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Format: 2-2-3, EE4060 Introduction to Nonlinear Dynamics and Chaos1.DescriptionThis course introduces the student to the basic concepts of nonlinear dynamics and chaos via numerical simulations and electric circuits. The primary goal is to understand the bifurcations and steady-state behavior of nonlinear dynamical systems. The secondary goal is to study the phenomenon of chaos using Chua’s circuit and memristor-based chaotic circuits.2.PrerequisitesMA-235 [Differential Equations for Engineers]EE-2050 [Circuits I: Steady State] or EE-201 [Linear Networks: Steady State Analysis] 3.Materials (REQUIRED)1.Nonlinear Dynamics and Chaos With Applications to Physics, Biology, Chemistryand Engineering. Strogatz, Steven H. Perseus Books, Reading, Massachusetts.1994.2. A Route to Chaos Using Nonlinear Circuits. Muthuswamy, Bharathwaj. PDF will beprovided.4.Course Learning ObjectivesUpon successful completion of the course, the student will be able to:1.Describe the fundamental differences between linear and nonlinear dynamicalsystems and the importance of studying nonlinear dynamics.2.Define the different bifurcation phenomenon of nonlinear systems in one, two andthree dimensions3.Apply bifurcation analysis to study practical systems such as laser models, Josephsonjunctions, op-amp oscillator circuits and the nonlinear pendulum4.Understand limit cycles and Poincare Maps5.Understand basic concepts of chaos using Chua’s circuit6.Perform literature review7.Prepare short presentations5. Course Topics1.Introduction, differences between linear and nonlinear dynamics (1 class)2.Fixed Points and Stability (2 classes)3.Bifurcations in one dimensions (2 classes)4.Examples of bifurcations in one dimensions – laser models (1 class)5.Flows on a circle – oscillators (2 classes)6.Midterm review (1 class)7.Examples of oscillations–op-amp oscillator circuits,Josephson junctions andnonlinear pendulum (2 classes)8.The phase plane – linear systems, conservative systems, reversible systems, limitcycles and two-dimensional bifurcations (3 classes)9.Introduction to chaotic systems – Chua’s circuit (1 class)10.Memristor-based chaotic circuits (1 class)11.Tools for analyzing chaotic systems – period-doubling bifurcations, PoincareMaps revisit (1 class)12.Some properties of the strange attractor (1 class)13.Applications of Chaos (1 class)14.Final presentation guidelines and course wrap up (1 class)15.Group presentations (1 lab section)16.In-lab midterm (1 lab section)6.Prerequisites by Topic1.Understanding of linear constant coefficient ODEs2.Basic circuit analysisboratory Topicsboratory experiment details and requirements are described in [2].2.Students are expected to prepare for the lab by doing all required pre-lab activitiesand finishing all remaining requirements during the lab itself.3.Limited laboratory reports will be required.4.During weeks 9 and 10 of the course, students will have an opportunity to implementdifferent versions of Chua’s circuit. They will be required to perform a basic bifurcation analysis,visualize their system in Mathematica,simulate their circuit using MultiSim and implement their version of Chua’s circuit on a breadboard. They will also be required to give a final presentation on their work.Weekly Course Topics8.。
基于蔡氏电路的通信保密系统的设计(1)混沌理论自上世纪70年代兴起以来于和各学科相互渗透，成为了各个领域内研究的热点。
在信息科学高度发达的今天，信息安全也与人们的生活息息相关，信息安全、无损的传输不仅对于军事有重要的意义，对于人们生活的影响也是巨大的。
混沌系统所具有的系统对于初始参数、系统参数极为敏感、混沌信号类似噪声等特点均适用于通信保密。
利用混沌系统产生的混沌信号对信号进行掩盖保密传输具有可行性与实用性。
随着现代科学技术的发展，计算机仿真技术得到广泛的运用使得系统的设计分析更加容易，本文通过采用Multisim以及Matlab仿真技术对混沌电路以及通信保密系统的特性进行验证、分析。
蔡氏电路是混沌理论转化为实际电路模型的典型电路，蔡氏电路具有完整的混沌系统的特性，因此蔡氏电路得到广泛的研究与运用。
本文首先通过对蔡氏电路的微分方程组利用Matlab进行数值求解，绘出对应状态变量的相轨迹图。
利用Multisim搭建仿真电路原理图，同样绘出相应状态变量的相轨迹图，并与Matlab的结果进行对比，确保仿真原理图所选的元件参数能够满足蔡氏电路微分方程的特性。
在Multisim提供的仿真环境下，无法直接观察电感电流的波形图，本文通过串联一个微小电阻，通过观测电阻两侧的电压作为电感电流信号。
调整蔡氏电路的参数，研究不同参数下的电路特性，分析系统参数对混沌信号的影响情况。
混沌电路对电路的参数变化极为敏感，为增强通信保密系统的工作稳定性，采用有源元件对无源电感进行等效。
对等效后的蔡氏电路的电压信号进行调制、耦合同步等关键技术处理，并对耦合的情况进行分析，以此来说明基于蔡氏电路的通信掩盖保密系统的工作原理，以及信号的耦合同步对于本系统的必要性。
在对完成了电路的改进、信号调制、耦合同步后的主从结构的蔡氏电路，通过增加减法器、反相器等基本模块构成的信号通道的实现传输信号与混沌掩盖保密信号的叠加、消去。
为了检验设计的模拟信号的通信保密系统的运行效能及可靠性，选取了正弦信号、chirp电压信号等模拟信号作为测试信号，测试系统对模拟量的保密传输性能；选取了锯齿信号、方波信号作为数字信号的测试信号，测试系统对数字信号的保密传输性能。
