Homoclinic bifurcations in Chua's circuit

In this paper we study the possible relationship between the Birth of the D ouble Scroll [L.O. Chua et al., IEEE-CAS 33 (11) (1986) 1073] and the homoc linic bifurcations in the: traditional Chua's equations. Using a one-dimens ional Poincare map we determine the existence of secondary symmetric homocl inic orbits of Shil'nikov type, born with the Chua's attractor, connecting unstable and stable manifolds of the trivial equilibrium point. In addition , taking into account the presence of other homoclinic orbits for the asymm etric attractor and heteroclinic orbits for the symmetric attractor (connec ting unstable and stable manifold of the non-trivial equilibrium points), w e suggest a hypothesis about the Birth of Double Scroll structure on the (a lpha, beta) plane. (C) 1999 Published by Elsevier Science B.V. All rights r eserved.