Sustained oscillations for density dependent Markov processes |
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Authors: | Peter H Baxendale Priscilla E Greenwood |
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Institution: | Department of Mathematics, University of Southern California, Los Angeles, CA, USA. baxendal@usc.edu |
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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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Keywords: | |
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