Cherenkov D.   Zuev S.  

Probabilistic model of nonlinear process

Reporter: Cherenkov D.

A description is given for the model of a dynamical system in terms of the probability of the system state. Such a description might be useful in forecasting and safety problems, where the system has nonlinear nature and, in particular, in case of dynamic chaos.

The dynamic system is considered as described by the differential equation y '= Q (t, y). It is assumed that the only observable y (t) of this system is measured by the device, the accuracy of which is equal to b/2, and the time is measured with some accuracy a/2. The absence of singular points near the initial and final states of the system is needed for the model.

Under these assumptions a probabilistic model of the system is presented: the model calculates the probability for the system to be in the neighborhood of the point (y1, t1), if in the beginning the system was in the neighborhood of (y0, t0).

The result is illustrated by the computer program that lets you to enter the function Q (t, y), the initial conditions, the accuracy and the end point. As a result, the program gives a picture of the evolution of the dynamic system in a "vague" curve or a family of such curves.

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