Discrete Dynamics in Nature and Society
Volume 1 (1997), Issue 3, Pages 233-241

About chaotization mechanisms of the distributed dynamical systems which are close to discrete

Yu. P. Bliokh, M. G. Lyubarsky, and V. O. Podobinsky

Plasma Electronics Institute of National Science Center "KFTI", Kharkov, Ukraine

Received 15 February 1997

Copyright © 1997 Yu. P. Bliokh et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The investigations of stochastization mechanisms of distributed dynamical systems (DDS) are developed not so complete as stochastization of dynamical systems with concentrated parameters (CDS). Therefore the corresponding DDS which is close (in one or other sense) to the CDS under consideration is used. Such substitution means some roughening of an initial problem. However, there are such important stochastization mechanisms understanding properties, which are connected with system “distributivity” on principle. In this paper the conception of a proximity to the CDS is introduced for one particular class of the DDS. It is shown that such kind of systems has two stochastization mechanisms, one of which is common to the DDS and the corresponding CDS. Another stochastization mechanism inherent in DDS disappears under transition from DDS to CDS.

Distributed dynamical system considered below is not abstract but describes the set of concrete physical devices, for example, microwave oscillators. It may be devices in which kinetic energy of an accelerated electron beam is transformed into electromagnetic radiation energy, or oscillators with delayed feedback.