Module 12: The Lorenz System

Folder description

Select the folder link above to access the video lectures and related content for this week. This week’s materials include the following:

  • 12A: Lorenz Attractor Simulation
  • 12B: Properties of the Lorenz Equations
  • 12C: Stability and Considerations
  • 12D: Strange Attractors
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Module at a Glance

Cell description

In this module we will use the Lorenz equations to motivate a study of chaos.

Objectives 

By the end of this module, you will be able to:

  • Summarize what it means for a system to be chaotic.
  • Apply bifurcation theory to the Lorenz system.
  • Classify attractors and strange attractor.
  • Construct secret messages using chaos.

How to complete this module:

  1. Watch the video lectures 12A through 12D.
  2. Complete the reading assignments.
  3. Respond to the discussion board question.
  4. Complete the quiz.
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Readings

Cell description

This week's reading assignment includes the following:

  • Strogatz, Steven HNonlinear Dynamics and Chaos with Student Solutions Manual: With Applications to Physics, Biology, Chemistry, and EngineeringCRC Press, 2018. 
    • Chapter 9 (pp. 309-348)
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Module 12 Discussion

Cell description

Watch this video about sending secret messages using chaos.

Discuss how chaos is applied in this demonstration and introduce new concepts about how chaos can be applied in innovative ways.

Name: Steven Strogatz - Nonlinear Dynamics and Chaos Part 5 (08:23)
Duration: 08:23
Added: 21 Aug 2019 02:53 PM
Added By: DIANE BANNER
Description:  
Tags: 625.718, stein

Due: Sunday 11:59 pm

 

