The essence of life - maintaining the system in a state of half-chaos

Half-chaos has unique properties that explain the essence of the life process and shift the range of allowed parameters of living object models, previously limited to the edge of chaos by the famous Kauffman hypothesis, to more adequate areas of chaos. It was detected by simulations of the evolution of dynamic complex networks, the descriptions of these studies are not simple. This simplified article (more in the book "Draft of the deductive theory of life") can significantly facilitate understanding the essence of half-chaos and the creation of description in the language of mathematics expected by mathematicians. Kauffman's hypothesis: 'life on the edge of chaos' is based on the statistical result of a model of fully random logical networks, but living objects are selected by a Darwinian mechanism, so they are not fully random. Also, limiting the model to two-state signals introduces a significant error in statistical studies. Kauffman's model allows two states of the system - either it is ordered and a small disturbance practically always fades out, or it is chaotic and a small disturbance causes practically always a large change in functioning. In between there is a narrow (in the system parameters) phase transition. In my research, the demand for a small attractor causes the system to cease to be fully random, and at the same time a third state appears – half-chaotic, in which small and large changes in functioning after a small disturbance have a similar share, even though the system parameters, if it were fully random, would give strong chaos. Leaving only the disturbing changes that give small changes in functioning does not lead out of the half-chaos state, it creates a Darwinian evolution of the system, it gives a definition of life. In the distribution of the size of changes in functioning, there is a large gap between small and large changes, which gives a natural limitation of small changes, a natural criterion of the identity of the evolving system and a criterion of elimination, which we did not have so far.