BIO-341 / 4 crédits

Enseignant(s): Naef Felix, Shillcock Julian Charles

Langue: Anglais


Summary

Life is non-linear. This course introduces dynamical systems as a technique for modelling simple biological processes. The emphasis is on the qualitative and numerical analysis of non-linear dynamical models. Examples are taken from biology and population models.

Content

Keywords

Non-linear dynamical systems; ordinary differential equations; qualitative analysis; numerical analysis, simulations; population models; bistability and hysteresis; biological oscillators; iterative maps in 1D, chaos and fractals.

Learning Prerequisites

Required courses

Informatics 1, II, III

Analysis I, II

Linear Algebra

Numerical Analysis

Recommended courses

Physics I, II

Important concepts to start the course

Analysis and linear algebra

Basic chemical kinetics

Learning Outcomes

By the end of the course, the student must be able to:

  • Explain simple dynamical models (terms and parameters)
  • Analyze dynamical models in 1D
  • Analyze models in 2D including phase portraits
  • Characterize fixed points and their stability
  • Implement simulations of models
  • Identify bifurcations in 1D models
  • Model biochemical reactions
  • Construct simple models
  • Critique simple models

Transversal skills

  • Plan and carry out activities in a way which makes optimal use of available time and other resources.
  • Write a scientific or technical report.
  • Demonstrate the capacity for critical thinking

Teaching methods

Lectures

Exercises

Expected student activities

Learn the theoretical material in the lectures

Solve the exercises using pencil and paper, and implement numerical simulations

Assessment methods

Written examination and graded exercises.

Supervision

Office hours No
Assistants Yes
Forum Yes

Resources

Bibliography

S. H. Strogatz Nonlinear dynamics and chaos (CRC Press)

J. D. Murray Mathematical BIology (Spring)

Notes/Handbook

Course notes in pdf format

Moodle Link

Dans les plans d'études

  • Semestre: Automne
  • Forme de l'examen: Ecrit (session d'hiver)
  • Matière examinée: Dynamical systems in biology
  • Cours: 2 Heure(s) hebdo x 14 semaines
  • Exercices: 2 Heure(s) hebdo x 14 semaines
  • Semestre: Automne
  • Forme de l'examen: Ecrit (session d'hiver)
  • Matière examinée: Dynamical systems in biology
  • Cours: 2 Heure(s) hebdo x 14 semaines
  • Exercices: 2 Heure(s) hebdo x 14 semaines

Semaine de référence

 LuMaMeJeVe
8-9     
9-10     
10-11     
11-12     
12-13     
13-14     
14-15     
15-16     
16-17     
17-18     
18-19     
19-20     
20-21     
21-22