TrainingsMasterMathématiques appliquées, statistiqueCoursesContinuous dynamical systems, linear algebra and modelling

Master Mathématiques appliquées, statistiqueUE Continuous dynamical systems, linear algebra and modelling

Content

The purpose of this course is twofolds. The first part of the course will concern linear algebra tools that can be usefull in the studies of biological systems. Cite for instance the notions of

  • Iterative methods, rate of convergence of vectorial sequences
  • Matrix reduction, Power method and Perron-Frobenius theorem
  • Linear regression ; analysis of variance, Principal Component Analysis ; Singular Values Decomposition

The second part of the course will be devoted to revision and deepening of the notion and properties of differential equations and systems of differential equations which underlie the main continuous models used in biology (dynamics of populations or cells, biochemical processes, etc.). We will address both qualitative (existence, global existence, equilibria, stability of the equilibria,, long-time behavior) and quantitative (positivity, parameter dependency) properties of the considered models.

In parallel to this theoretical study, numerical approximation will be studied and implemented during the computer sessions. Practicals will consist in using Python specialised libraries as scipy.integrate in order to visualise trajectories and systems behaviours.

Language used

Main language used by this course: Anglais.

Structure and organisation

Lectures will provide a summary of basic concepts, which will be applied in practical courses.

Volume of teachings

  • Lectures: 12 hours
  • Tutorials: 12 hours
  • Pratical works: 12 hours

The trainings which use this course