Hopf-Pitchfork Bifurcation in a Symmetrically Conservative Two-Mass System with Delay

Hopf-Pitchfork Bifurcation in a Symmetrically Conservative Two-Mass System with Delay AbstractA symmetrically conservative two-mass system with time delay is considered here. We analyse the influence of interaction coefficient and time delay on the Hopf-pitchfork bifurcation. The bifurcation diagrams and phase portraits are then obtained by computing the normal forms for the system in which, particularly, the unfolding form for case III is seldom given in delayed differential equations. Furthermore, we also find some interesting dynamical behaviours of the original system, such as the coexistence of two stable non-trivial equilibria and a pair of stable periodic orbits, which are verified both theoretically and numerically. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Zeitschrift für Naturforschung A de Gruyter

Hopf-Pitchfork Bifurcation in a Symmetrically Conservative Two-Mass System with Delay

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Publisher
De Gruyter
Copyright
©2018 Walter de Gruyter GmbH, Berlin/Boston
ISSN
0932-0784
eISSN
1865-7109
D.O.I.
10.1515/zna-2017-0443
Publisher site
See Article on Publisher Site

Abstract

AbstractA symmetrically conservative two-mass system with time delay is considered here. We analyse the influence of interaction coefficient and time delay on the Hopf-pitchfork bifurcation. The bifurcation diagrams and phase portraits are then obtained by computing the normal forms for the system in which, particularly, the unfolding form for case III is seldom given in delayed differential equations. Furthermore, we also find some interesting dynamical behaviours of the original system, such as the coexistence of two stable non-trivial equilibria and a pair of stable periodic orbits, which are verified both theoretically and numerically.

Journal

Zeitschrift für Naturforschung Ade Gruyter

Published: Jun 27, 2018

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