Periodic and Chaotic Dynamics in Childhood Infections

Schaffer, William M.; Olsen, Lars Folke; Truty, G.L.; Fulmer, Sandra L.; Graser, David J.

doi:10.1007/978-3-642-73688-9_35

Cited by 15 publications

(9 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The discovery that simple biological models can lead to chaos (May, 1976) seems to have left ecology in two alternate modes. On the one hand has been a search for evidence of chaos existing in nature (Schaffer, 1984(Schaffer, , 1987Kot, 1985a, 1986;Schaffer et al, 1988;Hassell et al, 1991), on the other hand a cataloging of ecological situations that have the potential for exhibiting chaos (May, 1976(May, , 1985May and Oster, 1976;Gilpin, 1979;Shaffer and Kot, 1985b;Allen, 1990;Hastings and Powell, 1991). While we now have a large number of ecological circumstances that clearly imply the potential of chaotic dynamics, and several suggestive cases of chaos in nature, the present offering suggests another avenue for research.…”

Section: Discussionmentioning

confidence: 99%

The qualitative behavior of coupled predator-prey oscillations as deduced from simple circle maps

Vandermeer

1994

Ecological Modelling

View full text Add to dashboard Cite

Qualitative patterns of the non-equilibrium behavior of coupled consumer/resource systems, formulated as a standard circle map, are explored. Patterns of demographic locking, reflected as a "devil's staircase", are observed in simulations of the MacArthur consumer/resource equations. As coupling strength increases the steps in the staircase become broader, eventually overlapping to form a chaotic pattern. In addition to the standard form of chaos formation from overlapping Arnold tongues, a pattern of period doubling in the non-invertible standard circle map corresponds to the pattern observed in the classic consumer/resource equations.

show abstract

Section: Discussionmentioning

confidence: 99%

The qualitative behavior of coupled predator-prey oscillations as deduced from simple circle maps

Vandermeer

1994

Ecological Modelling

View full text Add to dashboard Cite

show abstract

“…There are various approaches for selecting an appropriate value of lag m. A rule of thumb that Schaffer et al (1988) recommend is to adopt a lag length of 10% to 30% of The occurrences from Table 1 are not actually independent but under certain conditions we assume they are in order to make the detection; this is reasonable for normal training data. The approximation for q(t 0 ) when using SVR is Quantifies how well the model matches the temporal sequence.…”

Section: Methods Svr-based Novelty Detection For Time Seriesmentioning

confidence: 99%

Novelty detection for time series data analysis in water distribution systems using support vector machines

Mounce

Boxall

2010

Journal of Hydroinformatics

153

View full text Add to dashboard Cite

The sampling frequency and quantity of time series data collected from water distribution systems has been increasing in recent years, giving rise to the potential for improving system knowledge if suitable automated techniques can be applied, in particular, machine learning. Novelty (or anomaly) detection refers to the automatic identification of novel or abnormal patterns embedded in large amounts of ''normal'' data. When dealing with time series data (transformed into vectors), this means abnormal events embedded amongst many normal time series points. The support vector machine is a data-driven statistical technique that has been developed as a tool for classification and regression. The key features include statistical robustness with respect to non-Gaussian errors and outliers, the selection of the decision boundary in a principled way, and the introduction of nonlinearity in the feature space without explicitly requiring a nonlinear algorithm by means of kernel functions. In this research, support vector regression is used as a learning method for anomaly detection from water flow and pressure time series data. No use is made of past event histories collected through other information sources. The support vector regression methodology, whose robustness derives from the training error function, is applied to a case study.

show abstract

“…A pplication of the G rassberger & Procaccia algorithm suggested an attracto r with a dimension of 3.1. However, as was pointed out by G rassberger (1986^; see also Schaffer et al (1988)), the process of interpolation introduces spurious correlation between d ata points and artefactually low estimates of attracto r dim ensionality. U nfortunately, the length of the d ata set is too short either to make a strong positive or negative statem ent about a potential attractor.…”

Section: Biological Problemsmentioning

confidence: 92%

“…In addition, the m ap can be used to estim ate Lyapunov exponents. Finally, we point out that chaotic attractors arise in a num ber of ways ap art from through period doubling (Schaffer et al 1988). If interacting populations are affected by some external cyclic influence, for example daily or annual environm ental influences, the attracto r m ay appear like the surface of a hollow doughnut or torus.…”

Section: Analysis Of Time Series (A) R E C O N S Tr U C Tin G a Ttr A C To R Smentioning

confidence: 93%

Complex dynamics in multispecies communities

1990

Phil. Trans. R. Soc. Lond. B

View full text Add to dashboard Cite

Communities of living organisms have potentially very complex population dynamics. Two components of complexity are considered, the dimensionality of the attractor underlying the persistent dynamics, and the presence of chaos. The dimensionality of real biological communities is unknown while there is great controversy about the presence of chaos in population dynamics. The evidence for chaos, and changes in the popularity of chaos among empirical biologists, is reviewed. Two new techniques developed in the physical sciences, attractor reconstruction and the estimation of the correlation dimension, are described and examples of their use in biology discussed. Although these techniques offer exciting new prospects for investigating comm unity dynamics, there are some major problems in using them in biology. These problems include the length of biological time series, the ubiquity of noise, transient behaviour, Darwinian evolution and problems in interpretation. These problems are discussed and it is concluded that the best prospects of applying these techniques are using data collected in laboratory microcosms.

show abstract

Periodic and Chaotic Dynamics in Childhood Infections

Cited by 15 publications

References 20 publications

The qualitative behavior of coupled predator-prey oscillations as deduced from simple circle maps

The qualitative behavior of coupled predator-prey oscillations as deduced from simple circle maps

Novelty detection for time series data analysis in water distribution systems using support vector machines

Complex dynamics in multispecies communities

Contact Info

Product

Resources

About