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arXiv · 1807.06392

Equivalence between nonlinear dynamical systems and urn processes

Léon Brenig·Iram Gleria·Tarcísio M. Rocha Filho·Annibal Figueiredo·Benito Hernández-Bermejo
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Abstract

An equivalence is shown between a large class of deterministic dynamical systems and a class of stochastic processes, the balanced urn processes. These dynamical systems are governed by quasi-polynomial differential systems that are widely used in mathematical modeling while urn processes are actively studied in combinatorics and probability theory. The presented equivalence extends a theorem by Flajolet et al. (Flajolet, Dumas and Puyhaubert Discr. Math. Theor. Comp. Sc. AG - 2006, DMTCS Proceedings) already establishing an isomorphism between urn processes and a particular class of differential systems with monomial vector fields. The present result is based on the fact that such monomial differential systems are canonical forms for more general dynamical systems.

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Léon Brenig, Iram Gleria, Tarcísio M. Rocha Filho, Annibal Figueiredo, Benito Hernández-Bermejo. 2018-07-17. Equivalence between nonlinear dynamical systems and urn processes. https://doi.org/10.1088/1751-8121/aae770

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