Existence of heteroclinic orbits of the Shil’nikov type in a 3D quadratic autonomous chaotic system ✩

In this paper, the existence of heteroclinic orbits of Shil’nikov type in a three-dimensional quadratic autonomous system is proved. Four heteroclinic orbits and four critical points together constitute two cycles simultaneously. The dynamical behaviors of the system are also studied.  2005 Elsevier Inc. All rights reserved