Description of the chaotic state of a nonlinear dynamical system using a smoothed distribution function
DOI:
https://doi.org/10.33910/2687-153X-2025-6-4-196-206Keywords:
nonlinear dynamics, chaos, distribution function, probability density, chaotic attractor, fluctuations of the distribution function, radiation spectraAbstract
This paper considers the possibility of describing the chaotic state of dynamical systems using a distribution function. It is shown that for dissipative systems, a description employing a distribution function similar to that used in statistical physics is inadequate. This is explained by the fact that with long evolution times, the corresponding function ceases to be continuous. A definition for a smoothed distribution function, obtained through a specific averaging of the statistical distribution function, is proposed. The equation for the smoothed distribution function is derived. The results are applied to calculate the emission spectra of dynamical systems in a chaotic state.
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