TABLE OF CONTENTS Let us now return to the Figures 4.18 and 4.19 and consider the route to chaos from the nonresonant attractor S n to the cross-well chaotic motion. Both figures show that, with the increase of the frequency ?, the nonresonant attractor S n loses its stability at the saddle-node bifurcation snA, and then it disappears. After that, the system begins to execute the cross-well chaotic oscillations. To explain the sudden change of the character of motion, let us look carefully on the samples of time-histories of the chaotic motion, immediately after disappearance of the S n attractor.
First, on the schematic Figure 4.23, we select a frequency ? 1 just prior to the critical ? snA value, and we also select two other frequencies at higher values inside the chaotic region (frequencies ? 2 and ? 3, respectively). No doubt, at ? 1 the nonresonant T-periodic S n attractor does exist (Figure 4.24(a)). Then, at ? 2 and ? 3, the frequencies that belong to region of the cross-well chaos, somewhat strange phenomenon is observed. In long time intervals the system still executes single-well oscillations, close to those illustrated in the previous figure. However, these nearly regular oscillations are interrupted by bursts of limited time duration, when the system behavior is chaotic (Figure 4.24(b)). Moreover, time intervals of the regular and chaotic component of motion are unpredictable. We also notice...
