Figure 5. Burst dynamics explained with three-dimensional V_m trajectories and bifurcation diagrams.

(for bursts in Figure 4A with I_maxpump = 95 µA/cm²). Note: x-axis scales are different is each plot. (A) The first burst of spikes in Figure 4A plotted as a function of time are now plotted in 3-D as a function of E_Na and E_K (blue arrow: direction of V_m trajectory). (B) Bifurcation diagram for fixed E_K and I_pump as per Figure 4A pink star; E_Na is the slowly varying parameter. Lines and points are labeled (see also abbreviation list) and have the same meanings in (C). For E_Na at its Figure 4A pink star value (40.2 mV), the only stable solution is a periodic orbit (pink oval), with each cycle corresponding to a spike (in a burst). The oval-loop symbolizes one cycle of V_m oscillation at fixed E_Na. During a burst the E_Na decline shifts orbits leftward into the bistability regime (pink area) where there exist two stable solutions: a limit cycle and a stable fixed point. (C) Bifurcation diagram for E_K and I_pump fixed as per Figure 4A green dot. For E_Na at its Figure 4A green dot value (37.27 mV), the system (large green dot) is within the bistability regime (green area). V_m, attracted by this fixed point, has STOs (drawn as the green loop) until E_Na increases and superthreshold-oscillations (spikes) return. The PD region corresponds to period-doubling bifurcations. (D) Two-parameter phase diagram for E_K and E_Na. Pink solid and dashed curves represent LP (saddle-node bifurcation) and HB, respectively, when I_pump is fixed as in B. The green solid, dashed, and dash-dotted curves represent LP, HB and PD, respectively, when I_pump is fixed as in C. With varying I_pump the bistability regime shifts from the pink to the green area (the zone with both colors is the overlap of these two areas). The gray area between two green dash-dotted curves is a zone with PD bifurcations. The black loop shows E_K and E_Na orbits during a burst.