This article is cited in 8 papers

Original papers

Bifurcational mechanism of formation of developed multistability in a van der Pol oscillator with time-delayed feedback

B. I. Maksim^a, N. M. Ryskin<sup>b

a</sup> Yuri Gagarin State Technical University of Saratov, ul. Politechnicheskaya 77, Saratov, 410054, Russia
^b National Research Saratov State University, ul. Astrakhanskaya 83, Saratov, 410012, Russia

Abstract: 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, bifurcations, multistability.

UDC: 537.86/.87:530.182

MSC: 37M20

Received: 18.03.2017
Accepted: 10.04.2017

DOI: 10.20537/nd1702001

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