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Updated: Jun 6, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Sustained oscillations for density dependent Markov processes
Peter H Baxendale1, Priscilla E Greenwood
1Department of Mathematics, University of Southern California, Los Angeles, CA, USA. baxendal@usc.edu
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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