Statistical Memory Effects in Time Series Dynamics: Application to Parkinson’s Disease

In this work we present a new approach to the problem of diagnosing and forecasting various states in patients with Parkinson’s disease. Recently we have achieved the following result. In real complex systems the non-Markovity parameter (NMP) can serve as a reliable quantitative measure of the current state of a complex system and can help to estimate the deviation of this state from the normal one. Our preliminary studies of real complex systems in cardiology, neurophysiology, epidemiology and seismology have shown, that the NMP has diverse frequency dependence. It testifies to the competition between Markov and non-Markov, random and regular processes and makes a transfer from one relaxation scenario to the other possible. On this basis we can formulate the new method of diagnosing deflections in the central nervous system caused by Parkinson’s disease. We suggest the statistical theory of discrete non-Markov stochastic processes to calculate the NMP and the quantitative evaluation of various dynamic states of real complex systems. With the help of NMP we have found evident manifestation of Markov effects in a normal (healthy) state of the studied live system and its sharp decrease in the non-Markov states in the period of crises and catastrophes and various human diseases. The given observation creates a reliable basis for predicting crises and catastrophes, as well as for diagnosing and treating various human diseases, Parkinson’s disease, in particular.