1. Coupling the Yoccoz-Birkeland population model with price dynamics: chaotic livestock commodities market cycles
- Author
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Stefano Marmi, Duccio Papini, Sylvain Arlot, Laboratoire de Mathématiques d'Orsay (LMO), Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS), Sélection de modèles en apprentissage statistique (SELECT-POST), Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Scuola Normale Superiore di Pisa (SNS), Dipartimento di Matematica e Informatica - Universita Udine (DIMI), Università degli Studi di Udine - University of Udine [Italie], This work was started during a visit of SA to the Scuola Normale Superiore in Pisa and to the Complex Systems Center of the University of Siena, the hospitality of which is gratefully acknowledged. The authors acknowledge the support of the Centro di Ricerca Matematica Enniode Giorgi and of UniCredit Bank R&D group for financial support through the 'Dynamics and Information Theory Institute' at the Scuola Normale Superiore. Most of this work was done while SA was a researcher at CNRS (Département d’Informatique / Ecole Normale Supérieure, UMR8548 CNRS/ENS/INRIA), 45, rue d’Ulm, F-75230 PARIS Cedex 05, France). DP was supported by the INdAM-GNAMPA project 'Proprietà qualitative di alcuni problemi ai limiti'. We are also grateful to Paolo Nistri for contributing to the initial formulation of the model and to Nicola Zanda for useful discussions on livestocks farming (in particular Cinta Senese and pig)., Laboratoire de Mathématiques d'Orsay ( LMO ), Université Paris-Saclay-Centre National de la Recherche Scientifique ( CNRS ), Model selection in statistical learning ( SELECT ), Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -Laboratoire de Mathématiques d'Orsay ( LMO ), Université Paris-Saclay-Centre National de la Recherche Scientifique ( CNRS ) -Université Paris-Saclay-Centre National de la Recherche Scientifique ( CNRS ) -Centre National de la Recherche Scientifique ( CNRS ), Scuola Normale Superiore di Pisa ( SNS ), Scuola Normale Superiore di Pisa, Department of Mathematical and Computer Science, University of Udine, Arlot, S., Marmi, S., and Papini, D.
- Subjects
Spot contract ,Population dynamics ,Differential equation ,Population ,[ MATH.MATH-DS ] Mathematics [math]/Dynamical Systems [math.DS] ,[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS] ,Chaotic ,Chaotic livestock commodities cycles ,General Physics and Astronomy ,Dynamical Systems (math.DS) ,Population dynamic ,01 natural sciences ,Delays dynamical systems ,Strange attractor ,Supply and demand ,Attractor ,FOS: Mathematics ,Econometrics ,Quantitative Biology::Populations and Evolution ,0101 mathematics ,Mathematics - Dynamical Systems ,education ,Quantitative Biology - Populations and Evolution ,Settore MAT/07 - Fisica Matematica ,Mathematical Physics ,Mathematics ,education.field_of_study ,Applied Mathematics ,[SDV.BID.EVO]Life Sciences [q-bio]/Biodiversity/Populations and Evolution [q-bio.PE] ,010102 general mathematics ,Populations and Evolution (q-bio.PE) ,Delays dynamical system ,Statistical and Nonlinear Physics ,Integral equation ,010101 applied mathematics ,[ SDV.BID.EVO ] Life Sciences [q-bio]/Biodiversity/Populations and Evolution [q-bio.PE] ,Population model ,Chaotic livestock commodities cycle ,FOS: Biological sciences - Abstract
We propose a new model for the time evolution of livestock commodities 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 and we investigate numerically its properties: the strange attractor existing for the original Yoccoz-Birkeland model is persistent but its chaotic behaviour depends also from the price evolution in an essential way., 26 pages, 19 figures
- Published
- 2018