期刊名称：Proceedings of the National Academy of Sciences
印刷版ISSN：0027-8424
电子版ISSN：1091-6490
出版年度：2010
卷号：107
期号：18
页码：8097-8102
DOI：10.1073/pnas.0910414107
语种：English
出版社：The National Academy of Sciences of the United States of America
摘要：Complex spatio-temporal systems may exhibit irregular behaviors when driven far from equilibrium. Reaction-diffusion systems often lead to the formation of patterns and spatio-temporal chaos. When a limited number of observations is available, the reconstruction and identification of complex dynamical regimes become challenging problems. A method based on spatial recurrence properties is proposed to deal with this problem: generalized recurrence plots and generalized recurrence quantification analysis are exploited to show that detection of structural changes in spatially distributed systems can be performed by setting up appropriate diagrams accounting for different spatial recurrences. The method has been tested on two prototypical systems forming complex patterns: the complex Ginzburg-Landau equation and the Schnakenberg system. This work allowed us to identify changes in the stability of spiral wave solutions in the former system and to analyze the Turing bifurcations in the latter.
关键词：complex Ginzburg-Landau equation ; spatial recurrence plots ; spatially distributed systems ; Turing patterns ; reaction-diffusion systems
