迹图法和功率谱熵的方法来确定混沌系统的阈值， 并对两
种方法的效率和实际效果进行了比较。本文用这两种方法对非线性项含 x3和x3 x5的
Duffing方程进行分析，并确定了在频率「：三(,200 )上系统对应的的阈值。实验表明，两 种方法所得出的结果基本吻合。从实验过程和最后的结果中，我们可以看出：功率谱熵的方法 作为判别混沌系统运动状态的方法，具有较高的精度和效率。
关键词：混沌系统 阈值duffing 方程功率谱熵
Abstract： The paper introduces the research history and theory of chaos. The immunity to noise and the sensibility to weak signal make the chaos system very useful in weak signal detecting. Compari ng to traditi onal methods, the chaos system has its capacity in weak sig nal detect ion, and also has get great achievement. But h ow to determine the accuracy threshold of chaos system is the key problems of the use of chaos oscillator in weak sig nal detect ion. In many chaos systems, this paper mainly studied the chaos systems described by Duffing equation. In this paper, we use phase track and power spectral en tropy to detect the threshold of the chaos system, and make a comparis on betwee n the two methods. We use the two methods to study the Duffing equati on that
3 3 5
the nonlinear term include x or x x , and get the threshold of the chaos system
when the frequency ' (,200 ) . From the test, we get the conclusion that t