Stochastically stable globally coupled maps with bistable thermodynamic limit
Bardet JB, Keller G, Zweimüller R (2009)
Publication Type: Journal article, Original article
Publication year: 2009
Journal
Publisher: Springer Verlag (Germany)
Book Volume: 292
Pages Range: 237-270
Journal Issue: 1
DOI: 10.1007/s00220-009-0854-9
Abstract
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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APA:
Bardet, J.-B., Keller, G., & Zweimüller, R. (2009). Stochastically stable globally coupled maps with bistable thermodynamic limit. Communications in Mathematical Physics, 292(1), 237-270. https://doi.org/10.1007/s00220-009-0854-9
MLA:
Bardet, Jean-Baptiste, Gerhard Keller, and Roland Zweimüller. "Stochastically stable globally coupled maps with bistable thermodynamic limit." Communications in Mathematical Physics 292.1 (2009): 237-270.
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