Fig. 10.

Period-doubling cascade. a Branch with period-doubling cascade and stable non-trivial periodic solutions. We plot one period of several stable solutions along the branch, whereas we omit the unstable branch emanating from ${\text{HB}}_{\text{I}}$. Solutions feature increasing solution periods, $T_1\approx 12.6$, $T_2\approx 13.8$, $T_3\approx 14.9$, $T_4\approx 28.9$, corresponding to ${\mathit{\Omega }}_1\approx 0.500$, ${\mathit{\Omega }}_2\approx 0.455$, ${\mathit{\Omega }}_3\approx 0.422$, ${\mathit{\Omega }}_4\approx 0.217$, respectively. Parameters $\mathit{\omega }=0.5$, $a=0.5$, $b=-0.5$ $\mathit{\alpha }=0.5$ and $\mathit{\beta }=-0.05$. b Attractor found for $\mathit{\gamma }=3.42$; the coordination regime shows erratic phase changes, during which $x_1$ and $x_2$ alternate in the leading position. This regime involves fast velocity switches, as evidenced by the time traces of $y_1$ and $y_2$. Solid lines represent stable and dashed lines unstable states of (11)