Figure 2. One parameter bifurcation diagrams of stationary states of the robust burster cases from the leech heart interneuron database.

The bifurcation parameter is the conductance of the leak current, . The solid and dashed intervals of a bifurcation curve denote stable and unstable stationary state branches, respectively. Labeled points in panels B–F indicate bifurcations of stationary states: LP and AH stand for the fold and Andronov-Hopf bifurcations, respectively. The navy blue bars indicate the ranges of values supporting attracting bursting regimes, while the colored bars above them denote ranges supporting the coexistence of distinct attracting regimes. The color code of the bars is described in the key and is consistent between figures (Figures 2,4,6). Panels D, and F are magnifications of the diagrams around the range supporting bursting in panels C and E, respectively. The vertical navy blue lines in panels B, D, and F and Figure 4B indicate the original value for the case in the database. A: A stylized bifurcation diagram illustrating the naming convention for the intervals on the branches where stationary states are stable: hyp1, hyp2, dep1, and dep2. B: Magnification of the bifurcation diagram for case #288298 that displays a stable interval hyp2 on the middle branch delimited by two Andronov-Hopf bifurcations, AH2 and AH3. The green bar denotes a range supporting bursting and the hyp2 stationary state. C and D: In the case #1292494 there are three stable stationary state intervals. C: The red brown bar indicates a range of values supporting the coexistence of dep1 and dep2 stationary states. The Andronov-Hopf bifurcation (AH2) and the fold bifurcation LP3 determine the dep1 interval. The fold bifurcation (LP4) defines the right border of the dep2 interval. The left border of the bistability range is 0 nS. C and D: The magenta bar marks coexistence of dep1 and bursting. The bar is limited by the range supporting bursting on the left side and by Andronov-Hopf bifurcation AH2 on the right side. The cyan bar indicates coexistence of hyp1 and bursting between the Andronov-Hopf Bifurcation (AH1) and the border where bursting disappears. E and F: A case where the original value in the database falls into a range of bistability of bursting and hyp1 stationary state (cyan bar). The bistability range is defined by the Andronov-Hopf bifurcation (AH1) and the right border where bursting disappears.