A codimension-3 bifurcation problem and its application to electrical circuits

A bifurcation phenomenon which arises from the interaction of static and dynamic modes in the vicinity of a compound critical point of a nonlinear autonomous system is considered. The critical point is characterized by a double zero and a pair of pure imaginary eigenvalues of the Jacobian. A set of simplified differential equations is obtained by applying the unification technique coupled with the intrinsic harmonic balancing procedure. Based on the simplified equations, the equilibrium solutions, Hopf bifurcation solutions and quasiperiodic motions lying on 2-D tori, as well as the associated stability conditions, are explored. An example drawn from electrical circuits is analyzed to demonstrate the direct applicability of the analytic results.<>