Coupling the Yoccoz–Birkeland population model with price dynamics: chaotic livestock commodities market cycles
Stefano Marmi

We propose a new model for the time evolution of livestock commodities prices 
which exhibits endogenous deterministic stochastic behaviour. The model is 
based on the Yoccoz– Birkeland integral equation, a model first developed for
studying the time-evolution of single species with high average fertility, a
relatively short mating season and density-dependent reproduction rates. This
equation is then coupled with a differential equation describing the price of a
livestock commodity driven by the unbalance between its demand and supply.
At its birth the cattle population is split into two parts: reproducing females
and cattle for butchery. The relative amount of the two is determined by the
spot price of the meat. We prove the existence of an attractor (theorem A ) and
of a non-trivial periodic solution (theorem B ) and we investigate numerically
the properties of the attractor: the strange attractor existing for the original
Yoccoz– Birkeland model is persistent but its chaotic behaviour depends also
on the time evolution of the price in an essential way.