Curvature Index Failures in the Dynamics of an Electric Coupled Oscillator
Jorge Luis Moiola, Gustavo Revel
In this work, the dynamics of an electric coupled oscillator is studied. The attention is centered on the first and second curvature indexes or Lyapunov coefficients of a Hopf bifurcation. The analysis is performed using the frequency domain method to calculate analytical expression of the indexes, and then establish the location of the first two curvature singularities. Numerical continuations are used to determine the dynamical behavior of the system in the vicinity of these points. A relatively complex
structure of nested limit cycles was found near these
degeneracies.