Select the folder link above to access the video lectures and related content for this week. This week’s materials include the following:
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"html": "\n\n<img alt=\"Content Folder\" src=\"/images/ci/sets/set01/folder_on.gif\" class=\"item_icon\">\n\n<div class=\"item clearfix\" id=\"_7048803_1\">\n\n <h3 id=\"anonymous_element_9\">\n <span class=\"reorder editmode hideme\"><span><img src=\"/images/ci/icons/generic_updown.gif\" alt=\"\"></span></span>\n\n\n <a href=\"/webapps/blackboard/content/listContent.jsp?course_id=_194578_1&content_id=_7048803_1\"><span style=\"color:#0067AC;\">Lectures and Related Content</span></a>\n </h3><a href=\"#\" class=\"ally-alternative-formats ally-prominent-af-download-button\" data-ally-external-id=\"content:_7048803_1\" data-ally-upload-type=\"RichContent\" title=\"Alternative formats\" style=\"display: none\">\n <span class=\"ally-sr-only\">\n \n\n\n Lectures and Related Content\n </span>\n</a>\n\n \n </div>\n\n\n\n<div class=\"details\">\n <div class=\"vtbegenerated\"> \n <p>Select the folder link above to access the video lectures and related content for this week. This week’s materials include the following:</p> \n <ul> \n <li>10A: Saddle Node Bifurcation</li> \n <li>10B: Transcritical and Pitchfork Bifurcations</li> \n <li>10C: Supercritical Hopf Bifurcations</li> \n <li>10D: Subcritical Hopf Bifurcations</li> \n </ul> \n</div>\n </div>\n\n <div id=\"_7048803_1previewModule\" class=\"moduleSample\">\n </div>\n",
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}In this module we'll extend an understanding of bifurcations to two dimensional systems; observe changes in fixed points or limit cycles as parameters are varied.
Objectives
By the end of this module, you will be able to:
How to complete this module:
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"html": "\n\n<img alt=\"Item\" src=\"/images/ci/sets/set01/document_on.gif\" class=\"item_icon\">\n\n<div class=\"item clearfix\" id=\"_7048802_1\">\n\n <h3 id=\"anonymous_element_8\">\n <span class=\"reorder editmode hideme\"><span><img src=\"/images/ci/icons/generic_updown.gif\" alt=\"\"></span></span>\n\n\n\n <span style=\"color:#0067ac;\">Module at a Glance</span>\n </h3><a href=\"#\" class=\"ally-alternative-formats ally-prominent-af-download-button\" data-ally-external-id=\"content:_7048802_1\" data-ally-upload-type=\"RichContent\" title=\"Alternative formats\" style=\"display: none\">\n <span class=\"ally-sr-only\">\n \n\n\n\n Module at a Glance\n </span>\n</a>\n\n \n </div>\n\n\n\n<div class=\"details\">\n <div class=\"vtbegenerated\"> \n <p><br></p> \n <p>In this module we'll extend an understanding of bifurcations to two dimensional systems; observe changes in fixed points or limit cycles as parameters are varied.</p> \n <p><strong><span style=\"color: #0067ac;\">Objectives</span></strong> </p> \n <p>By the end of this module, you will be able to:</p> \n <ul> \n <li>Identify a saddle point bifurcation and understand the dynamics associated with this type of fixed point.</li> \n <li>Identify a transcritical bifurcation and understand the dynamics associated with this type of fixed point.</li> \n <li>Identify pitchfork bifurcations and understand the dynamics associated with this type of fixed point.</li> \n <li>Examine the dynamics of a Hopf bifurcation.</li> \n </ul> \n <p><span style=\"color: #0067ac;\"><strong>How to complete this module:</strong></span></p> \n <ol> \n <li>Watch the video lectures 10A through 10D.</li> \n <li>Complete the reading assignments.</li> \n <li>Respond to the discussion board question.</li> \n <li>Complete the assignment.</li> \n </ol> \n</div>\n </div>\n\n <div id=\"_7048802_1previewModule\" class=\"moduleSample\">\n </div>\n",
