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Transitivity and blowout bifurcations in a class of globally coupled maps

โœ Scribed by Paul Glendinning

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
326 KB
Volume
264
Category
Article
ISSN
0375-9601

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โœฆ Synopsis

A class of globally coupled one dimensional maps is studied. For the uncoupled one dimensional map it is possible to ลฝ compute the spectrum of Liapunov exponents exactly, and there is a natural equilibrium measure Sinai-Ruelle-Bowen . measure , so the corresponding 'typical' Liapunov exponent may also be computed. The globally coupled systems thus provide examples of blowout bifurcations in arbitrary dimension. In the two dimensional case these maps have parameter ลฝ . values at which there is a transitive topological attractor which is a filled-in quadrilateral and, simultaneously, the synchronized state is a Milnor attractor.

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