CODIMENSION-2 BIFURCATION OBSERVED IN A PHASE-CONVERTER CIRCUIT

We investigate bifurcations of the periodic solution observed in a pha se converter circuit. The system equations can be considered as a nonl inear coupled system with Duffing's equation and an equation describin g a parametric excitation circuit. In this system there are two types of solutions. One is with x = y = 0 which is the same as the solution of Duffing's equation (correspond to uncoupled case), another solution is with xy not equal 0. We obtain bifurcation sets of both solutions and discuss how does the coupling change the bifurcation structure. Fr om numerical analysis we obtain a codimension two bifurcation which is intersection of double period-doubling bifurcations. Periodic solutio ns generated by these bifurcations become chaotic stares through a cas cade of codimension three bifurcations which are intersections of D-ty pe of branchings and period-doubling bifurcations.