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}This week's reading assignment includes the following:
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"html": "\n\n<img alt=\"Tools Area\" src=\"/webapps/ATLS-AresCourseReserves-bb_bb60/images/ares.gif\" class=\"item_icon\">\n\n<div class=\"item clearfix\" id=\"_7048804_1\">\n\n <h3 id=\"anonymous_element_10\">\n <span class=\"reorder editmode hideme\"><span><img src=\"/images/ci/icons/generic_updown.gif\" alt=\"\"></span></span>\n\n\n <a href=\"/webapps/blackboard/content/launchLink.jsp?course_id=_194578_1&content_id=_7048804_1&mode=view\"><span style=\"color:#0067AC;\">Readings</span></a>\n </h3><a href=\"#\" class=\"ally-alternative-formats ally-prominent-af-download-button\" data-ally-external-id=\"content:_7048804_1\" data-ally-upload-type=\"RichContent\" title=\"Alternative formats\" style=\"display: none\">\n <span class=\"ally-sr-only\">\n \n\n\n Readings\n </span>\n</a>\n\n \n </div>\n\n\n\n<div class=\"details\">\n <div class=\"vtbegenerated\"> \n <p><span style=\"font-size: 13px;\">This week's reading assignment includes the following:</span></p> \n <ul> \n <li><span data-contrast=\"auto\" xml:lang=\"EN-US\">Strogatz, Steven H</span><span data-contrast=\"auto\" xml:lang=\"EN-US\">. </span><em><span data-contrast=\"none\" xml:lang=\"EN-US\">Nonlinear Dynamics and Chaos with Student Solutions Manual: With Applications to Physics, Biology, Chemistry, and Engineering</span></em><span data-contrast=\"auto\" xml:lang=\"EN-US\">. </span><span data-contrast=\"auto\" xml:lang=\"EN-US\">CRC Press, 2018.</span><span data-ccp-props=\"{"134233279":true,"469777462":[360],"469777927":[0],"469777928":[1]}\"> </span> \n <ul> \n <li><span data-contrast=\"auto\" xml:lang=\"EN-US\">Chapter 8</span><span data-contrast=\"auto\" xml:lang=\"EN-US\"> (pp. 244-263)</span></li> \n </ul> </li> \n </ul> \n</div>\n </div>\n\n <div id=\"_7048804_1previewModule\" class=\"moduleSample\">\n </div>\n",
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"body": "\n <div> \n <p><span>This week's reading assignment includes the following:</span></p> \n <ul> \n <li><span data-contrast=\"auto\" xml:lang=\"EN-US\">Strogatz, Steven H</span><span data-contrast=\"auto\" xml:lang=\"EN-US\">. </span><em><span data-contrast=\"none\" xml:lang=\"EN-US\">Nonlinear Dynamics and Chaos with Student Solutions Manual: With Applications to Physics, Biology, Chemistry, and Engineering</span></em><span data-contrast=\"auto\" xml:lang=\"EN-US\">. </span><span data-contrast=\"auto\" xml:lang=\"EN-US\">CRC Press, 2018.</span><span data-ccp-props=\"{"134233279":true,"469777462":[360],"469777927":[0],"469777928":[1]}\"> </span> \n <ul> \n <li><span data-contrast=\"auto\" xml:lang=\"EN-US\">Chapter 8</span><span data-contrast=\"auto\" xml:lang=\"EN-US\"> (pp. 244-263)</span></li> \n </ul> </li> \n </ul> \n</div>\n "
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}Due: Tuesday 11:59 pm
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"body": "\n <div> \n <ul> \n <li>Complete the following problems from chapter 8 of the Strogatz textbook: <strong>8.1.2</strong> (4 pts.); <strong>8.1.3</strong> (4 pts.); <strong>8.1.4</strong> (4 pts.); <strong>8.1.5</strong> (4 pts.); <strong>8.2.1</strong> (5 pts.)</li> \n <li>Upload your work in PDF format by selecting the link above.</li> \n </ul> \n \n <div> \n \n </div> \n <p><strong>Due: Tuesday 11:59 pm</strong></p> \n \n</div>\n "
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}Watch this video about the Belousov-Zhabotinsky reaction – an example of an oscillating chemical reaction. Feel free to skip past the chemistry. Work through the example on p.259 in the text and then 8.3.1. What does this example - and video - tell us about potential bifurcations?
