Investigation of Selected Mechanical Systems By Recurrence Plots Method

Recurrence of states, in the meaning that states are arbitrary close after some time, is a fundamental property of deterministic dynamical systems and is typical of nonlinear or chaotic systems. The main idea of the recurrence plots (RPs) method consists in revealing all the times when the phase space trajectory of the dynamical system visits roughly the same area in the phase space. Such recurrence of states is marked within a two-dimensional matrix with ones and zeros. Graphical representation of such a matrix is known in the literature as a recurrence plot. The paper concerns results of research into dynamic properties and determinism of selected mechanical systems. In order to analyze measured responses (time histories) of the considered systems with the use of the recurrence plots, the phase space of these systems was reconstructed by delay embedding. The smallest sufficient embedding dimensions were estimated with the use of the false nearest neighbors algorithm. For the purposes of time delay determining the method of mutual information function was used. All the necessary computations were performed with the use of the CRP Toolbox for MATLAB.