User:Johnsy/Modelling in Biology: Difference between revisions
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==Assignments== | ==Assignments== | ||
*[http://www.openwetware.org/images/1/13/MiB_Assignment_1.pdf Assignment 1] (Due 5 November 2007) | *[http://www.openwetware.org/images/1/13/MiB_Assignment_1.pdf Assignment 1] (Due 5 November 2007) | ||
**[http://www.openwetware.org/images/a/a5/MiB_Assignment_1.doc | **[http://www.openwetware.org/images/a/a5/MiB_Assignment_1.doc Solutions] | ||
**[http://www.openwetware.org/images/7/7c/EulerSDE.m EulerSDE.m] | |||
**[http://www.openwetware.org/images/2/2b/Euler.m Euler.m] | |||
**References for Assignment 1 | **References for Assignment 1 | ||
***[http://www.openwetware.org/images/1/16/DE_Systems-1-.pdf Differential Equation Systems] | ***[http://www.openwetware.org/images/1/16/DE_Systems-1-.pdf Differential Equation Systems] | ||
Revision as of 09:02, 27 October 2007
About - Introduction and background: linear vs. nonlinear. Phase plane analysis. Stochastic and Deterministic models. One-dimensional systems: fixed point analysis; global and local stability; bifurcations. Two-dimensional systems: oscillations and limit cycles. Hopf bifurcation and Poincare-Bendixson theorem.
Professor: Dr. Mauricio Barahona
Fall Term 2007 Lectures: Monday 10-11 (Mech Eng 664), Thursday 2-3 (RSM G.01)
Lab: Friday 10-11 (RSM 3.38)
Textbook: Strogatz, Steven. Nonlinear Dynamics and Chaos. Cambridge, MA: Westview Press, 1994.
Announcements
- Classes start Tuesday 9 October 2007
Assignments
- Assignment 1 (Due 5 November 2007)
- Solutions
- EulerSDE.m
- Euler.m
- References for Assignment 1
- Differential Equation Systems
- 18.03 Differential Equations Video Lectures from MIT - Relevant content begins at lecture 24.
- 18.03 Notes on Homogeneous Linear Systems - (.pdf) Good background reading
For Problem 1: Considering the differences in step size of the Runge-Kutta algorithm.
"The trouble is that excessively many computations will occur and each one carries a penalty in the form of round-off error. Computers don't have infinite accuracy. Round-off error occurs during every calculation, and will begin to accumulate in a serious way if dt is too small" (Strogatz, p 34)