We are starting to think like applied mathematicians!
| Name: | Recreating One of the Weirdest Reactions |
| Duration: | |
| Added: | 21 Aug 2019 09:21 AM |
| Added By: | DIANE BANNER |
| Description: |
Video CreditNile, Red. (2018 Jul. 16). Recreating One of…
|
| Tags: | stein, 625.718 |
| Name: | Three-way Coupled Pendulum & Neutrinos What the Physics (05:05) |
| Duration: | 05:05 |
| Added: | 21 Aug 2019 09:05 AM |
| Added By: | DIANE BANNER |
| Description: | |
| Tags: | stein, 625.718 |
Due: Sunday 11:59 pm
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"html": "\n\n<img alt=\"Course Link\" src=\"/images/ci/sets/set01/discussion_on.gif\" class=\"item_icon\">\n\n<div class=\"item clearfix\" id=\"_7048805_1\">\n\n <h3 id=\"anonymous_element_12\">\n <span class=\"reorder editmode hideme\"><span><img src=\"/images/ci/icons/generic_updown.gif\" alt=\"\"></span></span>\n\n <img title=\"linked item\" alt=\"linked item\" src=\"/images/ci/icons/file_link_ti.png\" class=\"item_icon\">\n\n <a href=\"/webapps/blackboard/content/launchLink.jsp?course_id=_194578_1&content_id=_7048805_1&mode=view\"><span style=\"color:#0067ac;\">Module 10 Discussion</span></a>\n </h3><a href=\"#\" class=\"ally-alternative-formats ally-prominent-af-download-button\" data-ally-external-id=\"content:_7048805_1\" data-ally-upload-type=\"RichContent\" title=\"Alternative formats\" style=\"display: none\">\n <span class=\"ally-sr-only\">\n \n\n \n\n Module 10 Discussion\n </span>\n</a>\n\n \n </div>\n\n\n\n<div class=\"details\">\n <div class=\"vtbegenerated\"> \n <p>Watch this video about the Belousov-Zhabotinsky reaction – an example of an oscillating chemical reaction. Feel free to skip past the chemistry. Work through the example on p.259 in the text and then 8.3.1. <br>What does this example - and video - tell us about potential bifurcations?</p> \n <ul> \n <li>How would the manifestation of a closed orbit be observed in a chemical reaction?</li> \n <li>Point out different bifurcations, if they are observed in the chemical reaction - and point to a frame of the video.</li> \n <li>Discuss how these trace back to characteristics of the Jacobian.</li> \n <li>Can we apply the Poincaré-Bendixson theorem?</li> \n </ul> \n <p>We are starting to think like applied mathematicians! </p> \n <div style=\"width: 604px; overflow: hidden;\"> \n <div style=\"float: left; clear: left;\"> \n <div style=\"float: left; clear: both;\"> \n <div style=\"width: 604px; 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_bgdjnvwr%2FshowDescription%2Ffalse%2FshowTitle%2Ffalse%2FshowTags%2Ffalse%2FshowDuration%2Ffalse%2FshowOwner%2Ffalse%2FshowUploadDate%2Ffalse%2FplayerSize%2F608x402%2FplayerSkin%2F30749451%2F&thumbnail=https://cdnsecakmi.kaltura.com/p/1458241/sp/145824100/thumbnail/entry_id/1_bgdjnvwr/version/100001&title=Recreating+One+of+the+Weirdest+Reactions&course_id=_194578_1&content_id=_7048805_1\"></iframe> \n </div> \n </div> \n <div id=\"container_0.047868895784856536\" 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_bgdjnvwr/showDescription/false/showTitle/false/showTags/false/showDuration/false/showOwner/false/showUploadDate/false/playerSize/608x402/playerSkin/30749451/&course_id=_194578_1\" target=\"_blank\" title=\"Recreating One of the Weirdest Reactions\"> <img