Abstract
An modeling attempt of behavior process of brain electric impulses for some patient by the solutions of 3D system of quadratic differential equations is undertaken. (This system of differential equations was got from a multivariate times series with the help of polynomial averages and least square method.) Transition conditions from a chaotic attractor to a limit cycle (and vice versa) of the system of differential equations are found. Exactly these conditions characterize beginning of process of disease by Parkinson’s illness at the patient.
Highlights
Last years theory of chaos, a nonlinear dynamics, and sciences about complication of one or another processes began to act important role in biology, medicine and row of contiguous fields
The theory of chaos allows rather to describe some aspects of behavior of the complex biological systems by certain numerical descriptions, such as the Lyapunov exponent, fractal dimension, multiplicity of limit cycle etc
One of important examples of such approach are epileptology methods. These methods being based on the study of brain electrical activity with the help of electroencephalograms (EEG)
Summary
Last years theory of chaos, a nonlinear dynamics, and sciences about complication of one or another processes began to act important role in biology, medicine and row of contiguous fields. Most valuable achievement will be not got some numerical values, but description and reformulation medical problems in terms of simulation tasks and measurement of signals [8]. One of important examples of such approach are epileptology methods These methods being based on the study of brain electrical activity with the help of electroencephalograms (EEG). From the experimental point of view a problem consists in that on the basis of time series of the measured values of rhythms of brain activity to recreate development of the dynamic system (it is a brain) in phase space. Further with the help of the got dynamic system it is necessary to study processes resulting in appearance epilepsy or Parkinson’s illness [6, 10]. In the present paper we consider the problem of reconstructing dynamical system (it is a system of differential equations describing impulses of brain activity) from multivariate time series
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