The goal of the class is to make students competent to solve and
identify  practical problems in biology of the type
dxi/dt=f(x1,x2,…,xi,…,xn) through the following student outcomes
in which they are able to:
1.	analyze the dynamics of a nonlinear dynamical system;
2.	simulate complicated nonlinear dynamical systems;
3.	identify complicated nonlinear dynamical systems;
4.	design experiments to identify complicated nonlinear 
dynamical systems.

In the first half of the course, students will be exposed to 
discrete and continuous models. There will be two unit exams and 
a final exam. Homework problems include analytical work and 
computational work. In the second half of the course, students 
will prepare weekly written reports and Powerpoint presentations 
on their work. 

Evaluation 

• Evaluation will be based on the ability to solve problems.

• Evaluation will also be based on written reports submitted
weekly in the second half of the course.  The course will be
writing intensive.

• Evaluation will be by peers and instructor based on weekly oral
reports in the second half of the course.

1. Apply Buckingham's Pi theorem to produce a dynamical 
dimensionless system.
2. Determine fixed points of the dynamical system; that is, 
solve the system f(x) = 0.
3. Find the Jacobian matrix of f(x) and evaluate it at each one 
of the relevant fixed points. 
4. Based upon eigenvalues, determine stability conditions, draw 
trajectories in the phase plane (if convenient), and, in 
general, describe the behavior of the dynamical system.
5. Determine and describe bifurcations in dynamical systems. The 
second half of the course will focus on tools that enable the 
modeling of synthetic and naturally occurring systems. The 
models will tend to be larger, and new approaches for 
identifying the models will be introduced so that students can 
become familiar with the data used to test systems biology 
models and its limitations.
6.  Simulating a genetic network with application to the qa gene 
cluster of Neurospora crassa.
7.  Building a genetic network using the toggle switch as an 
example.
8. Achieving stable oscillations with the repressilator.
9. Identifying genetic networks by ensemble methods using the 
repressilator as an example.
10.  Microarray analysis using RNA profiling data on the 
biological clock in N. crassa.
11.  Hypothesis testing in microarray analysis using ensemble 
methods on the qa gene cluster.
12. Model-guided discovery using the maximally informative next 
experiment (MINE).