000015773 001__ 15773
000015773 005__ 20161115135329.0
000015773 04107 $$aeng
000015773 046__ $$k2013-06-12
000015773 100__ $$aBlekhman, I.
000015773 24500 $$aMultimode Character of Dynamical Systems As a Cause of Their Complex ("Chaotic") Behavior

000015773 24630 $$n34.$$pComputational Methods in Structural Dynamics and Earhquake Engineering
000015773 260__ $$bNational Technical University of Athens, 2013
000015773 506__ $$arestricted
000015773 520__ $$2eng$$aThis study puts under consideration dynamic systems, whose visible complex (“chaotic”) behavior is caused by transition from one motion mode to another. Such motion modes may be represented in particular by some stable in the small periodic motions with different periods. Two types of such systems are singled out. In the first case a number of motion regimes with closely located domains of attraction coexist in the phase space of the system at certain values of parameters. The transition from one stable regime of motion to another is due to the inaccuracy of computer calculations and variation of parameters in the corresponding physical system. In the second case a systematic transition from one regime of motion (which is not necessarily stable) to another occurs due to the internal properties of the system. As an example is the situation, when one of the phase variables may be considered as a relatively slowly varying parameter passing through the existence and steadiness domains of various regimes. The behavior of a particle over a horizontal vibrating plane and emergence of a turbulent surface layer in liquid placed in a vibrating vessel are considered in this paper as illustrative examples. The resemblance of this process to that of the thermoconvection is pointed out. The other example is an analogue of the Lorenz oscillator marked by a phase pattern projection similar to the well-known ”butterfly“ pattern. Some thoughts corroborating Landau turbulence theory are suggested. It is noted that the complex motion under consideration is characteristic for sufficiently wide scope of dynamic systems such as a pendulum with a vibrating axis, the self-synchronizing oscillating and rotating objects, the systems with period doubling, the parametrically excited distributed systems. The author is grateful to A.L. Fradkov for the discussion and comments.

000015773 540__ $$aText je chráněný podle autorského zákona č. 121/2000 Sb.
000015773 653__ $$adynamical systems, multimode situation, complex behavior, chaos, examples.

000015773 7112_ $$aCOMPDYN 2013 - 4th International Thematic Conference$$cIsland of Kos (GR)$$d2013-06-12 / 2013-06-14$$gCOMPDYN2013
000015773 720__ $$aBlekhman, I.
000015773 8560_ $$ffischerc@itam.cas.cz
000015773 8564_ $$s924072$$uhttps://invenio.itam.cas.cz/record/15773/files/1432.pdf$$yOriginal version of the author's contribution as presented on CD, section: CD-MS 28 PERIODICITY EFFECTS AND PERIODICITY-BASED METHODS IN VIBRO-ACOUSTICS AND STRUCTURAL DYNAMICS
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000015773 962__ $$r15525
000015773 980__ $$aPAPER