Homoclinical structure of the chaotic attractor

In the reference [Akhmet MU. Devaney chaos of a relay system. Commun Nonlinear Sci Numer Simulat 2009;14:1486–93.], a relay system was introduced, which admits a chaotic attractor with Devaney’s ingredients. Now, we prove that the attractor consists of homoclinic solutions. A simulation of the attractor is provided for a pendulum equation. Similar results for impulsive differential equations were announced in the plenary talk [Akhmet MU. Hyperbolic sets of impact systems. Dyn Contin Discrete Impuls Syst Ser A Math Anal 2008;15(Suppl. S1):1–2. Proceedings of the 5th international conference on impulsive and hybrid dynamical systems and applications, Beijin: Watan Press; 2008.].