T-points in a Z2-symmetric electronic oscillator.: (I) Analysis

In this work we study the presence of T-points, a kind of codimension-two heteroclinic loop, in a Z(2)-symmetric electronic oscillator. Our analysis proves that, in the parameter plane, when the equilibria involved are saddle-focus, three spiraling curves of global codimension-one bifurcations emerge from this T-point, corresponding to homoclinic of the origin, homoclinic of the nontrivial equilibria and heteroclinic between the nontrivial equilibria connections. Some first-order features of these three curves are also shown. The analytical results, valid for all three-dimensional Z(2)-symmetric systems, are successfully checked in the modified van der Pol-Duffing electronic oscillator considered.