{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:JEEXUVPITOOAJX7BM4MB7WSIAN","short_pith_number":"pith:JEEXUVPI","schema_version":"1.0","canonical_sha256":"49097a55e89b9c04dfe167181fda4803403c07b7b5deaaff6cdcce6c79e16cae","source":{"kind":"arxiv","id":"1109.5689","version":1},"attestation_state":"computed","paper":{"title":"Codimension-two homoclinic bifurcations underlying spike adding in the Hindmarsh-Rose burster","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Alan Champneys, Daniele Linaro, Marco Storace, Mathieu Desroches","submitted_at":"2011-09-26T11:17:39Z","abstract_excerpt":"The well-studied Hindmarsh-Rose model of neural action potential is revisited from the point of view of global bifurcation analysis. This slow-fast system of three paremeterised differential equations is arguably the simplest reduction of Hodgkin-Huxley models capable of exhibiting all qualitatively important distinct kinds of spiking and bursting behaviour. First, keeping the singular perturbation parameter fixed, a comprehensive two-parameter bifurcation diagram is computed by brute force. Of particular concern is the parameter regime where lobe-shaped regions of irregular bursting undergo a"},"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":"1109.5689","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-09-26T11:17:39Z","cross_cats_sorted":[],"title_canon_sha256":"032c98be4bab4623c5ee417fd6504f007838d18e3c08c50916a4907bd9061394","abstract_canon_sha256":"8fee0f6b9a7148cd688240d3731a945139d1c736d3947a921e0b62b0ab6af73d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:12:11.408120Z","signature_b64":"yXRh2PXtUhrJN0ZcgZtN8njyEBsGWg8MV72d8hCNDt6meNN21N4bMQegDEgPE4fSLJh5sapNI7lb30mw63VXCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"49097a55e89b9c04dfe167181fda4803403c07b7b5deaaff6cdcce6c79e16cae","last_reissued_at":"2026-05-18T04:12:11.407688Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:12:11.407688Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Codimension-two homoclinic bifurcations underlying spike adding in the Hindmarsh-Rose burster","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Alan Champneys, Daniele Linaro, Marco Storace, Mathieu Desroches","submitted_at":"2011-09-26T11:17:39Z","abstract_excerpt":"The well-studied Hindmarsh-Rose model of neural action potential is revisited from the point of view of global bifurcation analysis. This slow-fast system of three paremeterised differential equations is arguably the simplest reduction of Hodgkin-Huxley models capable of exhibiting all qualitatively important distinct kinds of spiking and bursting behaviour. First, keeping the singular perturbation parameter fixed, a comprehensive two-parameter bifurcation diagram is computed by brute force. Of particular concern is the parameter regime where lobe-shaped regions of irregular bursting undergo a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5689","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1109.5689","created_at":"2026-05-18T04:12:11.407747+00:00"},{"alias_kind":"arxiv_version","alias_value":"1109.5689v1","created_at":"2026-05-18T04:12:11.407747+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.5689","created_at":"2026-05-18T04:12:11.407747+00:00"},{"alias_kind":"pith_short_12","alias_value":"JEEXUVPITOOA","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_16","alias_value":"JEEXUVPITOOAJX7B","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_8","alias_value":"JEEXUVPI","created_at":"2026-05-18T12:26:32.869790+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JEEXUVPITOOAJX7BM4MB7WSIAN","json":"https://pith.science/pith/JEEXUVPITOOAJX7BM4MB7WSIAN.json","graph_json":"https://pith.science/api/pith-number/JEEXUVPITOOAJX7BM4MB7WSIAN/graph.json","events_json":"https://pith.science/api/pith-number/JEEXUVPITOOAJX7BM4MB7WSIAN/events.json","paper":"https://pith.science/paper/JEEXUVPI"},"agent_actions":{"view_html":"https://pith.science/pith/JEEXUVPITOOAJX7BM4MB7WSIAN","download_json":"https://pith.science/pith/JEEXUVPITOOAJX7BM4MB7WSIAN.json","view_paper":"https://pith.science/paper/JEEXUVPI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1109.5689&json=true","fetch_graph":"https://pith.science/api/pith-number/JEEXUVPITOOAJX7BM4MB7WSIAN/graph.json","fetch_events":"https://pith.science/api/pith-number/JEEXUVPITOOAJX7BM4MB7WSIAN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JEEXUVPITOOAJX7BM4MB7WSIAN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JEEXUVPITOOAJX7BM4MB7WSIAN/action/storage_attestation","attest_author":"https://pith.science/pith/JEEXUVPITOOAJX7BM4MB7WSIAN/action/author_attestation","sign_citation":"https://pith.science/pith/JEEXUVPITOOAJX7BM4MB7WSIAN/action/citation_signature","submit_replication":"https://pith.science/pith/JEEXUVPITOOAJX7BM4MB7WSIAN/action/replication_record"}},"created_at":"2026-05-18T04:12:11.407747+00:00","updated_at":"2026-05-18T04:12:11.407747+00:00"}