Fig. 3

Dynamics of the HR system (Equations 4a-4c) at $s=-1.95$. (a)-(e) Time series of the voltage variable x at several values of $b_1$, with $b_1$ decreasing from top to bottom. (f) Bifurcation diagram, including branches of fixed points (black curve) and periodic orbits (two red curves, indicating maximal and minimal values of x over the orbit). Solid/dashed curves indicate stable/unstable solutions. The Hopf bifurcation (H) at $b_1\simeq -0.1927$ is supercritical. The torus bifurcations (TR) at $b_1\simeq -0.1926$ and $b_1\simeq -0.1603$ are also supercritical. Direct numerical simulations show that the system exhibits bursting (□, indicating maximal and minimal values of x) and AM spiking (△, indicating extrema of the modulation envelope) at values of $b_1$ between the two torus bifurcations.