Figure 3.

A system design exhibits both resonator and integrator behaviours as a parameter is incrementally varied. This figure studies design II. Other designs can be seen in the electronic supplementary material. (a) For lower values of the varied parameter, low-amplitude oscillations, i.e. resonator behaviour (Baer et al. 1989), was obtained (black line x(t); grey line, y(t); dashed line, S(t)). As the parameter is incrementally increased, the period increases, reflecting integrator behaviour (Rinzel & Ermentrout 1989). Parameter values: ϵ=1, ξ=0.06, ρ=100, σ₁=0, σ₂=0.4, with Δ=1.8+t/100. Initial conditions were x=0.93 and y=5.0668, the steady -state values for Δ=1.8. (b) One parameter (Δ) bifurcation diagram illustrating both a HB (resonator) and a SNIC bifurcation (integrator). x(t) is the activator concentration. Black solid line, stable x^*; dashed line, unstable x^*; thick grey line, stable LC; thin grey line, unstable LC.