Bistable limit cycle oscillations in chemical systems. II. Mechanisms for noise-induced transitions

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Abstract:

External noise coupled to Rössler's model of a nonlinear chemical system is considered, and noise-induced transitions between coexisting three-looped limit cycles are studied. Two mechanisms account for these transitions. These are analogs of mechanisms which have been identified for the noise-induced transitions of a stochastic, discrete-time dynamical system. The effects of changing the statistical properties of the external noise process are also investigated. The dynamical response of the system has a straightforward interpretation in terms of the structure of the basins of attraction. The correlation time of the noise process is one important determinant of the system's response to the fluctuations. In particular, if the correlation time is short, compared to the characteristic time for the oscillations of the system, the analogy with the discrete-time mechanisms for transitions breaks down. © 1987 American Institute of Physics.