Geometric Analysis of Ecological Models with Slow and Fast Processes

By Sergio Rinaldi, Marten Scheffer. Ecosystems, 2000

175 citations recorded by the source corpus.

Subfields: Genetics, Global and Planetary Change, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/e03aa06a095320a432b7e03ac622a4f34dc13e69

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Genetics

1. F. Brand
2. L. Persson
3. A. Roos
4. Arne Schröder
5. Stephen R. Carpenter
6. Sergei V. Petrovskii
7. Alan Hastings
8. H. Eugene Stanley

In Global and Planetary Change

1. F. Brand
2. A. Crépin
3. Stephen R. Carpenter
4. L. Persson
5. A. Roos
6. Arne Schröder
7. Sergei V. Petrovskii
8. Daqing Li

In Public Health, Environmental and Occupational Health

1. Stephen R. Carpenter
2. Sergei V. Petrovskii
3. Alan Hastings
4. H. Eugene Stanley
5. F. Brand
6. A. Crépin
7. Guiquan Sun
8. T. Fukami

Citations in the corpus

• Direct experimental evidence for alternative stable states: a review (2005, background): “If a fast variable is internally coupled to a slow variable and responds discontinuously to it, relaxation oscillations or slow-fast cycles may occur under some conditions (May 1977, Rinaldi and Scheffer 2000).”
• ECOLOGICAL FUTURES: BUILDING AN ECOLOGY OF THE LONG NOW1 (2002, background): “In other cases, slowly changing variables may expose thresholds, and thereby cause surprising dynamics that are hard to predict (Rinaldi and Scheffer 2000, Scheffer et al. 2000, Carpenter 2001).”
• Transient phenomena in ecology (2018, background): “where e << 1 is a non-negative dimensionless parameter that quantifies the difference between orders of magnitude for the time scales of prey (N) and predator (P) (32), and f and g are the growth rate of the prey population on the natural time scale for the prey and the growth rate of the predator p”
• Critical natural capital revisited: Ecological resilience and sustainable development (2009, background): “Following the threshold approach, ecological resilience corresponds to the distance of the current value of nutrient concentrations to the critical level ( Rinaldi and Scheffer, 2000; Scheffer et al., 2001; Petersonetal.,2003).Thus,ifthespecificshallowlakehadavery low nutrient level, the ecological”
• Using Fast and Slow Processes to Manage Resources with Thresholds (2007, methodology): “Geometric singular perturbation theory (Tikhonov 1952; Fenichel 1979) can be used to analyze multiple time scales – see for examples Ludwig et al. (1978), Milik et al. (1996), or Rinaldi and Scheffer (2000) .”
• Simulation modelling of ecological hierarchies in constructive dynamical systems (2007, background): “Such dynamics can be analyzed by the geometric singular perturbation approach (Rinaldi and Scheffer, 2000).”
• Network resilience (2020, background): “as increased autocorrelation between states, so that oscillations may become ‘stretched’ [230].”