Low-frequency phenomena in dynamical systems with many attractors

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Abstract
Power spectra of multistable systems have a low-frequency component corresponding to jumps among independent attractors. This situation is modeled with a one-dimensional cubic map disturbed by noise. Besides the dependence of the spectral slope on noise, we show that the Lyapunov exponent is made of two separate contributions corresponding to the attracting and repulsive regions, respectively, each weighted with its relative occupation time.