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The Journal of Mathematical Neuroscience
Fig. 5 | The Journal of Mathematical Neuroscience (JMN)

Fig. 5

From: A Mathematical Model of a Midbrain Dopamine Neuron Identifies Two Slow Variables Likely Responsible for Bursts Evoked by SK Channel Antagonists and Terminated by Depolarization Block

Fig. 5

Bifurcation analysis for inverted square wave bursting (color online). a Three-dimensional bifurcation diagram with \(h_{s}\) and \(o+i\) pool as control parameters and v as the third variable. Three major bifurcation curves are demonstrated with different colors (magenta: Hopf bifurcation (HB), blue: limit points (LP), green: saddle node on an invariant cycle (SNIC), cyan: saddle node (SN)). The control parameter \(o+i\) is expanded beyond its maximum of 1, in order to demonstrating the folding structure in 3D. The dashed edge of the surface indicates that it would not be visible if the surface were not transparent. b Two-parameter bifurcation diagram in the plane of \(h_{s}\) and \(o+i\) pool. The HB curve and LP curve merge at a zero-Hopf bifurcation (red open circle, denoted ZH). The black curve is the projection of bursting trajectory from the top of Fig. 4a in the same plane. Arrows indicate bifurcation points along the trajectory. c Rotated, expanded version of 3D bifurcation diagram from panel a. The black curve again indicates a 3-D version of the bursting trajectory

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