ArticleJournal of mathematical biology2011
Sustained oscillations for density dependent Markov processes.
Article in Journal of mathematical biology, 2011. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 10 papers.
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Who cites it
10 citing papers in PubMed.
- Attentional selection and communication through coherence: Scope and limitations.PLoS computational biology · 2024Article
- Determinants of Brain Rhythm Burst Statistics.Scientific reports · 2019Article
- Random fluctuations around a stable limit cycle in a stochastic system with parametric forcing.Journal of mathematical biology · 2019Article
- The stochastic Fitzhugh-Nagumo neuron model in the excitable regime embeds a leaky integrate-and-fire model.Journal of mathematical biology · 2019Article
- Stochastic oscillations and dragon king avalanches in self-organized quasi-critical systems.Scientific reports · 2019Article
- Editorial: Neuronal Stochastic Variability: Influences on Spiking Dynamics and Network Activity.Frontiers in computational neuroscience · 2016Article
- A century of transitions in New York City's measles dynamics.Journal of the Royal Society, Interface · 2015Article
- The ISI distribution of the stochastic Hodgkin-Huxley neuron.Frontiers in computational neuroscience · 2014Article
- The Morris-Lecar neuron model embeds a leaky integrate-and-fire model.Journal of mathematical biology · 2013Article
- Intrinsic noise alters the frequency spectrum of mesoscopic oscillatory chemical reaction systems.Scientific reports · 2011Article
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Authors and funding
2 authors.
Funding
No grant is acknowledged in the PubMed record.
Abstract
Simulations of models of epidemics, biochemical systems, and other bio-systems show that when deterministic models yield damped oscillations, stochastic counterparts show sustained oscillations at an amplitude well above the expected noise level. A characterization of damped oscillations in terms of the local linear structure of the associated dynamics is well known, but in general there remains the problem of identifying the stochastic process which is observed in stochastic simulations. Here we show that in a general limiting sense the stochastic path describes a circular motion modulated by a slowly varying Ornstein-Uhlenbeck process. Numerical examples are shown for the Volterra predator-prey model, Sel'kov's model for glycolysis, and a damped linear oscillator.
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