“Toy” Model: Fibonacci The Fibonacci sequence first appears in the book Liber Abaci (1202) by Leonardo of Pisa, known as Fibonacci.

Fibonacci considers the growth of an idealized (biologically unrealistic) rabbit population, assuming that: a newly born pair of rabbits, one male, one female, are put in a field; rabbits are able to mate at the age of one month so that at the end of its second month a female can produce another pair of rabbits; rabbits never die and a mating pair always produces one new pair (one male, one female) every month from the second month on.

The puzzle that Fibonacci posed was: how many pairs will there be in one year?

Fibonacci Model Y t+1 = A t, Y 0 = 1 A t+1 = A t + Y t, A 0 = 0 F t = A t + Y t ) F t+2 = F t+1 + F t,

Adults die after 2 months Y t+1 = A t A t+1 = A t + Y t - A t-1 F t = A t + Y t

Adults die after 2 months & birth rate parameter “r” Y t+1 = r A t A t+1 = A t + Y t - A t-1 F t = A t + Y t

Adults die after 3 months Y t+1 = r A t A t+1 = A t + Y t - A t-2 F t = A t + Y t