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The time series of the voltage variable V reveals the transition from spiking (Figure 8a) to bursting (Figure 8d) as the primary bifurcation parameter k increases.
We note however that the transition (as the primary bifurcation parameter k increases) from spiking to the sub-Hopf/fold cycle bursting in Figure 10 goes by way of a torus canards explosion, just as it did for the circle/fold cycle bursting in Figure 9.
The two two-parameter bifurcation diagrams share the same primary bifurcation parameter (the primary differentiation signal, S1) on the horizontal axis.
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The gyroscopic system is near its primary instability, i.e., the bifurcation parameter is such that the system possesses a double zero eigenvalue.
The bifurcation parameter in abscissa is the slope σ of the sigmoid function S. It shows, as expected, two primary bifurcated branches: one of stripes and one of "spots", which correspond to a periodic pattern with square symmetry.
Three critical points, and namely the primary bifurcation point, the primary higher limit point and the primary lower limit point were basis for the plot of relative critical pressure versus slenderness parameter.
L. Moreau, E. D. Sontag, and M. Arcak, "How feedback can tune a bifurcation parameter towards its unknown critical bifurcation value," in Proc.
Bifurcation parameter I (A) or z (B).
In addition, the Hopf bifurcation is a type codimension-one bifurcation, that is, the bifurcation results by one bifurcation parameter.
Let c 22 be the bifurcation parameter.
The forcing frequency of the horizontal oscillations is used as a bifurcation parameter.
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