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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.
Zeitschrift für Naturforschung A – de Gruyter
Published: Jun 27, 2018
Keywords: Conservative Two-Mass System; Hopf-pitchfork Bifurcation; Periodic Orbit; Stability; Time Delay
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