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Mathematical Models for Society and Biology, 2nd Edition by Edward Beltrami

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Chapter 11

Spatial Patterns

The Cat’s Tail and Spreading Slime

11.1 Background

In the previous chapter we encountered a class of models in which two separate dynamics are at work. A reaction term designates the positive growth rate of some organism or chemical within a region. The diffusion term is the rate at which this stuff is dispersed. In the specific example we considered, the algal cells are scattered to outside the region, where no growth can take place, and so reaction and diffusion oppose each other. In the present chapter these terms interact synergistically, and diffusion is the source of pattern formation and not an inhibitor.

Near the end of his life, after having completed his formidable work on computability and, later, the breaking ...

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