The authors study differential equations \(X_\varepsilon\) on \({\mathbb{R}}^3\) that, for \(\varepsilon = 0\), possess a line \(\Gamma\) of equilibria connected by a manifold of homoclinic loops. Such a study was started in \textit{A. Doelman} and \textit{P. Holmes} [Philos. Trans. R. Soc. Lond., Ser. A 354, 845-893 (1996; Zbl 0881.58044)] and \textit{H. Kokubu, K. Mischaikow} and \textit{H. Oka} [Nonlinearity 9, 1263-1280 (1996; Zbl 0898.34047)]. In this paper different perturbations are considered; it is assumed that the manifold of homoclinic loops splits and undergoes a quadratic homoclinic tangency under perturbation. Specifically, the system \[ \dot x = y, \qquad \dot y = x - x^2 + \varepsilon y (z^2 - a), \qquad \dot z = \varepsilon (1 + bx) \] is studied. It is shown that for \(a\) positive of order 1 and \(b\) negative of order \(|\ln \varepsilon|\), the return map on a transverse cross section has a topological horseshoe.