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Figure 8 | The Journal of Mathematical Neuroscience

Figure 8

From: The uncoupling limit of identical Hopf bifurcations with an application to perceptual bistability

Figure 8

Bifurcation diagram for \(\bar{\mathcal{S}}^{-}_{ \mathrm{osc}}\) in the case \(\beta _{\epsilon 0R} > 0\), \(C_{ \mathrm{det}} + \beta _{\epsilon 0R} > 0\) and \(\beta _{\epsilon 0R} < - C_{\mathrm{det}} + \sqrt{C^{2}_{\mathrm{det}} + \beta ^{2}_{\epsilon 0I}}\). The fixed point \(\bar{\mathcal{S}}^{-}_{\mathrm{osc}}\) appears at a supercritical pitchfork bifurcation of the origin occurring at the curve \(C^{-}_{\mathrm{HB}}\), undergoes a Hopf bifurcation \(\bar{ \mathcal{H}}\) at the curve \(\operatorname{Tr}^{-}=0\) and becomes unstable at the curve \(\operatorname{Det}^{-}=0\)

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