Intermittent and Quasi-periodic Routes to Chaos in Vibroimpact System

There is a detailed numerical investigation of dynamical behaviour of two-body 2-DOF vibroimpact system under periodical excitation in this work. Authors found two main routes to chaos – intermittent and quasi-periodic ones. Different ways for detection of the motion kind were given: periodic, quasi-periodic or chaotic. These ways were both usual methods and relatively young mathematical tool – continuous wavelet transform CWT. The usual methods are the construction of phase trajectories, Poincaré maps, Fourier spectra, the largest Lyapunov exponents calculation, and fractal structure watching. But intermittency was “caught” just by CWT applying. Authors found the transient chaos and have obtained its beautiful Poincaré map – “Leaflet de Poincaré” which demonstrates well-pronounced fractal structure. Also the peculiarity of the largest Lyapunov exponent estimation for non-smooth discontinuous dynamical system was described. Was given the brief description of interesting phenomena unique for non-smooth discontinuous systems that were observed before. Exposition is accompanied by a lot of graphs and Tables that illustrate the results of huge numerical experiments volume.