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 doubleplate 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.