@article{PAR00009439,
  title = {{P}olynomial search and global modeling : two algorithms for modeling chaos},
  author = {{M}angiarotti, {S}ylvain and {C}oudret, {R}. and {D}rapeau, {L}aurent and {J}arlan, {L}ionel},
  editor = {},
  language = {{ENG}},
  abstract = {{G}lobal modeling aims to build mathematical models of concise description. {P}olynomial {M}odel {S}earch ({P}o{M}o{S}) and {G}lobal {M}odeling ({G}lo{M}o) are two complementary algorithms (freely downloadable at the following address: http://www.cesbio.ups-tlse.fr/us/pomos_et_glomo.html) designed for the modeling of observed dynamical systems based on a small set of time series. {M}odels considered in these algorithms are based on ordinary differential equations built on a polynomial formulation. {M}ore specifically, {P}o{M}o{S} aims at finding polynomial formulations from a given set of 1 to {N} time series, whereas {G}lo{M}o is designed for single time series and aims to identify the parameters for a selected structure. {G}lo{M}o also provides basic features to visualize integrated trajectories and to characterize their structure when it is simple enough: {O}ne allows for drawing the first return map for a chosen {P}oincare section in the reconstructed space; another one computes the {L}yapunov exponent along the trajectory. {I}n the present paper, global modeling from single time series is considered. {A} description of the algorithms is given and three examples are provided. {T}he first example is based on the three variables of the {R}ossler attractor. {T}he second one comes from an experimental analysis of the copper electrodissolution in phosphoric acid for which a less parsimonious global model was obtained in a previous study. {T}he third example is an exploratory case and concerns the cycle of rainfed wheat under semiarid climatic conditions as observed through a vegetation index derived from a spatial sensor.},
  keywords = {},
  booktitle = {},
  journal = {{P}hysical {R}eview {E}},
  volume = {86},
  numero = {4},
  pages = {046205 [14 ]},
  ISSN = {1539-3755},
  year = {2012},
  DOI = {10.1103/{P}hys{R}ev{E}.86.046205},
  URL = {https://www.documentation.ird.fr/hor/{PAR}00009439},
}