SINGULAR FEATURES OF LARGE FLUCTUATIONS IN OSCILLATING CHEMICAL-SYSTEMS

We investigate the way in which large fluctuations in an oscillating, spatially homogeneous chemical system take place. Starting from a mast er equation, we study both the stationary probability density of such a system far from its limit cycle and the optimal (most probable) fluc tuational paths in its space of species concentrations. The flow field of optimal fluctuational paths may contain singularities, such as swi tching lines. A ''switching line'' separates regions in the space of s pecies concentrations that are reached, with high probability, along t opologically different sorts of fluctuational paths. If an unstable fo cus lies inside the limit cycle, the pattern of optimal fluctuational paths is singular and self-similar near the unstable focus. In fact, a switching line spirals down to the focus. The logarithm of the statio nary probability density has a self-similar singular structure near th e focus as well. For a homogeneous Selkov model, we provide a numerica l analysis of the pattern of optimal fluctuational paths and compare i t with analytic results.