Bifurcational Mechanism of Multistability Formation and Frequency Entrainment in a van der Pol Oscillator with an Additional Oscillatory Circuit

被引：6

作者：

Astakhov, Sergey ^{[1
]}

Astakhov, Oleg ^{[2
]}

Astakhov, Vladimir ^{[3
]}

Kurths, Juergen ^{[4
]}

机构：

[1] Yuri Gagarin Tech Univ Saratov, Informat Secur Automated Syst Dept, Politekhnicheskaya St 77, Saratov 410054, Russia

[2] Saratov NG Chernyshevskii State Univ, Dept Dynam Modeling & Biomed Engn, Astrakhanskaya St 83, Saratov 410012, Russia

[3] Yuri Gagarin Tech Univ Saratov, Radioelect & Telecommun Dept, Politekhnicheskaya St 77, Saratov 410054, Russia

[4] Potsdam Inst Climate Impact Res PIK, D-14473 Potsdam, Germany

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2016年 / 26卷 / 07期

关键词：

Multimode oscillators; bifurcations; multistability formation;

D O I：

10.1142/S0218127416501248

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, the bifurcational mechanism of frequency entrainment in a van der Pol oscillator coupled with an additional oscillatory circuit is studied. It is shown that bistability observed in the system is based on two bifurcations: a supercritical Andronov-Hopf bifurcation and a sub-critical Neimark-Sacker bifurcation. The attracting basin boundaries are determined by stable and unstable invariant manifolds of a saddle two-dimensional torus.

引用

页数：10

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