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About chaotization mechanisms of the distributed dynamical systems which are close to discrete. (English) Zbl 0943.37017

Summary: The investigations of stochastization mechanisms of distributed dynamical systems (DDS) are developed less completely than those of dynamical systems with concentrated parameters (CDS). Therefore the corresponding CDS which is close (in one or another sense) to the DDS under consideration is used. Such substitution means some roughening of an initial problem. However, there are important stochastization mechanism understanding properties, which are connected with system “distributivity” in principle. In this paper the conception of proximity to the CDS is introduced for one particular class of the DDS. It is shown that such kind of system 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.
The distributed dynamical system considered is not abstract but describes a set of concrete physical devices, for example, microwave oscillators. That may be devices in which kinetic energy of an accelerated electron beam is transformed into electromagnetic radiation energy, or oscillators with delayed feedback.

MSC:

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37N35 Dynamical systems in control
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