RESUMO
We introduce a measure to quantify spatiotemporal turbulence in extended systems. It is based on the statistical analysis of a coherent structure decomposition of the evolving system. Applied to a cellular excitable medium and a reaction-diffusion model describing the oxidation of CO on Pt(100), it reveals power-law scaling of the size distribution of coherent space-time structures for the state of spiral turbulence. The coherent structure decomposition is also used to define an entropy measure, which sharply increases in these systems at the transition to turbulence.
RESUMO
The dynamical behavior of species competing for a common resource is studied with a reaction-diffusion system based on cubic autocatalysis. Randomly seeded populations self-segregate to form a complex network of domains separated by distinct interfaces. For chaotic populations in one-dimensional media, the interfaces exhibit irregular motions on long time scales. In two-dimensional media, the interface motions are governed by curvature-induced drift.
RESUMO
Conventional analysis of ambulatory longterm manometry of the small intestine has revealed abnormalities in patients with the irritable bowel syndrome (IBS). The aim was to use methods from non-linear dynamics, in particular the concepts of symbolic dynamics and entropy, in order to discriminate motility in IBS from healthy subjects. 24-h jejunal motility was recorded in 30 IBS patients and 30 healthy subjects. Computerized analysis of contraction amplitudes and intercontractile intervals was performed. Both time series were analysed by symbolic dynamics and entropy to quantify the degree of randomness inherent in the signal. During phase II IBS patients exhibited significantly increased entropies for the intercontractile intervals (IBS: 0.978 +/- 0.016, C: 0.965 +/- 0.020, P = 0.004) and for the contraction amplitudes (IBS: 0.978 +/- 0.008, C: 0.970 +/- 0.026, P = 0.05) compared with healthy subjects. In addition, a significantly increased mean contraction amplitude (mmHg) was found in patients (IBS: 25.2 +/- 4.8, C: 22.2 +/- 3.1, P = 0.003). Considering a combination of both parameters, a diagnostic accuracy of 82% was achieved. We conclude that phase II motility of the small intestine is more random in IBS than in health. Symbolic dynamics seems to be a promising new concept for the analysis of long-term gastrointestinal motility recordings.
