【作者】 王亚男；

【导师】 徐勇；

【作者基本信息】 河北工业大学 ， 应用数学， 2010， 硕士

【摘要】 混沌作为一种复杂的非线性运动行为，在生物学、物理学、化学、工程学和信息学等领域得到了广泛的研究。马蹄型混沌吸引子生成的理论研究和电路实现己成为混沌研究领域的一个新方向。为了获得马蹄型混沌吸引子需要对系统方程中的非线性函数进行特殊设计，通常采用的函数构造方法有多转折分段线性函数法、阶段函数法、滞后函数法和饱和函数法等。本文首先研究了吕金虎等人提出的用饱和函数逼近生成马蹄型混沌吸引子的方法，包括生成一维n-马蹄，二维n×m-格子马蹄以及三维n×m×l-格子马蹄混沌吸引子。这种方法是利用饱和函数控制一个三维自治系统生成多马蹄混沌吸引子。本文考虑用光滑的反正切函数来替代饱和函数。本文在第四部分提出了用反正切函数生成马蹄型混沌吸引子的方法，包括用反正切函数和分段的反正切函数生成马蹄型混沌吸引子。文中从对称性、耗散性、稳定性等方面分析了反正切函数和分段反正切函数生成马蹄型混沌吸引子的可能，并通过计算机仿真得到了混沌吸引子。更多还原

【Abstract】 Chaotic systems are well known for their very complex nonlinear systems, and have been intensivelystudied in various fields such as biology, physics, chemistry, engineering and information. Multiscroll chaoticattractor generating theory research and chaotic circuit implementation have become a new direction ofChaotic systems research. In order to obtain multiscroll chaotic attractor, one needs to have a special designon nonlinear function usually by the way of function constructing such as turning piecewise linear functionmethod, stage function method, lag function method and saturated function method, etc.This paper firstly makes a study of what has been brought forward by Lu Jinhu, in which saturatedfunction approximation would generate a multiscroll chaotic attractor, including one-dimensional n -scroll,two-dimensional n×m -grid scroll, and 3-D n×m×l -grid scroll chaotic attractors. This method is to usesaturated function to control a 3d autonomy system, as a result, to generate multiscroll chaotic attractor. Thispaper will make a study of using smooth inverse tangent function to replace saturated function.In the fourth part of this paper, it puts forward the method of using inverse tangent functions––including inverse tangent function and segmentation inverse tangent functions–– to generate multiscrollchaotic attractor. It also analyzes the possibility of this method from the aspects of symmetry, dissipative sexand stability. And it has get the chaotic attractor through computer simulation.更多还原