一个超混沌系统在MATLAB环境下的仿真实现

毕业设计（论文）题目一个超混沌系统在MATLAB环境下的仿真实现系（院）物理与电子科学系专业物理学班级2005级1班学生姓名XXX学号2005080119指导教师XXX职称二〇一一年六月十八日独创声明本人郑重声明：所呈交的毕业设计(论文)，是本人在指导老师的指导下，独立进行研究工作所取得的成果，成果不存在知识产权争议。尽我所知，除文中已经注明引用的内容外，本设计（论文）不含任何其他个人或集体已经发表或撰写过的作品成果。对本文的研究做出重要贡献的个人和集体均已在文中以明确方式标明。本声明的法律后果由本人承担。作者签名:二〇一〇年六月一十八日毕业设计（论文）使用授权声明本人完全了解滨州学院关于收集、保存、使用毕业设计（论文）的规定。本人愿意按照学校要求提交学位论文的印刷本和电子版，同意学校保存学位论文的印刷本和电子版，或采用影印、数字化或其它复制手段保存设计（论文）；同意学校在不以营利为目的的前提下，建立目录检索与阅览服务系统，公布设计（论文）的部分或全部内容，允许他人依法合理使用。（保密论文在解密后遵守此规定）作者签名:二〇一〇年六月一十八日I一个超混沌系统在MATLAB环境下的仿真实现摘要在混沌、超混沌理论研究成果的基础上，利用外加驱动信号方法改进一个四阶超混沌系统，通过对外界驱动信号频率的控制，实现系统的动力学特性。对新构建的超混沌系统的特性进行了详细分析，包括验证其超混沌性质，相空间轨迹分析，Lyapunov指数谱分析等，仿真结果关键词：超混沌；lyapunov指数；EWB；超混沌电路；MATLABIIAhyperchaoscircuitwassimulatedinMATLABsimulationAbstractBasedonchaoticandthehyperchaotictheoryresearch,byusingplussingadrivesignaltothefourth-orderhyperchaossystemtoimprovethefourth-orderhyperchaossystem,throughtocontroltheexternaldrivesignalfrequency,realizeingthesystem’dynamiccharacteristics.Theconstructionofthenewcharacteristicsofhyperchaossystemareanalyzedindetail,includingitshyperchaosnature,pathanalysis,phasespaceLyapunovindexandbifurcationdiagramanalysisandsimulationresultsshowthatthesystemcharacteristics.Isabundant.Usingthesignalfrequencycontrolanddrivecancompletelyaccuratecontroloftheentiresystemdynamicscharacteristic.Finally,designasimulatedcircuit,andsimulatinEWBenvironment,throughthecomparisonofsimulationresultsbetweenMATLABandEWB,Furtherverifytheconsistencybetweenexperimentresultsandnumericalsimulation.Keyword：hyperchaos；Lyapunovexponents；bifurcation；hyperchaoticCircuiti目录引言······································································································1第一章动力系统形态及其分析···································································21.1动力系统···························································································21.1.1动力学系统的基本概念······································································21.1.2几种常见的平衡态············································································41.1.3吸引子和结构稳定性·········································································61.2分岔································································································71.2.1分岔的基本概念···············································································71.2.2非线性映射及其分岔·········································································8第二章混沌系统判别方法讨论··································································102.1混沌的特性及其判别方法·····································································102.1.1混沌的定义····················································································102.1.2混沌运动的基本特征········································································112.2超混沌特性及其判别方法·····································································112.3混沌电路研究方法··············································································12第三章一个新的超混沌系统设计及其性能分析·············································123.1超混沌系统·······················································································123.1.1一个四阶的超混沌系统·····································································123.1.2平衡点及稳定性分析········································································133.1.3系统相空间轨迹分析········································································133.2一个新的超混沌系统···········································································153.2.1一个新的超混沌系统的设计·······························································153.2.2系统相空间轨迹分析········································································163.2.3李雅普诺夫指数分析········································································173.2.4系统的电路设计和实验结果·······························································17结论·····································································································23参考文献·······························································································24ii谢辞·····································································································251引言混沌科学是一门新兴的学科，混沌（Chaos）是一种貌似无规则的运动，指在确定性非线性系统中，不需要附加任何随机因素亦可出现的行为（内在随机性）。混沌系统的最大特点就在于系统的演化对初始条件的十分敏感，因此从长期意义上看，系统的未来行为是不可预测的。2第一章动力系统形态及其分析1.1动力系统1.1.1动力学系统的基本概念下面以一个简单的二阶非线性常微分方程描述的非线性动力系统为例，介绍动力系统中的一些基本概念。二阶非线性常微分方程记为),(...xxfx1-(1)式中，x表示质点的位置，dtdxx/.表示其速度，..x为其加速度，),(.xxf是作用于单位质点上的力。1-(1)式中的x、.x表征了该系统任意时刻t的运动状态，称之为相。x、.x的数值则对应着平面),(.xx上的一个点，并把平面),(.xx称之为相平面。在相平面中，引入轨线的概念，将一维系统化为二维系统。为此，令.xy，则1-（1）式化为常微分方程组),(..yxfyyx1-(2)由式1-(2)中的)(tx和)(ty，可知在相平面),(yx上为一曲线簇。它定性的描述了系统状态在全部运动状态时间（从t到t）内的变化。其轨线上常用箭头来表示时间t增加的方向。1-(2)式更一般的形式为图1叉形分岔图2霍夫分岔图3鞍-结分岔1.2.2非线性映射及其分岔我们从最简单的一维映射开始，考虑一般形式的线段I到自身的映射，即一维ImReImReImRe3第二章混沌系统判别方法讨论2.1混沌的特性及其判别方法混沌是非线性动力学系统所特有的一种运动形式，它广泛地存在于自然界，诸如物理﹑化学﹑生物学﹑地质学以及社会科学等各种科学领域。混沌实际上并不“混”，既非纯粹的“无序”，又非纯粹的“有序”，而是两者的统一，具有内在的规律性和普适性，内部包含着丰富的信息资源及可开发应用的潜能。-30-20-100102030-30-20-10010203040xy-30-20-1001020300102030405060xz(a)x-y相平面相轨迹图(b)x-z相平面相轨迹图图3.1系统3-(1)的相平面轨迹4结论对系统的