Fig. 7.

Steady states for $\xi <1$ and $\beta >2$. We plot mussel density m against the parameter $\lambda$ for the steady-state solutions of () when $\xi =0.15$ and $\beta =6$. Solid $/$ dashed lines indicate stable $/$ unstable steady states, calculated by numerical continuation using auto (Doedel 1981; Doedel et al. 1991, 2006), with $\lambda$ as continuation parameter. Dots indicate the steady states for the reduced losses ($\lambda =1$) and increased production ($\lambda =0$) models; these are $(a,m)=(\alpha ,0)$ plus (11), (12) and (13). The five different cases shown in the figure are separated by four critical values of $\alpha /\beta$: 1, $1/{\lambda }_{\text{min}}^0\approx 1.55$, 2, and $1/\xi \approx 6.67$; a full description is given in the main text. To improve clarity, the plot for $\alpha /\beta =8.0$ is shown in two parts with different horizontal magnifications. These plots should be compared with Fig. 3, which shows the corresponding plots when $\beta <2$: the steady states are the same but there are differences in stability for $\alpha /\beta =1.8$ and 2.5