border=\"0\" src=\"https://cdnsecakmi.kaltura.com/p/1458241/sp/145824100/thumbnail/entry_id/1_bgdjnvwr/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_bgdjnvwr/showDescription/false/showTitle/false/showTags/false/showDuration/false/showOwner/false/showUploadDate/false/playerSize/608x402/playerSkin/30749451/&course_id=_194578_1\" target=\"_blank\" title=\"Recreating One of the Weirdest Reactions\"> 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>Recreating One of the Weirdest Reactions</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;\"> </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 09:21 AM</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;\"> \n <div title=\"Video CreditNile, Red. (2018 Jul. 16). Recreating One of the Weirdest Reactions [Video File]. Retrieved from https://www.youtube.com/watch?v=LL3kVtc-4vY\">\n Video CreditNile, Red. (2018 Jul. 16). Recreating One of… \n </div> </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;\">stein, 625.718</td> \n </tr> \n </tbody> \n </table> \n </div> \n </div> \n </div> \n </div> \n </div> \n <div id=\"container_0.6857602639382102\" 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_t8t5u84g/showDescription/false/showTitle/false/showTags/false/showDuration/false/showOwner/false/showUploadDate/false/playerSize/608x402/playerSkin/30749451/&course_id=_194578_1\" target=\"_blank\" title=\"Three-way Coupled Pendulum & Neutrinos What the Physics (05:05)\"> <img border=\"0\" src=\"https://cdnsecakmi.kaltura.com/p/1458241/sp/145824100/thumbnail/entry_id/1_t8t5u84g/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_t8t5u84g/showDescription/false/showTitle/false/showTags/false/showDuration/false/showOwner/false/showUploadDate/false/playerSize/608x402/playerSkin/30749451/&course_id=_194578_1\" target=\"_blank\" title=\"Three-way Coupled Pendulum & Neutrinos What the Physics (05:05)\"> 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>Three-way Coupled Pendulum & Neutrinos What the Physics (05:05)</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;\">05:05</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 09:05 AM</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;\"> </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;\">stein, 625.718</td> \n </tr> \n </tbody> \n </table> \n </div> \n </div> \n </div> \n <p><br></p> \n <div style=\"font-family: 'Open Sans', sans-serif; text-shadow: none !important; letter-spacing: normal !important;\"> \n <strong style=\"font-family: inherit; text-shadow: none !important; letter-spacing: normal !important; margin: 0px; padding: 0px; border: 0px; outline: 0px; font-weight: bold; font-style: inherit; font-size: 13px;\"><span data-contrast=\"auto\" xml:lang=\"EN-US\" style=\"font-family: inherit; text-shadow: none !important; letter-spacing: normal !important; margin: 0px; padding: 0px; border: 0px; outline: 0px; font-weight: inherit; font-style: inherit; font-size: 13px;\"></span></strong> \n </div> \n <p><strong style=\"font-family: 'Open Sans', sans-serif; text-shadow: none !important; letter-spacing: normal; margin: 0px; padding: 0px; border: 0px; outline: 0px; font-weight: bold; font-style: normal; font-size: 13px; color: #000000; font-variant-ligatures: normal; font-variant-caps: normal; orphans: 2; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: #ffffff; text-decoration-style: initial; text-decoration-color: initial;\">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</div>\n </div>\n\n <div id=\"_7048805_1previewModule\" class=\"moduleSample\">\n </div>\n",
"url": "https://blackboard.jhu.edu/webapps/blackboard/content/launchLink.jsp?course_id=_194578_1&content_id=_7048805_1&mode=view",
