Nonlinear Dynamics in Biological Systems

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Coures Outline and Syllabus

This course is an introduction to nonlinear dynamics with applications to biology targeted to senior engineering students and 1 year graduate students in engineering and quantitative life sciences.

Syllabus

Course Outline

We will use Strogatz as our main text and supplement with outside biological examples.

Organize Team Groups and Topics

Group 1: Dr. Rickus has a request that one group work on Bacterial Paper Rock Scissors. this is a project where 3 genetically engineered bacterial strains compete against each other in such away that 1 beats/kills 2, 2 beats/kills 3, and 3beats/kills 1. anyone game?

Group 2 Circadian Rhyth. my name is ladida anyone wanna join

Group 3: A fellow grad student and I are looking for two or three more people interested in investigating cellular differentiation. Contact slnoble@purdue.edu

Group 4: A chemistry graduate student is looking for a group interested in intracellullar calcium oscillations. Contact mcgreen@purdue.edu

other possible ideas: microbial competion, metabolism, neuronal oscillations, cell cycle, fermentation

Lecture Notes and Topics

Monday August 20 Lecture 1 powerpoint Wed Aug 22 in class covered: projects, email list, class wiki, state space, existence and uniqueness, trajectory, dimensionality, possible behavior of 1,2,3 D systems, coverting higher order and time dependent equations to state space, intro to stability, intro to vector fields, autocatalysis example Chapter 1 notes

Background Math to Brush Up On

these following things should be 2nd nature to you. if they are hazing from the summer fun, it would be best to brush up now.

1. sketching of common functions: exponentials [math]\displaystyle{ exp(ax) }[/math], [math]\displaystyle{ sin(x) }[/math], [math]\displaystyle{ cos(x) }[/math], [math]\displaystyle{ x / x+1 }[/math], more generally [math]\displaystyle{ ax^n /(x^n+b) }[/math]
2. taking derivatives
3. solving simple linear ODEs [math]\displaystyle{ dx/dt = kx }[/math]
4. finding eigenvalues and eigenvectors
5. Taylor series expansion