Periodic travelling waves in cyclic predator–prey systems

By Jonathan A. Sherratt. 2001

145 citations recorded by the source corpus.

Subfields: Ecology, Genetics, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/e4ff03eb95453161c25f2d5ff654c739ce65db03

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Citations in the corpus

Where am I and why? Synthesizing range biology and the eco-evolutionary dynamics of dispersal (2014, result): “These findings are very similar to those of Sherratt (2001).”
Self-organised spatial patterns and chaos in a ratio-dependent predator–prey system (2011, background): “Interestingly, whilst earlier work focussed almost exclusively on pattern formation due to the Turing instability, more recently the attention has shifted to non-Turing mechanisms, in particular, to those that result in spatiotemporal chaos (e.g. Pascual 1993; Sherratt 2001).”
Invasion theory and biological control (2002, background): “The detailed dynamics of spatially explicit predator‐prey systems are notoriously complex and include limit cycles, cyclical travelling waves and spatiotemporal chaos (Hassell et al. 1991; Neubert et al. 2000; Sherratt 2001 ).”
Finite-Difference Schemes for Reaction–Diffusion Equations Modeling Predator–Prey Interactions in MATLAB (2007, background): “For certain parameter choices (see Garvie and Trenchea, 2005a for additional details ), the kinetics have a stable limit cycle surrounding the unstable stationary point (u * , v * ), i.e., the densities of predators and prey cycle periodically in time.”
Transition to spatiotemporal chaos can resolve the paradox of enrichment (2004, background): “Particularly, it has been recently shown that spontaneous spatiotemporal pattern formation is an intrinsic property of a predator–prey system(Pascual, 1993; Sherratt et al., 1995, 1997; Petrovskii and Malchow, 1999, 2001; Sherratt, 2001; Medvinsky et al., 2002) .”
Spatiotemporal Complexity of Plankton and Fish Dynamics (2002, background): “…to a widely accepted approach (Murray, 1989; Levin, Powell, and Steele, 1993; Malchow, 1993; Holmes et al., 1994; Shigesada and Kawasaki, 1997; Sherratt, 2001), the functioning of a prey-predator community can be described by a reaction-diffusion system of the form ut(r, t) = D∇2u(r, t) +…”