"title": "Module 10 Discussion"
},
"html": "\n\n<img alt=\"Course Link\" src=\"/images/ci/sets/set01/discussion_on.gif\" class=\"item_icon\">\n\n<div class=\"item clearfix\" id=\"_7048805_1\">\n\n <h3 id=\"anonymous_element_12\">\n <span class=\"reorder editmode hideme\"><span><img src=\"/images/ci/icons/generic_updown.gif\" alt=\"\"></span></span>\n\n <img title=\"linked item\" alt=\"linked item\" src=\"/images/ci/icons/file_link_ti.png\" class=\"item_icon\">\n\n <a href=\"/webapps/blackboard/content/launchLink.jsp?course_id=_194578_1&content_id=_7048805_1&mode=view\"><span style=\"color:#0067ac;\">Module 10 Discussion</span></a>\n </h3><a href=\"#\" class=\"ally-alternative-formats ally-prominent-af-download-button\" data-ally-external-id=\"content:_7048805_1\" data-ally-upload-type=\"RichContent\" title=\"Alternative formats\" style=\"display: none\">\n <span class=\"ally-sr-only\">\n \n\n \n\n Module 10 Discussion\n </span>\n</a>\n\n \n </div>\n\n\n\n<div class=\"details\">\n <div class=\"vtbegenerated\"> \n <p>Watch this video about the Belousov-Zhabotinsky reaction – an example of an oscillating chemical reaction. Feel free to skip past the chemistry. Work through the example on p.259 in the text and then 8.3.1. <br>What does this example - and video - tell us about potential bifurcations?</p> \n <ul> \n <li>How would the manifestation of a closed orbit be observed in a chemical reaction?</li> \n <li>Point out different bifurcations, if they are observed in the chemical reaction - and point to a frame of the video.</li> \n <li>Discuss how these trace back to characteristics of the Jacobian.</li> \n <li>Can we apply the Poincaré-Bendixson theorem?</li> \n </ul> \n <p>We are starting to think like applied mathematicians! </p> \n <div style=\"width: 604px; overflow: hidden;\"> \n <div style=\"float: left; clear: left;\"> \n <div style=\"float: left; clear: both;\"> \n <div style=\"width: 604px; 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_bgdjnvwr%2FshowDescription%2Ffalse%2FshowTitle%2Ffalse%2FshowTags%2Ffalse%2FshowDuration%2Ffalse%2FshowOwner%2Ffalse%2FshowUploadDate%2Ffalse%2FplayerSize%2F608x402%2FplayerSkin%2F30749451%2F&thumbnail=https://cdnsecakmi.kaltura.com/p/1458241/sp/145824100/thumbnail/entry_id/1_bgdjnvwr/version/100001&title=Recreating+One+of+the+Weirdest+Reactions&course_id=_194578_1&content_id=_7048805_1\"></iframe> \n </div> \n </div> \n <div id=\"container_0.047868895784856536\" 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_bgdjnvwr/showDescription/false/showTitle/false/showTags/false/showDuration/false/showOwner/false/showUploadDate/false/playerSize/608x402/playerSkin/30749451/&course_id=_194578_1\" target=\"_blank\" title=\"Recreating One of the Weirdest Reactions\"> <img border=\"0\" src=\"https://cdnsecakmi.kaltura.com/p/1458241/sp/145824100/thumbnail/entry_id/1_bgdjnvwr/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_bgdjnvwr/showDescription/false/showTitle/false/showTags/false/showDuration/false/showOwner/false/showUploadDate/false/playerSize/608x402/playerSkin/30749451/&course_id=_194578_1\" target=\"_blank\" title=\"Recreating One of the Weirdest Reactions\"> 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>Recreating One of the Weirdest Reactions</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;\"> </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 09:21 