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We numerically identify this point GH 1 along the branch of H 1 by finding an emanating branch of limit point of cycles LPC 1 with Knut.
Both branches then have a Hopf bifurcation from which a branch of limit cycles emerges, unstable in the 3-1 cand and stable in the 2-2 case.
A branch of limit cycles emerging from a Hopf bifurcation when (g = 2sqrt{N}/ mu_{E} (alpha-1)): here a complex pair crosses the imaginary axis.
Most significantly, we find a Hopf bifurcation that leads to a branch of limit cycles when a pair of complex eigenvalues crosses the imaginary axis.
A branch of limit cycles from a Hopf bifurcation (at (g^{H})) in which the three-cluster pattern is maintained, that is, activity can be characterized by ((x_{E}, x_{I1}, x_{I2})).
From each (I_{1}/I_{2}) branch we find: A branch of limit cycles from a Hopf bifurcation (at (g^{H})) in which the three-cluster pattern is maintained, that is, activity can be characterized by ((x_{E}, x_{I1}, x_{I2})).
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The nonlinearities are adjusted to permit the formation of a either a subcritical or supercritical branch of limit-cycle oscillations.
Fig. 9 The descending branch of limiting hysteresis loop of different air gap length ratios, a 0.001, b 0.002, c 0.003.
Using the arctangent function and the hyperbolic function, the descending branch of limiting hysteresis loop of measured closed-core can be fitted.
Based on the Preisach core magnetization theory, the air-gapped core CT model is established, in which the data required for the core modeling is the descending branch of limiting hysteresis loop.
As shown in Fig. 4, the measured CT core is closed, with circular shape, the average magnetic path length l = 0.62 m, sectional area A = 2.508 × 10− 3 m 2. Fig. 4 Descending branch of limiting hysteresis loop of closed-core and its fitted curve.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com