On bifurcations into nonresonant quasi-periodic motions

The stability, instability, and bifurcation behaviour of a nonlinear autonomous system in the vicinity of a compound critical point is studied in detail. The critical point is characterized by two distinct pairs of pure imaginary eigenvalues of the Jacobian, and the system is described by two independent parameters. The analysis is based on a generalized perturbation procedure which employs multiple-time-scale Fourier series and embraces the intrinsic harmonic balancing and unification technique introduced earlier. This more comprehensive perturbation approach leads to explicit asymptotic results concerning periodic and nonresonant quasiperiodic motions which take place on an invariant torus. An electrical network is analyzed to illustrate the direct applicability of the analytical results.