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We analyse the dynamics around this type of cycle in the case when trajectories near the two equilibria turn in the same direction around a 1-dimensional connection - the saddle-foci have the same chirality. When part of the symmetry is broken, the 2-dimensional invariant manifolds intersect transversely creating a heteroclinic network of Bykov cycles.\n  We show that the proximity of symmetry creates hetero"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1504.01659","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-04-07T16:24:54Z","cross_cats_sorted":[],"title_canon_sha256":"c60baf40c75fe447f5bc7bf8a42e3ce1e7fde1548f578659791911b3b6846e88","abstract_canon_sha256":"2e8ea50e13b240c28ca5a9b8585238d6a053983db952a9d4d33a5834edf858ce"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:38.791077Z","signature_b64":"phjQvWFwi8NeloP7D8cx8Q/vvnUVCuA7Z6ZaLqnRCU1kRY5npVcSLon2NcIEgtXtDPYYO+HYCRvwNbEQPgu3DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2c950e4182812773b1feb20175457190419a6e70997e45cd4554601e116299f9","last_reissued_at":"2026-05-18T01:19:38.790513Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:38.790513Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Global bifurcations close to symmetry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Alexandre A. 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