Hopf bifurcation and the centers on center manifold for a class of three-dimensional Circuit system

In this paper, Hopf bifurcation and center problem for a generic three-dimensional Chua's circuit system are studied. Applying the formal series method of computing singular point quantities to investigate the two cases of the generic circuit system, we find necessary conditions for the existence of centers on a local center manifold for the systems, then Darboux method is applied to show the sufficiency. Further, we determine the maximum number of limit cycles that can bifurcate from the corresponding equilibrium via Hopf bifurcation.