reaction diffusion equations a tutorial for biologists e. grenier
TRANSCRIPT
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Reaction diffusion equations
A tutorial for biologists
E. Grenier
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Introduction
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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)
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Propagation of epidemies
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SIR system
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SIR system
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SIR system
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Propagation de la rage
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SIR system
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SIR system
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SIR system
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SIR system
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Spiral waves
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Spiral waves
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Spiral waves
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Spiral waves
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Pattern formation
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Pattern formation
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Pattern formation
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Pattern formation
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Pattern formation
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Pattern formation