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| HAL: hal-00348761, version 1 |
| arXiv: 0812.4040 |
| DOI: 10.1007/s00220-009-0854-9 |
| Detailed view |  Export this paper |
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| Communications in Mathematical Physics 292, 1 (2009) 237-270 |
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| Stochastically stable globally coupled maps with bistable thermodynamic limit |
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Jean-Baptiste Bardet 1, 2Gerhard Keller 3 |
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| (2009-11) |
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| We study systems of globally coupled interval maps, where the identical individual maps have two expanding, fractional linear, onto branches, and where the coupling is introduced via a parameter - common to all individual maps - that depends in an analytic way on the mean field of the system. We show: 1) For the range of coupling parameters we consider, finite-size coupled systems always have a unique invariant probability density which is strictly positive and analytic, and all finite-size systems exhibit exponential decay of correlations. 2) For the same range of parameters, the self-consistent Perron-Frobenius operator which captures essential aspects of the corresponding infinite-size system (arising as the limit of the above when the system size tends to infinity), undergoes a supercritical pitchfork bifurcation from a unique stable equilibrium to the coexistence of two stable and one unstable equilibrium. |
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| 1: | Institut de Recherche Mathématique de Rennes (IRMAR) |
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CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne |
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| 2: | Laboratoire de Mathématiques Raphaël Salem (LMRS) |
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CNRS : UMR6085 – Université de Rouen |
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| 3: | Department Mathematik [Erlangen] |
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Universität Erlangen-Nürnberg |
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| 4: | Fakultät für Mathematik |
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Universität Wien |
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| Subject | : | Mathematics/Dynamical Systems Mathematics/Probability |
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| hal-00348761, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00348761 | |
| oai:hal.archives-ouvertes.fr:hal-00348761 | |
| From: Jean-Baptiste Bardet | |
| Submitted on: Sunday, 21 December 2008 18:03:51 | |
| Updated on: Friday, 20 November 2009 11:51:57 | |
