Nonlinear Dynamics in Biological Systems: Difference between revisions
| Line 53: | Line 53: | ||
in class covered: identify the bifurcations in the May cow problem, what is a bifurcation, critical parameter values, saddle node bifurcations, introduce bifurcation diagrams | in class covered: identify the bifurcations in the May cow problem, what is a bifurcation, critical parameter values, saddle node bifurcations, introduce bifurcation diagrams | ||
'''Wed | '''Wed Aug 29th''' | ||
in classe covered: transcritical bifurcations, pitchfork (super and subcritical) | in classe covered: transcritical bifurcations, pitchfork (super and subcritical) | ||
'''Fri Aug 31st''' | |||
tumor problem - 2 parameter, 1D system with multiple bifurcations. creating stability diagrams | |||
==Background Math to Brush Up On== | ==Background Math to Brush Up On== | ||
Revision as of 06:46, 30 August 2007
Click here to return to main Rickus Lab page
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
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
neurological signals (3): Brandon Davis, Nicole Meehan, Omeed Paydar, Andrew Pierce
neuronal firing:(4) Timu Gallien, Julie Morby, Michelle Scheidt, Mark Wilson
cadiac modeling(5), Matt Croxall, Meghan Floyd, Erica Halsey, Shari Hatfield, Rohit Shah
bacterial rock paper scissors(3):Team Grad Minority. Alex DiMauro, Trisha Eustaquio, and Nick Snead
circadian rhythms(4): Jeremy Schaeffer, Arun Mohan , Drew Lengerich, Shaunak A Kothari
cell differentiation(4): Sarah Noble, Paul Critser, Prasad Siddavatam, Jiji Chen
team name: The Bowman Group, members: Chris Fancher, Todd Shuba, and Ben Zajeski and area of interest: Fermentation
Hospital sustainability(4): Steve Higbee, Halle Burton, Tyler MacBroom, Steven Lee
Team Name: The Metabolites, Members: Brooke Beier, Eric Brandner, Elizabeth Casey, Eric HodgmanAreas of interest: Metabolism and neuron cells, Potential Project Area: Metabolic flux of neuron cells during firing
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
Fri Aug 24th in class covered: projects, review stability of fixed points, look at linear examples, linear stability analysis, classic May problem: cows in the field
Mon Aug 27th in class covered: identify the bifurcations in the May cow problem, what is a bifurcation, critical parameter values, saddle node bifurcations, introduce bifurcation diagrams
Wed Aug 29th in classe covered: transcritical bifurcations, pitchfork (super and subcritical)
Fri Aug 31st tumor problem - 2 parameter, 1D system with multiple bifurcations. creating stability diagrams
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]\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], polynomials
- taking derivatives of common functions
- solving simple linear ODEs [math]\displaystyle{ dx/dt = kx }[/math]
- finding eigenvalues and eigenvectors
- Taylor series expansion
- solving polynomials
- complex numbers
