Bifurcational Mechanism of Multistability Formation and Frequency Entrainment in a van der Pol Oscillator with an Additional Oscillatory Circuit-Reference-Cited by-同舟云学术

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

Published:2016-06-30 Issue:07 Volume:26 Page:1650124
ISSN:0218-1274
Container-title:International Journal of Bifurcation and Chaos
language:en
Short-container-title:Int. J. Bifurcation Chaos

Author:

Astakhov Sergey¹,Astakhov Oleg²,Astakhov Vladimir³,Kurths Jürgen⁴

Affiliation:

1. Information Security of Automated Systems Dept., Yuri Gagarin Technical University of Saratov, Politekhnicheskaya st. 77, Saratov 410054, Russian Federation

2. Department of Dynamic Modeling and Biomedical Engineering, Saratov State University, Astrakhanskaya st. 83, Saratov 410012, Russian Federation

3. Radioelectronics and Telecommunications Dept., Yuri Gagarin Technical University of Saratov, Politekhnicheskaya st. 77, Saratov 410054, Russian Federation

4. Potsdam Institute for Climate Impact Research (PIK), Potsdam 14473, Germany

Abstract

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218127416501248

Reference18 articles.

1. Multistability formation and synchronization loss in coupled Hénon maps: Two sides of the single bifurcational mechanism

2. Simulating, Analyzing, and Animating Dynamical Systems

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