In vivo neural activity of electrosensory pyramidal cells: Biophysical characterization and phenomenological modeling

doi:10.1371/journal.pcbi.1013711

In vivo neural activity of electrosensory pyramidal cells: Biophysical characterization and phenomenological modeling

Fig 5

Bifurcation analysis of the deterministic modified Hindmarsh-Rose (HR) model shows similar dynamic regimes as those of the full model.

(A) One-parameter bifurcation diagram of the voltage variable (V) of the modified HR model with respect to the applied current (), illustrating the various regimes of behavior corresponding to branches of stable equilibria (orange line), branches of unstable equilibria (dashed black line), branches of stable periodic orbits (green lines), branches of bursting orbits (dashed green line), and branches of unstable periodic orbits (dashed blue line). Within the range of considered, the model undergoes several types of bifurcation points, including 2 saddle-node bifurcations (SN1, SN2), 6 Hopf bifurcations (HB1-HB6), 2 saddle-node bifurcations of periodic orbits (SNP1, SNP2), 2 homoclinic bifurcations (HM1, HM2), 2 period-doubling bifurcations (PD1, PD2) and 1 torus bifurcation (TS), some of which define the boundaries of the various regimes of behavior identified. The two insets provide magnified views of the areas enclosed by the bounding boxes in the main figure: the top inset corresponds to the larger, more physiologically relevant box, while the bottom one corresponds to the smaller, unphysiological box. (B) Plot of the firing rate of the modified HR model over a 20 sec interval with respect to , highlighting chaotic dynamics consistent with the biophysical model (compare to S4B Fig). (C) A sample of three principal firing patterns: tonic spiking (, left), ghostbursting in the form of doublets (, middle) and chaotic ghostbursting (, right). These patterns demonstrate the rich repertoire of activity captured by the modified HR model.

doi: https://doi.org/10.1371/journal.pcbi.1013711.g005