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| There is evidence of cyclic behavior and fluctuations in prices of livestock commodities (pork cycle) which have drawn the attention of economists for a long time.
Possible causes of the persistence of such cycles could be endogenous instable dynamics due to underlying nonlinearities and specific features of livestock commodities production such as the significant time lag that usually occurs between herd building and meat production.
A recent model of population dynamics by Yoccoz and Birkeland includes some of these features.
The model is formulated as a delayed integral equation, where the delay takes into account the maturation time of pups, and the fertility function decreases non-linearly as the fertile population increases.
Such deterministic model can produce complex dynamics with a high sensitivity to initial conditions.
On the other hand, the effect of production delays on price fluctuations was considered by B\'elair and Mackey in 1989 by means of an integro-differential equation modeling the price dynamics of a single commodity market depending on supply and demand.
Having in mind livestock commodities production (meat), we propose and study a model that couples a population dynamics model similar to Yoccoz-Birkeland's one and a market dynamics model inspired by that of B\'elair and Mackey. |
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