Logistic mapping as the means of the description of the speech rhythm in the vicinity of the critical point

The concept of the speech rhythm as a sequence of duration of the segments in the acoustic signal is introduced. These segments are obtained in accordance with a principle "is a voice-is not a voice" (principle "Voice/Unvoice"). By an evaluation of Kolmogorov entropy for the empirically obtained rhythms is shown that the rhythm of normal speech is exhibiting irregular chaotic dynamics and the rhythm of samples consisting only of violations of smoothness in stutterer\´s speech is exhibiting regular dynamic process with a zero entropy. Thus the rhythm of speech is exhibiting dynamics of a system near to critical point. The direct evaluation of indexes of a critical behavior shows, that for exposition of dynamics of speech rhythm it is possible to use Feigenbaum scenario of route to chaos for logistics mapping with control parameter. Hopfield discrete neural net is offered to be use as neurodynamics model of a complex system with critical behavior. The total modification of the "synaptic weights" in such net during "learning" is featured by the same Feigenbaum scenario of route to chaos for logistics mapping in which parameter of "learning" in net is used as control parameter. The requirement is fixed at which both the segments of the rhythm accepted by such model and segments of the rhythm generated by this net are identical lo total modification of the "synaptic weights" on the each step of the net\´s evolution during learning. The outcomes are used in practice of correction of stuttering in Saint Petersburg Research Institute of Ear, Throat, Nose and Speech.