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Decayless kink oscillations of solar coronal loops are studied in terms of alow-dimensional model based on a randomly driven Rayleigh oscillator withcoefficients experiencing random fluctuations. The model considers kinkoscillations as natural modes of coronal loops, decaying by linear resonantabsorption. The damping is counteracted by random motions of the loopfootpoints and the interaction of the loop with external quasi-steady flowswith random fluctuations. In other words, the model combines theself-oscillatory and randomly driven mechanisms for the decayless behaviour.The random signals are taken to be of the stationary red noise nature. In thenoiseless case, the model has an asymptotically stationary oscillatorysolution, i.e., a kink self-oscillation. It is established that the kinkoscillation period is practically independent of noise. This finding justifiesthe seismological estimations of the kink and Alfv\'en speeds and the magneticfield in an oscillating loop by kink oscillations, based on the observedoscillation period. The oscillatory patterns are found to be almost harmonic.Noisy fluctuations of external flows modulate the amplitude of the almostmonochromatic oscillatory pattern symmetrically, while random motions of theloop footpoints cause antisymmetric amplitude modulation. Such modulations arealso consistent with the observed behaviour.

Do Periods of Decayless Kink Oscillations of Solar Coronal Loops Depend on Noise?