Assessing the quality of stochastic oscillations

ABRAMSON, GUILLERMO; RISAU GUSMAN, SEBASTIAN

Trieste

Conferencia; Conference and Research Workshop: Perspectives on Nonlinear Dynamics; 2007

              We analyze the relationship between the macroscopic and microscopic de-scriptions of two-state systems, in particular the regime in which the microscopic oneshows sustained ?stochastic oscillations? while the macroscopic tends to a fixed point. Wepropose a quantification of the oscillatory appearance of the fluctuating populations, andshow that good stochastic oscillations are present if a parameter of the macroscopic modelis small, and that no microscopic model will show oscillations if that parameter is large.The transition between these two regimes is smooth. In other words, given a macroscopicdeterministic model, one can know whether any microscopic stochastic model that has itas a limit, will display good sustained stochastic oscillations.