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overflow: hidden;\"> \n  <div style=\"float: left; clear: left;\"> \n   <div style=\"float: left; clear: both;\"> \n    <iframe width=\"320\" height=\"240\" style=\"width: 604px; height: 386px;\" frameborder=\"0\" scrolling=\"no\" allowfullscreen=\"true\" allow=\"autoplay *; fullscreen *; encrypted-media *; camera *; microphone *;\" src=\"/webapps/osv-kaltura-bb_bb60/content/iframe.jsp?url=..%2FLtiMashupPlayIframeWrapperResponsive%3FplayUrl%3D%2Fbrowseandembed%2Findex%2Fmedia%2Fentryid%2F1_wmdschpe%2FshowDescription%2Ffalse%2FshowTitle%2Ffalse%2FshowTags%2Ffalse%2FshowDuration%2Ffalse%2FshowOwner%2Ffalse%2FshowUploadDate%2Ffalse%2FplayerSize%2F608x402%2FplayerSkin%2F30749451%2F&amp;thumbnail=https://cdnsecakmi.kaltura.com/p/1458241/sp/145824100/thumbnail/entry_id/1_wmdschpe/version/100001&amp;title=Steven+Strogatz+-+Nonlinear+Dynamics+and+Chaos+Part+5+%2808%3A23%29&amp;course_id=_194578_1&amp;content_id=_7048826_1\"></iframe> \n   </div> \n  </div> \n  <div id=\"container_0.19352922716542464\" class=\"hide-icon hidden\" style=\"margin-top: 30px; 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color: #333333;\" href=\"../LtiMashupPlayIframeWrapperResponsive?playUrl=/browseandembed/index/media/entryid/1_wmdschpe/showDescription/false/showTitle/false/showTags/false/showDuration/false/showOwner/false/showUploadDate/false/playerSize/608x402/playerSkin/30749451/&amp;course_id=_194578_1\" target=\"_blank\" title=\"Steven Strogatz - Nonlinear Dynamics and Chaos Part 5 (08:23)\"> Watch Media </a> \n    </div> \n   </div> \n   <div style=\"float: left; clear: right;\"> \n    <table style=\"margin: 0px !important; border-collapse: collapse;\"> \n     <tbody> \n      <tr style=\"vertical-align: top;\"> \n       <td style=\"padding: 0px !important;\"><b>Name:</b></td> \n       <td style=\"padding: 0px 0px 0px 20px !important;\"><b>Steven Strogatz - Nonlinear Dynamics and Chaos Part 5 (08:23)</b></td> \n      </tr> \n      <tr style=\"vertical-align: top;\"> \n       <td style=\"padding: 0px !important;\">Duration:</td> \n       <td style=\"padding: 0px 0px 0px 20px !important;\">08:23</td> \n      </tr> \n      <tr style=\"vertical-align: top;\"> \n       <td style=\"padding: 0px !important;\">Added:</td> \n       <td style=\"padding: 0px 0px 0px 20px !important;\">21 Aug 2019 02:53 PM</td> \n      </tr> \n      <tr style=\"vertical-align: top;\"> \n       <td style=\"padding: 0px !important;\">Added By:</td> \n       <td style=\"padding: 0px 0px 0px 20px !important;\">DIANE BANNER</td> \n      </tr> \n      <tr style=\"vertical-align: top;\"> \n       <td style=\"padding: 0px !important;\">Description:</td> \n       <td style=\"padding: 0px 0px 0px 20px !important;\">&nbsp;</td> \n      </tr> \n      <tr style=\"vertical-align: top;\"> \n       <td style=\"padding: 0px !important;\">Tags:</td> \n       <td style=\"padding: 0px 0px 0px 20px !important;\">625.718, stein</td> \n      </tr> \n     </tbody> \n    </table> \n   </div> \n  </div> \n </div> \n <p><strong style=\"font-family: 'Open Sans', sans-serif; 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overflow: hidden;\"> \n  <div style=\"float: left; clear: left;\"> \n   <div style=\"float: left; clear: both;\"> \n    <iframe width=\"320\" height=\"240\" style=\"width: 604px; height: 386px;\" frameborder=\"0\" scrolling=\"no\" allowfullscreen=\"true\" allow=\"autoplay *; fullscreen *; encrypted-media *; camera *; microphone *;\" src=\"/webapps/osv-kaltura-bb_bb60/content/iframe.jsp?url=..%2FLtiMashupPlayIframeWrapperResponsive%3FplayUrl%3D%2Fbrowseandembed%2Findex%2Fmedia%2Fentryid%2F1_wmdschpe%2FshowDescription%2Ffalse%2FshowTitle%2Ffalse%2FshowTags%2Ffalse%2FshowDuration%2Ffalse%2FshowOwner%2Ffalse%2FshowUploadDate%2Ffalse%2FplayerSize%2F608x402%2FplayerSkin%2F30749451%2F&amp;thumbnail=https://cdnsecakmi.kaltura.com/p/1458241/sp/145824100/thumbnail/entry_id/1_wmdschpe/version/100001&amp;title=Steven+Strogatz+-+Nonlinear+Dynamics+and+Chaos+Part+5+%2808%3A23%29&amp;course_id=_194578_1&amp;content_id=_7048826_1\"></iframe> \n   </div> \n  </div> \n  <div id=\"container_0.19352922716542464\" class=\"hide-icon hidden\" style=\"margin-top: 30px; float: left; clear: left;\"> \n   <div style=\"float: left; clear: left; margin-right: 8px;\"> \n    <div style=\"float: left; clear: both;\"> \n     <a class=\"lb\" style=\"text-decoration: none; color: #333333;\" href=\"../LtiMashupPlayIframeWrapperResponsive?playUrl=/browseandembed/index/media/entryid/1_wmdschpe/showDescription/false/showTitle/false/showTags/false/showDuration/false/showOwner/false/showUploadDate/false/playerSize/608x402/playerSkin/30749451/&amp;course_id=_194578_1\" target=\"_blank\" title=\"Steven Strogatz - Nonlinear Dynamics and Chaos Part 5 (08:23)\"> <img border=\"0\" src=\"https://cdnsecakmi.kaltura.com/p/1458241/sp/145824100/thumbnail/entry_id/1_wmdschpe/version/100001\"> </a> \n    </div> \n    <div style=\"float: left; clear: both; width: 100%; background: url('/images/ci/ng/rumble_button_back.gif') 50% 50%; padding-top: 2px; padding-bottom: 2px; text-decoration: none; color: #333333; text-align: center;\"> \n     <a class=\"lb\" style=\"text-decoration: none; color: #333333;\" href=\"../LtiMashupPlayIframeWrapperResponsive?playUrl=/browseandembed/index/media/entryid/1_wmdschpe/showDescription/false/showTitle/false/showTags/false/showDuration/false/showOwner/false/showUploadDate/false/playerSize/608x402/playerSkin/30749451/&amp;course_id=_194578_1\" target=\"_blank\" title=\"Steven Strogatz - Nonlinear Dynamics and Chaos Part 5 (08:23)\"> Watch Media </a> \n    </div> \n   </div> \n   <div style=\"float: left; clear: right;\"> \n    <table style=\"margin: 0px !important; border-collapse: collapse;\"> \n     <tbody> \n      <tr style=\"vertical-align: top;\"> \n       <td style=\"padding: 0px !important;\"><b>Name:</b></td> \n       <td style=\"padding: 0px 0px 0px 20px !important;\"><b>Steven Strogatz - Nonlinear Dynamics and Chaos Part 5 (08:23)</b></td> \n      </tr> \n      <tr style=\"vertical-align: top;\"> \n       <td style=\"padding: 0px !important;\">Duration:</td> \n       <td style=\"padding: 0px 0px 0px 20px !important;\">08:23</td> \n      </tr> \n      <tr style=\"vertical-align: top;\"> \n       <td style=\"padding: 0px !important;\">Added:</td> \n       <td style=\"padding: 0px 0px 0px 20px !important;\">21 Aug 2019 02:53 PM</td> \n      </tr> \n      <tr style=\"vertical-align: top;\"> \n       <td style=\"padding: 0px !important;\">Added By:</td> \n       <td style=\"padding: 0px 0px 0px 20px !important;\">DIANE BANNER</td> \n      </tr> \n      <tr style=\"vertical-align: top;\"> \n       <td style=\"padding: 0px !important;\">Description:</td> \n       <td style=\"padding: 0px 0px 0px 20px !important;\">&nbsp;</td> \n      </tr> \n      <tr style=\"vertical-align: top;\"> \n       <td style=\"padding: 0px !important;\">Tags:</td> \n       <td style=\"padding: 0px 0px 0px 20px !important;\">625.718, stein</td> \n      </tr> \n     </tbody> \n    </table> \n   </div> \n  </div> \n </div> \n <p><strong style=\"font-family: 'Open Sans', sans-serif; font-size: 13px;\">Due: Sunday 11:59 pm</strong></p> \n <p style=\"font-family: inherit; text-shadow: none !important; letter-spacing: normal !important; margin: 0px 0px 1em; padding: 0px; border: 0px; outline: 0px; font-weight: inherit; font-style: inherit; font-size: 13px;\"></p> \n <p><strong>&nbsp;</strong></p> \n</div>\n  </div>\n\n <div id=\"_7048826_1previewModule\" class=\"moduleSample\">\n </div>\n",
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        "title": "Module 12 Discussion",
        "body": "\n    <div> \n <p>Watch this video about sending secret messages using chaos.</p> \n <p>Discuss how chaos is applied in this demonstration and introduce new concepts about how chaos can be applied in innovative ways.</p> \n <div> \n  <div> \n   <div> \n     \n   </div> \n  </div> \n  <div id=\"container_0.19352922716542464\"> \n   <div> \n    <div> \n     <a href=\"../LtiMashupPlayIframeWrapperResponsive?playUrl=/browseandembed/index/media/entryid/1_wmdschpe/showDescription/false/showTitle/false/showTags/false/showDuration/false/showOwner/false/showUploadDate/false/playerSize/608x402/playerSkin/30749451/&amp;course_id=_194578_1\" target=\"_blank\" title=\"Steven Strogatz - Nonlinear Dynamics and Chaos Part 5 (08:23)\">  </a> \n    </div> \n    <div> \n     <a href=\"../LtiMashupPlayIframeWrapperResponsive?playUrl=/browseandembed/index/media/entryid/1_wmdschpe/showDescription/false/showTitle/false/showTags/false/showDuration/false/showOwner/false/showUploadDate/false/playerSize/608x402/playerSkin/30749451/&amp;course_id=_194578_1\" target=\"_blank\" title=\"Steven Strogatz - Nonlinear Dynamics and Chaos Part 5 (08:23)\"> Watch Media </a> \n    </div> \n   </div> \n   <div> \n    <table> \n     <tbody> \n      <tr> \n       <td><b>Name:</b></td> \n       <td><b>Steven Strogatz - Nonlinear Dynamics and Chaos Part 5 (08:23)</b></td> \n      </tr> \n      <tr> \n       <td>Duration:</td> \n       <td>08:23</td> \n      </tr> \n      <tr> \n       <td>Added:</td> \n       <td>21 Aug 2019 02:53 PM</td> \n      </tr> \n      <tr> \n       <td>Added By:</td> \n       <td>DIANE BANNER</td> \n      </tr> \n      <tr> \n       <td>Description:</td> \n       <td>&nbsp;</td> \n      </tr> \n      <tr> \n       <td>Tags:</td> \n       <td>625.718, stein</td> \n      </tr> \n     </tbody> \n    </table> \n   </div> \n  </div> \n </div> \n <p><strong>Due: Sunday 11:59 pm</strong></p> \n  \n <p><strong>&nbsp;</strong></p> \n</div>\n  "
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