Wavelet transform using for analysis of vibroimpact system chaotic behavior

Abstract

Chaotic behaviour of dynamical systems, their routes to chaos, and the intermittency are interesting and investigated subjects in nonlinear dynamics. The studying of these phenomena in nonsmooth dynamical systems is of the special scientists' interest. In this paper we apply relatively young mathematical tool -continuous wavelet transform CWT -for investigating the chaotic behavior and intermittency in particular in strongly nonlinear non-smooth discontinuous 2-DOF vibroimpact system. We show that CWT applying allows to detect and determine the chaotic motion and the intermittency with great confidence and reliability, gives the possibility to demonstrate route to chaos via intermittency, to distinguish and analyze the laminar and turbulent phases.

Transitional regimes under route to chaos in vibroimpact system

“…. Its dynamical behaviour was studied in details in our previous works [4,5] and references therein. Its amplitudefrequency responses in wide frequency range are depicted at Fig.…”

“…In [5] we showed the view of surfaces of wavelet coefficients (3D plots) and their projections for periodic and chaotic motion. They had different wellpronounced views.…”

“…It was very useful for distinguishing periodic and chaotic regimes. We have "caught" the intermittency due to its helping [5]. It is worth to point out that the intermittency finding is not such an easy task.…”

“…We have studied the quasi-periodic and intermittent routes to chaos in vibroimpact system in our previous works [4,5] and references therein.…”