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

Received: 28 April 1997
Accepted: 26 August 1997

Abstract

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.