ArticleProceedings of the National Academy of Sciences of the United States of America2009
Locating the transition from periodic oscillations to spatiotemporal chaos in the wake of invasion.
Article in Proceedings of the National Academy of Sciences of the United States of America, 2009. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 7 papers.
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Who cites it
7 citing papers in PubMed.
- A Comparison of the "Reduced Losses" and "Increased Production" Models for Mussel Bed Dynamics.Bulletin of mathematical biology · 2021Article
- Chaos theory discloses triggers and drivers of plankton dynamics in stable environment.Scientific reports · 2019Article
- Pattern selection and hysteresis in the Rietkerk model for banded vegetation in semi-arid environments.Journal of the Royal Society, Interface · 2014Article
- Absolute stability and dynamical stabilisation in predator-prey systems.Journal of mathematical biology · 2014Article
- Article
- Towards the rational design of synthetic cells with prescribed population dynamics.Journal of the Royal Society, Interface · 2012Article
- Identifying the dynamics of complex spatio-temporal systems by spatial recurrence properties.Proceedings of the National Academy of Sciences of the United States of America · 2010Article
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Authors and funding
3 authors.
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Abstract
In systems with cyclic dynamics, invasions often generate periodic spatiotemporal oscillations, which undergo a subsequent transition to chaos. The periodic oscillations have the form of a wavetrain and occur in a band of constant width. In applications, a key question is whether one expects spatiotemporal data to be dominated by regular or irregular oscillations or to involve a significant proportion of both. This depends on the width of the wavetrain band. Here, we present mathematical theory that enables the direct calculation of this width. Our method synthesizes recent developments in stability theory and computation. It is developed for only 1 equation system, but because this is a normal form close to a Hopf bifurcation, the results can be applied directly to a wide range of models. We illustrate this by considering a classic example from ecology: wavetrains in the wake of the invasion of a prey population by predators.
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