Statistical characteristics of chaoticity and incomplete chaoticity of irregular oscillations generated by a strongly nonlinear autonomous system with two degrees of freedom

The notion of the interval of nonergodicity as one of the statistical characteristics for time realizations of an irregular process is introduced. A method for determination of this factor based from the analysis of autocorrelation functions of truncated realizations is developed. The chaoticity of irregular oscillations in a strongly nonlinear autonomous system with two degrees of freedom is proved using the criterion of decomposition of time correlations. The statistical indication of the existence of incomplete chaoticity of oscillations in the case of incomplete decomposition of correlations is formulated. Conditions of weak distortions of the energy spectrum for truncated realizations are determined. Probability distribution functions for the characteristics of an irregular time process in the studied system are considered.