mathchaos

In "the code", Marcus du Sautoy, tries to explain Chaos Theory


So at a certain point, he starts with this silly equation

He starts talking about lemmings and how the rate of growth fluctuates and can lead to very unpredictable chaos

Pnext = R * P - R * P * P

simplified to

Pnext = R * P(1-P)

Wich is the same.

where R is the reproduction rate he says it is less than 2 most of the time P is the current population Pnext is the surviving the offspring, I think

so next time around P = P + Pnext

When I saw this I thought; wait a minute

There is no way to ever have a positive number for the next generation. Except if growth or population is negative.

Whatever I tried with this everything went extinct.

What am I doing wrong?

Thanks


Solution

  • Population P is a number between 0 and 1. Think of it as the proportion of the maximum that the ecosystem can support. P=1 means the entire population dies of starvation the next year because it ate all the food.