In the middle of the 20th century, W. Weaver, one of the founders of information theory, propose a hypothesis about special systems of the third type (living systems). In the article, W. Weaver directly points out the inability to describe living systems within the framework of determinism and stochastics. However, no one even tried to study the third type systems from these positions over the past 70 years. 20 years ago, we proved the Eskov-Zinchenko effect in the form of a lack of statistical stability of samples of human movement parameters. A new mathematical apparatus is now proposed to accurately describe the behavior of such systems. It is based on an analogue of Heisenberg’s uncertainty principle.

The article considers the Information-analytical system of cardiographic information functional diagnostics, which allows expanding the functionality of using miniature medical devices for non-invasive diagnostics of parameters of complex dynamic biomedical systems, using the example of cardio-intervals of the cardiovascular system. The system is based on not only the methods of the deterministic-stochastic approach but also the methods of the theory of chaos-self-organization, as a new scientific approach in the natural sciences. The method is based on calculating the parameters of quasi attractors and analyzing matrices of pairwise comparisons of time series of complex biomedical systems, which allows quantitatively and qualitatively describing the chaotic dynamics of the system state vector behaviour, obtaining objective information about changes in the functional state of the system, and also warning about these changes in time (if pathologies), which creates conditions for the status of the functional systems of the human body physiological monitoring.

More than 70 years ago, W. Weaver introduced the classification of all systems of nature. A special place in this classification was allocated to the third type systems, which (as was proved over the past 20 years) do not possess statistical stability. For such systems, it is proposed to construct pairwise comparison matrices of samples that demonstrate the lack of their homogeneity. In this regard, new invariants and new models are introduced to describe the stationary modes of the third type systems and their kinematics (motion) in state phase space. The parameters of the pseudo-attractors are calculated.

Today, the evidence of the Eskov–Zinchenko effect is becoming increasingly widespread. In this case, it is proved that any set of human body parameters is unique (statistically unique). Now we are also applying this effect to the neural networks of the brain. An analysis of electroencephalograms shows that brain biopotentials are not statistically stable. For the electroencephalograms analysis, it is proposed to create paired sample comparison matrices and find numbers k of the sample pairs that can have one (common) general population. It was found that these numbers k depend on the physiological state of the test subject. For example, for epileptic patients, number k increases dramatically, and it usually does not exceed 30-45% of all 105 pairs in each of such paired comparison matrices.

In the article, the results of the development of an algorithm for creating inhomogeneous three-dimensional porous media based on stochastic fractals are presented. The issues of estimating the parameters of porosity of the media are considered. It has been shown that the fractal dimension of porous media is preserved for any slice scales and the size of the fractal grid used to build porous media, as well as the fractal dimension of matrices and porous media depends on the binary filtration parameter that forms the given porosity by changing the ratio of matrices, open and closed pores, to the total sample volume.