Study of chaotic dynamics of the parameters of biomedical systems

In the article, the study of chaotic dynamics of complex non-stationary biomedical systems, and in particular, a special type of chaos arising in the parameters that describe these systems is discussed. A special type of chaos is understood as the existence of irreproducible aperiodic regimes in the dynamic systems: x(t₀) = var and f(x_i) = var, when t → ∞. In contrast to the Lorenz deterministic chaos, in such systems not only the process is irreproducible, but the initial state of the system is also always irreproducible x(t₀). The study is based on the use of methods of nonparametric mathematical statistics, methods of nonlinear dynamics (calculation of the senior Lyapunov exponent), as well as calculation of the parameters of quasi-attractors, which qualitatively and quantitatively describe the chaotic dynamics of biomedical signals. Using the analysis of autocorrelation, it was shown that the parameters of biomedical systems, using the example of cardio signal elements (time series of cardio intervals) of the cardiovascular system, have a strictly chaotic structure and a non- linear trend line. The calculation of the senior Lyapunov exponent showed that there is a constant change of sign (+, -, 0) at different time intervals of the cardio signal, which also proves the presence of chaos, different from Lorentz chaos, which has a positive sign for the senior Lyapunov exponent, as well as a repeated initial state of the system x(t₀). A method has been developed that made it possible to quantitatively and qualitatively describe the chaotic dynamics of the behavior of the state vector of the system, obtain objective information about changes in the functional state of the system, and also warn about these changes in time (if pathologies), what creates conditions for physiological monitoring of the status of the functional systems of the human body.