Random fluctuations around a stable limit cycle in a stochastic system with parametric forcing.

Seminar/Forum

Random fluctuations around a stable limit cycle in a stochastic system with parametric forcing.

Often population-size data exhibits stochastic behavior that appears to include some periodicity. In terms of populations, such a time series may contain a limit cycle arising through seasonal variation of a parameter such as disease transmission rate. An attractive model is a stochastic differential system with periodic parametric forcing whose solution is a stochastically perturbed limit cycle. Here we show that the structure of such stochastic fluctuation around a limit cycle is analogous to that of stochastic fluctuation about a fixed point. Further, we show that the stochastic path can be expressed, approximately, as a product which reveals, in terms of Floquet theory, the roles of the frequencies of the limit cycle and of the stochastic perturbation. This result, based on a new limit theorem near a Hopf point, yields an understanding of the previously computed power spectral density..

Joint work with May Ann Mata and Rebecca Tyson, on line with J. Math. Biolo.

Presenter

  • Professor Emeritus Cindy Greenwood
    Professor Emeritus Cindy Greenwood, University of British Columbia