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Identifying the dynamics of complex spatio-temporal systems by spatial recurrence properties.

ABSTRACT: 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.

SUBMITTER: Mocenni C

PROVIDER: S-EPMC2889534 | biostudies-literature | 2010 May

REPOSITORIES: biostudies-literature

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Identifying the dynamics of complex spatio-temporal systems by spatial recurrence properties.

Mocenni Chiara C Facchini Angelo A Vicino Antonio A

Proceedings of the National Academy of Sciences of the United States of America 20100419 18

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 an ...[more]

PMID: 20404202

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Project description:BackgroundThe spatio-temporal patterns of infectious diseases that are environmentally driven reflect the combined effects of transmission dynamics and environmental heterogeneity. They contain important information on different routes of transmission, including the role of environmental reservoirs. Consideration of the spatial component in infectious disease dynamics has led to insights on the propagation of fronts at the level of counties in rabies in the US, and the metapopulation behavior at the level of cities in childhood diseases such as measles in the UK, both at relatively coarse scales. As epidemiological data on individual infections become available, spatio-temporal patterns can be examined at higher resolutions.MethodsThe extensive spatio-temporal data set for cholera in Matlab, Bangladesh, maps the individual location of cases from 1983 to 2003. This unique record allows us to examine the spatial structure of cholera outbreaks, to address the role of primary transmission, occurring from an aquatic reservoir to the human host, and that of secondary transmission, involving a feedback between current and past levels of infection. We use Ripley's K and L indices and bootstrapping methods to evaluate the occurrence of spatial clustering in the cases during outbreaks using different temporal windows. The spatial location of cases was also confronted against the spatial location of water sources.ResultsSpatial clustering of cholera cases was detected at different temporal and spatial scales. Cases relative to water sources also exhibit spatial clustering.ConclusionsThe clustering of cases supports an important role of secondary transmission in the dynamics of cholera epidemics in Matlab, Bangladesh. The spatial clustering of cases relative to water sources, and its timing, suggests an effective role of water reservoirs during the onset of cholera outbreaks. Once primary transmission has initiated an outbreak, secondary transmission takes over and plays a fundamental role in shaping the epidemics in this endemic area.

Dataset Information

Identifying the dynamics of complex spatio-temporal systems by spatial recurrence properties.

Publications

Identifying the dynamics of complex spatio-temporal systems by spatial recurrence properties.

Similar Datasets

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