AM</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;\"> \n <div title=\"Video CreditNile, Red. (2018 Jul. 16). Recreating One of the Weirdest Reactions [Video File]. Retrieved from https://www.youtube.com/watch?v=LL3kVtc-4vY\">\n Video CreditNile, Red. (2018 Jul. 16). Recreating One of… \n </div> </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;\">stein, 625.718</td> \n </tr> \n </tbody> \n </table> \n </div> \n </div> \n </div> \n </div> \n </div> \n <div id=\"container_0.6857602639382102\" 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_t8t5u84g/showDescription/false/showTitle/false/showTags/false/showDuration/false/showOwner/false/showUploadDate/false/playerSize/608x402/playerSkin/30749451/&course_id=_194578_1\" target=\"_blank\" title=\"Three-way Coupled Pendulum & Neutrinos What the Physics (05:05)\"> <img border=\"0\" src=\"https://cdnsecakmi.kaltura.com/p/1458241/sp/145824100/thumbnail/entry_id/1_t8t5u84g/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_t8t5u84g/showDescription/false/showTitle/false/showTags/false/showDuration/false/showOwner/false/showUploadDate/false/playerSize/608x402/playerSkin/30749451/&course_id=_194578_1\" target=\"_blank\" title=\"Three-way Coupled Pendulum & Neutrinos What the Physics (05:05)\"> 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>Three-way Coupled Pendulum & Neutrinos What the Physics (05:05)</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;\">05:05</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 09:05 AM</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;\"> </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;\">stein, 625.718</td> \n </tr> \n </tbody> \n </table> \n </div> \n </div> \n </div> \n <p><br></p> \n <div style=\"font-family: 'Open Sans', sans-serif; text-shadow: none !important; letter-spacing: normal !important;\"> \n <strong style=\"font-family: inherit; text-shadow: none !important; letter-spacing: normal !important; margin: 0px; padding: 0px; border: 0px; outline: 0px; font-weight: bold; font-style: inherit; font-size: 13px;\"><span data-contrast=\"auto\" xml:lang=\"EN-US\" style=\"font-family: inherit; text-shadow: none !important; letter-spacing: normal !important; margin: 0px; padding: 0px; border: 0px; outline: 0px; font-weight: inherit; font-style: inherit; font-size: 13px;\"></span></strong> \n </div> \n <p><strong style=\"font-family: 'Open Sans', sans-serif; text-shadow: none !important; letter-spacing: normal; margin: 0px; padding: 0px; border: 0px; outline: 0px; font-weight: bold; font-style: normal; font-size: 13px; color: #000000; font-variant-ligatures: normal; font-variant-caps: normal; orphans: 2; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: #ffffff; text-decoration-style: initial; text-decoration-color: initial;\">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</div>\n </div>\n\n <div id=\"_7048805_1previewModule\" class=\"moduleSample\">\n </div>\n",
"url": "https://blackboard.jhu.edu/webapps/blackboard/content/launchLink.jsp?course_id=_194578_1&content_id=_7048805_1&mode=view",
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"title": "Module 10 Discussion",
