Fig. 2

Left: Example of a periodic delay function, the saw-function. Right: plot of the CVs in the plane $(c,\sigma )$, the line labelled P is the pitchfork line, the line labelled H is the Hopf curve. The two bounds of Proposition 3.15 are also shown. Parameters are: $L_0=\mathrm{Id}$, $J(x)=s_1(-1+1.5cos(2x))\frac{2}{\pi }$, $\beta =\frac{1}{4},s_1=\frac{1}{4}$. The labels 1, 2, 3, indicate approximate positions in the parameter space $(c,\sigma )$ at which the trajectories shown in Figure 3 are computed.