1. Some combinatorial aspects of discrete non-linear population dynamics
- Author
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Thierry Huillet, Nicolas Grosjean, Laboratoire de Physique Théorique et Modélisation (LPTM - UMR 8089), and Centre National de la Recherche Scientifique (CNRS)-CY Cergy Paris Université (CY)
- Subjects
Class (set theory) ,General Mathematics ,Population ,FOS: Physical sciences ,General Physics and Astronomy ,non-linear population dynamics without and with immigration ,01 natural sciences ,logistic map ,010104 statistics & probability ,Linearization ,Calculus ,Applied mathematics ,0101 mathematics ,Quantitative Biology - Populations and Evolution ,10. No inequality ,education ,Real number ,Mathematics ,education.field_of_study ,[SDV.GEN.GPO]Life Sciences [q-bio]/Genetics/Populations and Evolution [q-bio.PE] ,Applied Mathematics ,010102 general mathematics ,Populations and Evolution (q-bio.PE) ,Statistical and Nonlinear Physics ,Nonlinear Sciences - Chaotic Dynamics ,Nonlinear system ,Population model ,FOS: Biological sciences ,[NLIN.NLIN-CD]Nonlinear Sciences [physics]/Chaotic Dynamics [nlin.CD] ,Carleman transfer matrix ,Chaotic Dynamics (nlin.CD) ,Logistic map ,Analytic function - Abstract
International audience; Motivated by issues arising in population dynamics, we consider the problem of iterating a given analytic function a number of times. We use the celebrated technique known as Carleman linearization that turns (for a certain class of functions) this problem into simply taking the power of a real number. We expand this method, showing in particular that it can be used for population models with immigration, and we also apply it to the famous logistic map. We also are able to give a number of results for the invariant density of this map, some being related to the Carleman linearization.
- Published
- 2016
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