Geodesic
Isolated Hopf bifurcation of symmetric weakly damped systems
Theoretical and applied mechanics, Tome 25 (1999) no. 1, p. 33 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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This paper deals with the dynamic stability of autonomous weakly damped symmetric (potential) systems. Conditions for the occurrence of a limit cycle mode of instability are established via a through discussion of the effect of the damping matrix on the Jacobian eigenvalues. It was found that such a response may occur through a new type of local dynamic bifurcation identified as an isolated Ilopf bifurcation as well as through a double zero (eigenvalue) local dynamic bifurcation. As a consequence of this, undamped stable symmetric systems may become unstable with the inclusion of damping. Numerical results confirm the validity of the theoretical findings presented herein. 
@article{TAM_1999_25_1_a2,
     author = {Anthony N. Kounadis},
     title = {Isolated {Hopf} bifurcation of symmetric weakly damped systems},
     journal = {Theoretical and applied mechanics},
     pages = {33 },
     year = {1999},
     volume = {25},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAM_1999_25_1_a2/}
}
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Anthony N. Kounadis. Isolated Hopf bifurcation of symmetric weakly damped systems. Theoretical and applied mechanics, Tome 25 (1999) no. 1, p. 33 . http://geodesic.mathdoc.fr/item/TAM_1999_25_1_a2/