Module 3: Bifurcations (cont.)

Lectures and Related Content

Folder description

Please click the folder link above to access the Module 3 instructional content. Module 3 contains the following:

03A: Overdamped Bead on a Rotating Hoop
03B: Dimensional Analysis and Scaling
03C: Bifurcation without Symmetry

Technical

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Module at a Glance ObjectivesHow to complete this module:

Cell description

In this module we explore how the flow of a one-dimensional dynamic system is dependent on the parameters and observe dynamics as parameters change.

Objectives

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

Reduce second order ordinary differential equations to first order differential equations and analyze using bifurcation theory.
Apply bifurcation theory for dynamical systems without perfect symmetry.
Investigate the real-world example of a fish hatchery with insect infestation.

How to complete this module:

Watch the video lectures 3A through 3C.
Complete the reading assignments.
Participate in the discussion board question.
Complete the assignment.

Technical

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Readings

Cell description

This week's reading assignment includes the following:

Strogatz, Steven H. Nonlinear Dynamics and Chaos with Student Solutions Manual: With Applications to Physics, Biology, Chemistry, and Engineering. CRC Press, 2018.
- Chapter 3 (pp. 62-80)

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Module 3 Discussion - Infectious Disease Outbreak

Cell description

Select the link above to access the discussion forum. After viewing the posted  video respond to the following prompt. In addition, comment on at least two of your classmates’ posts.

This video is a lecture from Professor Strogatz concerning an Infectious Disease Outbreak. Discuss a parameter of the outbreak, how the parameters are related, or how the parameters affect bifurcation. In addition, comment on at least two of your classmates’ posts.

Due: Sunday 11:59 pm

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Module 3 Assignment

Cell description

Complete the following problems from chapter 3 of the Strogatz textbook: 3.5.2 (5 pts.); 3.5.3 (4 pts.); 3.6.1 (3 pts.); 3.6.3 (5 pts.); 3.6.4 (3 pts.)
Upload your work in PDF format by selecting the link above.

Due: Tuesday 11:59 pm

Technical

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    "html": "\n\n<img alt=\"Assignment\" src=\"/images/ci/sets/set01/assignment_on.gif\" class=\"item_icon\">\n\n<div class=\"item clearfix\" id=\"_7048727_1\">\n\n <h3>\n  <span class=\"reorder editmode hideme\"><span><img src=\"/images/ci/icons/generic_updown.gif\" alt=\"\"></span></span>\n\n\n            <a href=\"/webapps/assignment/uploadAssignment?content_id=_7048727_1&amp;course_id=_194578_1&amp;group_id=&amp;mode=view\"><span style=\"color:#0067ac;\">Module 3 Assignment</span></a>\n      </h3><a href=\"#\" class=\"ally-alternative-formats ally-prominent-af-download-button\" data-ally-external-id=\"content:_7048727_1\" data-ally-upload-type=\"RichContent\" title=\"Alternative formats\" style=\"display: none\">\n    <span class=\"ally-sr-only\">\n  \n\n\n            Module 3 Assignment\n      </span>\n</a>\n\n   \n </div>\n\n\n\n<div class=\"details\">\n    <div class=\"vtbegenerated\"> \n <ul> \n  <li>Complete the following problems from chapter 3 of&nbsp;the Strogatz textbook: <strong>3.5.2</strong> (5 pts.);&nbsp; <strong>3.5.3</strong> (4 pts.);&nbsp; <strong>3.6.1</strong> (3 pts.);&nbsp; <strong>3.6.3</strong> (5 pts.);&nbsp; <strong>3.6.4</strong> (3 pts.)</li> \n  <li>Upload your work in PDF format by selecting the link above.</li> \n </ul> \n <p style=\"margin-left: 30px;\"></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: Tuesday 11:59&nbsp;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 style=\"margin-left: 30px;\"></p> \n</div>\n  </div>\n\n <div id=\"_7048727_1previewModule\" class=\"moduleSample\">\n </div>\n",
    "url": "https://blackboard.jhu.edu/webapps/assignment/uploadAssignment?content_id=_7048727_1&course_id=_194578_1&group_id=&mode=view",
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        "title": "Module 3 Assignment",
        "body": "\n    <div> \n <ul> \n  <li>Complete the following problems from chapter 3 of&nbsp;the Strogatz textbook: <strong>3.5.2</strong> (5 pts.);&nbsp; <strong>3.5.3</strong> (4 pts.);&nbsp; <strong>3.6.1</strong> (3 pts.);&nbsp; <strong>3.6.3</strong> (5 pts.);&nbsp; <strong>3.6.4</strong> (3 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&nbsp;pm</strong></p> \n  \n  \n</div>\n  "
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