Curvature index failures in the dynamics of an electric coupled circuit

G. REVEL; D. M. ALONSO; J. L. MOIOLA

Potsdam

Congreso; Third International IEEE Scientific Conference on Physics and Control (PhysCon 2007); 2007

International Physics and Control Society

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.