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Fig. 4 | The Journal of Mathematical Neuroscience

Fig. 4

From: Data Assimilation Methods for Neuronal State and Parameter Estimation

Fig. 4

Three different excitability regimes of the Morris–Lecar model. The bifurcation diagrams in the top row depict stable fixed points (red), unstable fixed points (black), stable limit cycles (blue), and unstable limit cycles (green). Gray dots indicate bifurcation points, and the dashed gray lines indicate the value of \(I_{ \textrm{app}}\) corresponding to the traces shown for V (middle row) and n (bottom row). (A) As \(I_{\textrm{app}}\) is increased from 0 or decreased from 250 nA, the branches of stable fixed points lose stability through subcritical Hopf bifurcation, and unstable limit cycles are born. The branch of stable limit cycles that exists at \(I_{\textrm{app}}=100\) nA eventually collides with these unstable limit cycles and is destroyed in a saddle-node of periodic orbits (SNPO) bifurcation as \(I_{\textrm{app}}\) is increased or decreased from this value. (B) As \(I_{\textrm{app}}\) is increased from 0, a branch of stable fixed points is destroyed through saddle-node bifurcation with the branch of unstable fixed points. As \(I_{\textrm{app}}\) is decreased from 150 nA, a branch of stable fixed points loses stability through subcritical Hopf bifurcation, and unstable limit cycles are born. The branch of stable limit cycles that exists at \(I_{\mathrm{app}}=100\) nA is destroyed through a SNPO bifurcation as \(I_{\mathrm{app}}\) is increased and a SNIC bifurcation as \(I_{\mathrm{app}}\) is decreased. (C) Same as (B), except that the stable limit cycles that exist at \(I_{\mathrm{app}}=36\) nA are destroyed through a homoclinic orbit bifurcation as \(I_{ \mathrm{app}}\) is decreased

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