reaction diffusion equations a tutorial for biologists e. grenier

Reaction diffusion equations

A tutorial for biologists

E. Grenier

Introduction

Introduction: what is a diffusion equation ?

A diffusion equation, or heat equation models for instance

• The evolution of the temperature in a room

• The evolution of the concentration of chemical components in a solution

• The repartition of a population of animals, each animal walking at random

• The evolution of the concentration of ionic species in extracellular space

It models the general behavior of particules or indiviuals which move at random

• Ions move at random in extracellular space through thermal agitation

• Animals move at random (and interact of course, but this interaction is not included in diffusion equation)

Propagation of epidemies

SIR system

SIR system

SIR system

Propagation de la rage

SIR system

SIR system

SIR system

SIR system

Spiral waves

Spiral waves

Spiral waves

Spiral waves

Pattern formation

Pattern formation

Pattern formation

Pattern formation

Pattern formation

Pattern formation