Fig. 4

An example of sub-Hopf/fold cycle bursting in the HR system (Equations 4a-4c), with $(b_1,s)=(-0.162,-1.95)$. The other parameter values are given by Equation 5. (a) Time series of the fast x variable. (b) Time series of the slow z variable. (c) The bursting trajectory (blue curve) plotted in projection onto the $(z,x)$ phase space, along with the bifurcation diagram of the fast system at this value of s. The bifurcation diagram includes branches of fixed points and periodic orbits, and follows the plotting conventions in Figure 2. The inset shows the Poincaré map of the bursting trajectory near SNp, also plotted in projection onto the $(z,x)$ phase space. The Poincaré surface $\mathrm{\Sigma }\equiv \{(x,y,z)|0=sa{x}^3-s{x}^2-y-bz\}$ is chosen so that the iterates correspond to local extrema in x of the trajectory.