Šil'nikov-Hopf bifurcations
The authors present a numerical bifurcation study of the dynamical behavior of a structural dynamics model of a periodically forced suspended cable. The simplified equations of motion are: \(\ddot x+ \mu \dot x+ c_1 x+ c_2 x^2+ c_3 x^3= P\cos(\Omega t)\); \(c_1\), \(c_2\), \(c_3\) are fixed parameters. One- and two-parameter diagrams of local bifurcation phenomena near the subharmonic 1:2 resonance are computed. Various global bifurcation phenomena near the resonance, including transitions to chaotic oscillations, are exposed by computation of invariant manifolds of saddle cycles.
scientific article; zbMATH DE number 768997