Figure 1

(Color online) Phase diagrams displaying sequences of chaotic regions (colors; lighter shadings) which recur as the driving amplitude $B$ of the Duffing oscillator increases. These phase diagrams discriminate between regularity, indicated by the darker shadings, corresponding to negative Lyapunov exponents, and chaos, indicated by the colors (lighter shadings), corresponding to positive exponents. The sequences of chaotic regions contained inside the two sets of boxes are magnified in Figs. 2, 3.Reuse & Permissions

Figure 2

(Color online) Details of the chaotic phases contained inside the blue boxes in Fig. 1 displaying structural similarities as the forcing amplitude $B$ increases. The right side shows magnified views of the white boxes on the left. Darker islands on the right are shrimps [20]. Numbers refer to the period of individual shrimps in multiples of $2\pi$, the period of the external drive. Distinct period-adding cascades converge toward the accumulation horizons at the boundary of the dark zone of period 3 in the lower left corner. The right side illustrates the great similarity of structuring as $B$ grows. Details inside the box in (d) are shown magnified in Fig. 4. The coloring scheme is the same as described in Fig. 1. Note differences in scales.Reuse & Permissions

Figure 3

(Color online) Zoom of the green boxes of Fig. 1 evidencing complex bifurcation sets embedded in chaotic phases with close structural similarity as $B$ grows. The inner structuring of this sequence of chaotic regions is very distinct from the sequence in Fig. 2. Both sequences are typical of flows. The coloring is the same as described in Fig. 1.Reuse & Permissions

Figure 4

(Color online) (a) Zoom of the accumulation horizon seen in Figs. 2a, 2d. Numbers denote periods in multiples of $2\pi$, the period of the external drive. (b) Magnification of the box in (a). The period-adding cascade indicated by the green dots accumulates along the upper dashed line, defined by Eq. (2), toward the red dot on the accumulation horizon, the lowest dashed line, defined by Eq. (3), boundary between positive and negative Lyapunov exponents. The coloring is the same as described in Fig. 1.Reuse & Permissions