Brainstormings

july 16 

Diffusion based phase oscillators synchronization 

1. Diffusion based phase oscillators synchronization  (real model)
2. Diffusion based phase oscillators synchronization  (complex model without diffusion)
3. Diffusion based phase oscillators synchronization  (complex model with diffusion)
   1. Self-interaction
   2. Linear phase : solutions
   3. Fast degradation limit
   4. Slow degradation limit
4. Diffusion based phase oscillators synchronization  (continuous complex model with diffusion)

Stuff to do

     5. Summary for the article

1. Motivation/Background

2. The model

    2.1 Description

    2.2 Self-interaction

3. Stationary solutions

4. Limiting cases

   4.1 Fast degradation limit

   4.2 Slow degradation limit

5. Phase diagram (dispersion)

   5.1 Ferromagnetic and antiferromagnetic solutions

   5.2 Three dimensional surface

6. ? Stability ?

Nonlinear oscillator

A synchronized quorum of genetic clocks

• Analysis of the 2D model
• Analysis of the 3D model
• Analysis of the 6D model

Add diffusion on each specie to make the stability easier

• Linear stability
  • Simple case

Model with realistic parameters 

Case study 

FitzHugh-Nagumo

Fisher-Kolmogorov

Ginzburg-Landau

Coupling between cell cycle and circadian oscillator 

Arnold tongues

• More on Arnold tongues

Dependence of cell cycle on temperature

Counting cells

Random stuff :

Pubmed Parsing : Cluster of the top 200 journals

Phase reconstruction from static data : toy model