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課程簡介 Course Introduction
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開課年度學期 Year / Term
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113 學年度 第 1 學期
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開課班級 Department
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電機工程學系 電機四 電機碩合
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授課方式 Instructional Method
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課堂教學 、 中文
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課程電腦代號 Course Reference Number
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182047
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課程名稱(中文) Course Title(Chinese)
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混沌控制系統
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課程名稱(英文) Course Title(English)
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Chaos Control Systems
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學分數/時數 Credit Hours
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3 /
3
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必(選)修 Requirement / Elective Course
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選修
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授課老師 Instructor
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蕭鳳翔
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助教 Teaching Assistant
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上課時間 Meeting Time
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星期四，節次A、B、C
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上課教室 Classroom
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ZF301
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Office Hours
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| 獲獎及補助情形 Awards and Grants |
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| 聯合國永續發展目標 (SDGs跨域類別) Sustainable Development Goals, SDGs |
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課程目標 Learning Objectives
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教導學生明瞭混沌系統之特性及混沌運動所呈現之物理現象與形成機制；傳授學生描述與分析混沌系統的方法與技巧，期使學生能將所學的知識，應用於解釋與解決各個不同科技領域當中與混沌相關的課題。
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先修 ( 前置 ) 課程 Prerequisite
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| 彈性教學規劃 Flexible Teaching/Planning Schedules |
| ＊本課程實施16+2週彈性教學方案，其中第17、18週之彈性規劃如下： |
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課程大綱 Course Syllabus
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| 週次 Week |
課程單元大綱 Unit |
教學方式 Instructional Method/Style/Teaching Style |
參考資料或相關作業 References or Related Materials |
評量方式 Grading |
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1
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Introduction-What is chaos? Definition of the ‘deterministic chaos’, chaos and nonlinear dynamical system, brief history of chaos
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2
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Phenomenology of chaos-three examples of chaotic systems, period doubling phenomenon, bifurcation diagram, universal features of chaos
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3
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Phenomenology of chaos-other chaotic examples, summary of analytic tools；State-space dynamics of dynamical systems-state space, standard form of dynamical system, autonomous and non-autonomous systems, no-intersection rule, attractor
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4
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1-D state-space dynamics-fixed point and stability, linear stability analysis of fixed point, structural stability, dissipative system；2-D state-space dynamics-linear stability analysis of fixed point, eigenvalues & eigenvectors of the Jacobian matrix, dynamics of fixed point
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5
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2-D state-space dynamics-limit cycle, Poincare-Bendixson theorem, stability of limit cycle, Poincare map, Floquet multiplier, Lyapunov exponent, dissipative system in 2-D state space；Trajectories in 2-D state space-phase plane methods, phase portraits, conservative system
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6
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Trajectories in 2-D state space-index theorem, gradient system, Poincare-Bendixson theorem, trapping of limit cycle, applications in Biology； Bifurcation-normal form of bifurcation in 1-D & 2-D systems, saddle-node bifurcation, transcritical bifurcation, pitch-fork bifurcation, Hopf bifurcation
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7
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3-D state-space dynamics-linear stability analysis of fixed point, Poincare plane, stability of limit cycle, quasi-periodic motion, torus；Nonlinear stability-hyperbolic fixed point, persistence of hyperbolicity, Hartman & Grobman theorem, Lyapunov function, Lyapunov stability theorem
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8
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Routes to chaos (through bifurcation)
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9
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Diagnostic tools for chaos-Fourier spectrum, auto-correlation function；Diagnostic tools for chaos-Lyapunov exponent for trajectories, return map
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10
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Measures of chaos: (identifying and quantifying chaos) Fourier spectrum, correlation function, Lyapunov exponent, Poincare section, return-map method.
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11
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1-D iterated maps-Quadratic map, Feigenbaum constant, Li-Yorke theorem, Sarkovskii theorem, U-sequence, Schwarzian derivative & Singer’s theorem, critical point and supercycle, boundaries of attracting regions in bifurcation diagram；1-D iterated maps-size-scaling law, renormalization group theory, derivations of Feigenbaum’s universal constants, composition law, intermittency and crises revisited
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12
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1-D iterated maps-Tent map, symbolic dynamics, Baker’s map and Bernoulli shift, concept of topological equivalency, Bernoulli shift and chaotic trajectory, definition of ‘strong chaos’, statistical description of deterministic chaos
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13
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1-D iterated maps-Circle map, frequency locking, quasi-periodicity, Arnold’s tongues, Devil’s staircase；2-D iterated maps-Henon map, fractal attractor, Smale’s Horseshoe map, symbolic dynamics
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14
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2-D iterated maps-topological equivalency between Horseshoe map and Bernoulli shift operation, Horseshoe map and homoclinic intersection
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quiz (暫定)
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15
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Fractals-fractals in Nature, self-similarity, fractal dimension；Fractals-capacity dimension, Cantor set, mathematical fractal sets, Hausdorff dimension, correlation dimension, Lyapunov dimension
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16
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Fractal basin boundaries-fractal basin boundaries for pendulum system, fractal basin boundaries for Henon map, Mandelbrot set, Julia set；Nonlinear time series analysis-embedding theorem, state-space reconstruction technique
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17
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Nonlinear time series analysis-implementation and application；Software and demonstration of computer simulation
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18
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Final term project presentation
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單一課程對應校能力指標程度 The Degree to Which Single Course Corresponds to School Competence
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| 編號 No. |
校核心能力 School Core Competencies |
符合程度 Degree of conformity |
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單一課程對應系能力指標程度 The Degree to Which Single Course Corresponds to Department Competence
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| 編號 No. |
類別 Category |
系核心能力 Department Core Competencies |
符合程度 Degree of conformity |
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01
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系所
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運用數理、邏輯及基本電機之能力
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4
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02
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系所
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熟悉電機軟硬體專業技術之能力
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3
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03
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系所
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獨立思考、主動求知與研究創新之能力
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4
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04
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系所
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培養實作與分析實驗成果之能力
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1
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05
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系所
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理解社會責任與學術倫理之能力
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3
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06
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系所
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有效溝通表達與團隊合作之能力
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2
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07
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系所
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中英文語文及寫作之能力
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0
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08
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系所
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資訊蒐集、分析及彙整之能力
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0
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單一課程對應院能力指標程度 The Degree to Which Single Course Corresponds to College Competence
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| 編號 No. |
院核心能力 College Core Competencies |
符合程度 Degree of conformity |
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1
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語文能力
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2
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2
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溝通與合作能力
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4
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3
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創新與實踐能力
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1
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4
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專業知能
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3
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教科書或參考用書 Textbooks or Reference Books
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館藏書名 Library Books
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備註 Remarks
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自編講義
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※請尊重智慧財產權，不得非法影印教科書※
※ Please respect intellectual property rights and do not illegally photocopy textbooks. ※
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教學方法 Teaching Method
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教學方法 Teaching Method
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百分比 Percentage
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講述
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70 %
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討論
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30 %
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| 總和 Total |
100 % |
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成績評量方式 Grading
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| 評量方式 Grading |
百分比 Percentage |
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作業報告(short report)(3~4次)
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60 %
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期末計劃(final term project)
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40 %
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| 總和 Total |
100 % |
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課程大綱補充資料 Supplementary Material of Course Syllabus
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