Geodesic
Isolated Hopf bifurcation of symmetric weakly damped systems
Theoretical and applied mechanics, Tome 25 (1999) no. 1, p. 33 .

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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 },
     publisher = {mathdoc},
     volume = {25},
     number = {1},
     year = {1999},
     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/