The cumulant approach for investigating the noise influence on mode-locking bifurcations

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Abstract
The influence of noise on mode-locking bifurcations is investigated for the circle map and for coupled logistic maps. The technique based on the cumulant expansion is used for the bifurcation analysis of these systems. It is shown that this cumulant analysis in Gaussian approximation provides a suitable description of the influence of weak noise. We find that the universal scaling properties for the circle map in the critical point for the golden-mean sequence are the same as those obtained analytically using the path integral technique. We find the same scaling behaviour in the case of weak multiplicative noise.

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