Stochastic description of a period-2 limit cycle
Centre for Nonlinear Phenomena and
Complex Systems, Université Libre de Bruxelles Campus
plaine C.P. 231, 1050 Brussels, Belgium
Accepted: 26 August 1997
The effect of internal noise on the period-2 behavior is investigated in low-dimensional dynamical systems. To treat the morphological complexity of such attractors, a general stochastic formulation using a suitable moving frame in the Gaussian approximation is set up. Its applicability is illustrated on a specific model, the Willamowski-Rössler chemical scheme. Using this approach, we are able to interpret the direct simulations of the master equation which show significant changes with respect to the deterministic behavior. Specifically, a band merging in the multi-periodic regime which at first sight seems to disrupt the bifurcation cascade is observed. Marked inhomogeneities in the fluctuations distribution along the period-2 attractor explaining these features are brought out.
PACS: 05.40.+j – Fluctuation phenomena, random processes, and Brownian motion / 05.45.+b – Theory and models of chaotic systems / 82.20.Wt – Computational modeling; simulation
© EDP Sciences, 1997