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Fig. 3 | The Journal of Mathematical Neuroscience

Fig. 3

From: A showcase of torus canards in neuronal bursters

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 0.1927 is supercritical. The torus bifurcations (TR) at b 1 0.1926 and b 1 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.

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