caa a22 4500 44532998X CHVBK 20180317142734.0 cr unu---uuuuu 170323e20110901xx s 000 0 eng 10.1007/s00285-010-0376-2 doi (NATIONALLICENCE)springer-10.1007/s00285-010-0376-2 Sustained oscillations for density dependent Markov processes [Elektronische Daten] [Peter Baxendale, Priscilla Greenwood] 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. Springer-Verlag, 2010 Sustained oscillations nationallicence Density dependent Markov processes nationallicence Ornstein-Uhlenbeck process nationallicence Stochastic averaging nationallicence Martingale problem nationallicence Baxendale Peter Department of Mathematics, University of Southern California, Los Angeles, CA, USA aut Greenwood Priscilla Department of Mathematics, University of British Columbia, Vancouver, BC, Canada aut Journal of Mathematical Biology Springer-Verlag 63/3(2011-09-01), 433-457 0303-6812 63:3<433 2011 63 285 https://doi.org/10.1007/s00285-010-0376-2 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00285-010-0376-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Baxendale Peter Department of Mathematics, University of Southern California, Los Angeles, CA, USA aut NATIONALLICENCE 700 1- Greenwood Priscilla Department of Mathematics, University of British Columbia, Vancouver, BC, Canada aut NATIONALLICENCE 773 0- Journal of Mathematical Biology Springer-Verlag 63/3(2011-09-01), 433-457 0303-6812 63:3<433 2011 63 285 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer