Integrability and bifurcation of a three-dimensional circuit differential system

<p style='text-indent:20px;'>We study integrability and bifurcations of a three-dimensional circuit differential system. The emerging periodic solutions under Hopf bifurcation zero-Hopf is investigated using the center manifolds averaging theory. equilibrium non-isolated lies on line filled in with equilibria. A Lyapunov function found global stability origin proven case when it simple locally asymptotically stable equilibrium. We also model foliations phase space by invariant surfaces. It shown that an foliation at most two limit cycles can bifurcate from weak focus.</p>