"body": "\n <div> \n <p>Watch this video about the Belousov-Zhabotinsky reaction – an example of an oscillating chemical reaction. Feel free to skip past the chemistry. Work through the example on p.259 in the text and then 8.3.1. What does this example - and video - tell us about potential bifurcations?</p> \n <ul> \n <li>How would the manifestation of a closed orbit be observed in a chemical reaction?</li> \n <li>Point out different bifurcations, if they are observed in the chemical reaction - and point to a frame of the video.</li> \n <li>Discuss how these trace back to characteristics of the Jacobian.</li> \n <li>Can we apply the Poincaré-Bendixson theorem?</li> \n </ul> \n <p>We are starting to think like applied mathematicians! </p> \n <div> \n <div> \n <div> \n <div> \n <div> \n <div> \n \n </div> \n </div> \n <div id=\"container_0.047868895784856536\"> \n <div> \n <div> \n <a href=\"../LtiMashupPlayIframeWrapperResponsive?playUrl=/browseandembed/index/media/entryid/1_bgdjnvwr/showDescription/false/showTitle/false/showTags/false/showDuration/false/showOwner/false/showUploadDate/false/playerSize/608x402/playerSkin/30749451/&course_id=_194578_1\" target=\"_blank\" title=\"Recreating One of the Weirdest Reactions\"> </a> \n </div> \n <div> \n <a href=\"../LtiMashupPlayIframeWrapperResponsive?playUrl=/browseandembed/index/media/entryid/1_bgdjnvwr/showDescription/false/showTitle/false/showTags/false/showDuration/false/showOwner/false/showUploadDate/false/playerSize/608x402/playerSkin/30749451/&course_id=_194578_1\" target=\"_blank\" title=\"Recreating One of the Weirdest Reactions\"> Watch Media </a> \n </div> \n </div> \n <div> \n <table> \n <tbody> \n <tr> \n <td><b>Name:</b></td> \n <td><b>Recreating One of the Weirdest Reactions</b></td> \n </tr> \n <tr> \n <td>Duration:</td> \n <td> </td> \n </tr> \n <tr> \n <td>Added:</td> \n <td>21 Aug 2019 09:21 AM</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> \n <div title=\"Video CreditNile, Red. (2018 Jul. 16). Recreating One of the Weirdest Reactions [Video File]. Retrieved from https://www.youtube.com/watch?v=LL3kVtc-4vY\">\n Video CreditNile, Red. (2018 Jul. 16). Recreating One of… \n </div> </td> \n </tr> \n <tr> \n <td>Tags:</td> \n <td>stein, 625.718</td> \n </tr> \n </tbody> \n </table> \n </div> \n </div> \n </div> \n </div> \n </div> \n <div id=\"container_0.6857602639382102\"> \n <div> \n <div> \n <a href=\"../LtiMashupPlayIframeWrapperResponsive?playUrl=/browseandembed/index/media/entryid/1_t8t5u84g/showDescription/false/showTitle/false/showTags/false/showDuration/false/showOwner/false/showUploadDate/false/playerSize/608x402/playerSkin/30749451/&course_id=_194578_1\" target=\"_blank\" title=\"Three-way Coupled Pendulum & Neutrinos What the Physics (05:05)\"> </a> \n </div> \n <div> \n <a href=\"../LtiMashupPlayIframeWrapperResponsive?playUrl=/browseandembed/index/media/entryid/1_t8t5u84g/showDescription/false/showTitle/false/showTags/false/showDuration/false/showOwner/false/showUploadDate/false/playerSize/608x402/playerSkin/30749451/&course_id=_194578_1\" target=\"_blank\" title=\"Three-way Coupled Pendulum & Neutrinos What the Physics (05:05)\"> Watch Media </a> \n </div> \n </div> \n <div> \n <table> \n <tbody> \n <tr> \n <td><b>Name:</b></td> \n <td><b>Three-way Coupled Pendulum & Neutrinos What the Physics (05:05)</b></td> \n </tr> \n <tr> \n <td>Duration:</td> \n <td>05:05</td> \n </tr> \n <tr> \n <td>Added:</td> \n <td>21 Aug 2019 09:05 AM</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> </td> \n </tr> \n <tr> \n <td>Tags:</td> \n <td>stein, 625.718</td> \n </tr> \n </tbody> \n </table> \n </div> \n </div> \n </div> \n \n <div> \n \n </div> \n <p><strong>Due: Sunday 11:59 pm</strong></p> \n \n</div>\n "
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