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After slightly increasing the parameter, while keeping the 1-dimensional connections unaltered, we concentrate our study in the case where the 2-dimensional invariant manifolds of the equilibria do not intersect. We will show that, for a set of parameters close enough to zero with positive Lebesgue measure, the dynamics exhibits strange attractors winding around the \"ghost'' of a torus and supporting Sinai-Ruelle-Bowen (SRB) measures. We also prove the existence of a sequence of parameter values for which the family exhibits a superstable sink and describe the transition from a Bykov network to a strange attractor.&lt;\/p&gt;<\/jats:p>","DOI":"10.3934\/dcds.2021193","type":"journal-article","created":{"date-parts":[[2021,12,22]],"date-time":"2021-12-22T08:58:37Z","timestamp":1640163517000},"page":"2355","source":"Crossref","is-referenced-by-count":7,"title":["\"Large\" strange attractors in the unfolding of a heteroclinic attractor"],"prefix":"10.3934","volume":"42","author":[{"given":"Alexandre","family":"Rodrigues","sequence":"first","affiliation":[{}]}],"member":"2321","reference":[{"key":"key-10.3934\/dcds.2021193-1","doi-asserted-by":"publisher","unstructured":"V. S. Afraimovich, S.-B. Hsu, H. E. Lin.Chaotic behavior of three competing species of May\u2013Leonard model under small periodic perturbations, <i>Internat. J. Bifur. Chaos Appl. Sci. 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