reaction diffusion equations a tutorial for biologists e. grenier
TRANSCRIPT
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