Manifestation of Chaos in Real Complex Systems: Case of Parkinson’s Disease

In this paper we present a new approach to the research of manifestations of chaos in real complex system. Recently we have achieved the following information. In real complex systems the informational measure of chaos (IMC) can serve as a reliable quantitative estimation of the state of a complex system and help to estimate the deviation of this state from its normal condition. As the IMC we suggest the statistical spectrum of the non-Markovity parameter (NMP) and its frequency behavior. Our preliminary studies of real complex systems in cardiology, neurophysiology and seismology have shown, that the NMP has diverse frequency dependence. It testifies to the competition between Markovian and non-Markovian, random and regular processes and makes a crossover from one relaxation scenario to the other possible. On this basis we can formulate the new concept in the study of the manifestation of chaos. We suggest the statistical theory of discrete non-Markov stochastic processes to calculate the NMP and the quantitative evaluation of the IMC in real complex systems. With the help of the IMC we have found out the evident manifestation of chaos in a normal (healthy) state of the studied system, its sharp reduction in the period of crises and catastrophes and various human diseases. It means, one can improve the state of a patient (of any system) appreciably by increasing the IMC of the studied live system. The given observation creates a reliable basis for predicting crises and catastrophes, as well as for diagnosing and treatment various human diseases, Parkinson’s disease, in particular.