Geodesic
Bifurcational mechanism of formation of developed multistability in a van der Pol oscillator with time-delayed feedback
Russian journal of nonlinear dynamics, Tome 13 (2017) no. 2, pp. 151-164

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The mechanism of formation of multistability in a van der Pol generator with time-delayed feedback is studied. It is found that the developed multistability is formed through a sequence of two types of bifurcations: supercritical Andronov–Hopf bifurcation and subcritical Neimark–Sacker bifurcation. With variation of the control parameters, the fixed point repeatedly undergoes supercritical Andronov–Hopf bifurcation, which leads to an increase in the number of saddle cycles. The limit cycles acquire stability after a number of subcritical Neimark– Sacker bifurcations. The dynamics of the system is studied in a wide range of control parameters values.
Keywords: Time delay, multistability.
Mots-clés : bifurcations 
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     author = {B. I. Maksim and N. M. Ryskin},
     title = {Bifurcational mechanism of formation of developed multistability in a van der {Pol} oscillator with time-delayed feedback},
     journal = {Russian journal of nonlinear dynamics},
     pages = {151--164},
     publisher = {mathdoc},
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     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ND_2017_13_2_a0/}
}
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B. I. Maksim; N. M. Ryskin. Bifurcational mechanism of formation of developed multistability in a van der Pol oscillator with time-delayed feedback. Russian journal of nonlinear dynamics, Tome 13 (2017) no. 2, pp. 151-164. http://geodesic.mathdoc.fr/item/ND_2017_13_2_a0/