Lecture Notes

Collected lectures notes in computational biology

Dynamical systems

(l3 level) The lecture was dispensed by Dr. Silvia De Monte then Dr François Blanquart in the Biology department of the École normale supérieure de Paris. I taught the tutorial session in 2016 2017 and in 2018 along with Phuong Nguyen.

Numerical bifurcation diagrams and bistable systems

Trajectories
Phase diagram
Isoclines  Flow  Equilibrium points 
Nature of the equilbirum points
Complete phase diagram 
Bifurcation diagram
Numerical continuation 
Assymetrical System
Single parameter bifurcation  The Cusp bifurcation: a bifurcation of codimension 2 

Fitzhugh-Nagumo model: an excitable system

Phase Diagram
Isoclines  Flow  Equilibrium points  Nature of the equilibria  Complete phase diagram 
Bifurcation diagram
Bifucation on the external stimulus I  Codim 2 bifurcation on I and b 
Non autonomous system
Stochastic Differential Equation