Measuring the criticality of a Hopf bifurcation

Uteshev, Alexei Yu.; Kalmár‐Nagy, Tamás

doi:10.1007/s11071-020-05914-x

Cited by 4 publications

(1 citation statement)

References 23 publications

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“…The corresponding phase plot as shown in Fig. 13(b) confirms the existence of Hopf as a typical wire framed paraboloid [42,43] is formed.…”

Section: Hopf Bifurcationsupporting

confidence: 53%

Instability attenuation and bifurcation studies of a non-ideal rotor involving time-delayed feedback

Dasgupta

2022

Nonlinear Dyn

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In non-ideal vibratory system, the excitation is a nonlinear function of system response. The dynamic behavior of such system is often characterized by an energy source with limited power. The study of instability phenomena in non-ideal rotor driven through a non-ideal energy source is of considerable current interest. The non-ideal rotor system often gets destabilized on exceeding a critical input power near the resonance. This kind of instability is termed as Sommerfeld effect marked with nonlinear jump phenomena. This paper investigates the attenuation of nonlinear jump phenomena and numerical study of bifurcations of a non-ideal unbalanced rotor system with internal damping using time delayed feedback via active magnetic bearings. The results show that the time delay indeed plays a critical role on the suppression of the jump phenomena. Following, some new insights are also revealed through a numerical study of saddle node, Hopf and trans-critical bifurcations with time delay as a bifurcation parameter. The transient analysis confirms the results obtained analytically through the steady-state consideration.

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“…The corresponding phase plot as shown in Fig. 13(b) confirms the existence of Hopf as a typical wire framed paraboloid [42,43] is formed.…”

Section: Hopf Bifurcationsupporting

confidence: 53%