# Difference between revisions of "Nonlinear Dynamics in Biological Systems"

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==Lecture Notes and Topics== | ==Lecture Notes and Topics== |

## Revision as of 10:11, 24 August 2007

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## Contents

## General Announcements

## Coures Outline and Syllabus

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

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

## Questions for Professor Rickus or TA Mike

## 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? Yes, group 'Grad Minority' is interested in taking on this project

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 more people interested in intracellullar calcium oscillations (i.e. calcium induced calcium release). As of Friday after class, need 3-4 people. Contact mcgreen@purdue.edu

**Group 5**: Chris Fancher, Todd Shuba, and Ben Zajeski are looking for one or two more people interested in fermentation.
Just add your name if you are interested.

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

## 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.

- sketching of common functions: exponentials [math]exp(ax)[/math], [math]sin(x)[/math], [math]cos(x)[/math], [math]x / x+1[/math], more generally [math]ax^n /(x^n+b)[/math], polynomials
- taking derivatives of common functions
- solving simple linear ODEs [math]dx/dt = kx[/math]
- finding eigenvalues and eigenvectors
- Taylor series expansion
- solving polynomials
- complex numbers