Authors: Hedrih, Katica (Stevanović) 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: The integrity of dynamical systems
Journal: Nonlinear Analysis, Theory, Methods and Applications
Volume: 63
Issue: 5-7
First page: 854
Last page: 871
Issue Date: 30-Nov-2005
Rank: M22
ISSN: 0362-546X
DOI: 10.1016/j.na.2004.12.037
Abstract: 
This paper opens a discussion on what are the basic properties, contents and concept of integrity of dynamical systems. The main research problem for the study of the integrity of dynamical systems is to recover measures of integrity of dynamical system structures and dynamical system processes by which we can conclude that system dynamics is stable, whether the system possesses integrity or whether that system loses integrity. By using two examples of free and forced transversal vibrations of the elastically connected double-plate systems and corresponding system with a discontinuity in elastical connection, we show some basic properties of the integrity of basic dynamical system. The integrity of corresponding dynamical processes in the behaviour of the whole system and its subsystems or in component processes and in response of the whole system with respect to corresponding system with discontinuity have been studied by using methods of Bernoulli's particular integral and Lagrange's method of constants variation. It is shown that one-frequency regimes change into multi-frequency regimes induced by discontinuity in the system, which represents the loss of integrity of the system and marks the appearance of the loss of integrity of corresponding processes.
Keywords: Discontinuity | Double plate system | Dynamical system | Integrity | Measure | Multi-frequency | Nonlinearity
Publisher: Elsevier
Project: Real Problems On Mechanics 

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