Mathematical Modeling of Complex Systems, (Dynamical Systems, Networks and Applications)(27 hours): Program

This class deals mainly with the analysis of Dynamical Systems embedded in a Network structure. Each node represents a unit which evolves dynamically and interact with other units. The interactions are represented by edges. The class consists in 9x3 hours sessions. The course will alternate lectures and active participation of students, and contains a mix of theory, computations and numerical simulations.
This course is part of an experimental COIL (Collaborative Online International Learning) initiative which includes in particular participation of students from Morroco, China and United States. The program is as follows.

Schedule

  1. Lecture 1: An introduction to classical Networks. Examples in Neuroscience context
  2. Lecture 2: Qualitative Analysis of Reaction-Diffusion Systems in Neuroscience Context. Extension to Synchronization of Networks of RD Systems
  3. Lecture 3: Mathematical Models and Dementia
  4. Lecture 4: Mathematical Modeling of Emotions
  5. Lecture 5: A simple Nonautonomous Network SIR Model for COVID19 DATA
  6. Lecture 6: Slow-Fast, MMOs and Canards in ODEs, Coupled Systems and PDEs
  7. Lecture 7: Free discussion around a few papers on the following topics: 1-How the fly's brain work (Lyu, Abbott,Maimon 2022),2- fondations of Chaos Theory and Ergodic Theory (two papers of Eckman and Ruelle, and Ruelle),3- Introduction to the Theory of the Topological Degree and Application to PDEs
  8. Lecture 8: Reduced models to generate signals that resemble brain rhythms.
  9. Lecture 9: Dendrite architecture determine mitochondrial localization patterns in vivo

Material for the class

Material is available upon request. Send an email: benjamin.ambrosio@univ-lehavre.fr