{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:NHODRD73GEKEOQXOLZL2TQ4I2I","short_pith_number":"pith:NHODRD73","schema_version":"1.0","canonical_sha256":"69dc388ffb31144742ee5e57a9c388d23b44b955ada001e5544f601e30c626f1","source":{"kind":"arxiv","id":"1710.09649","version":1},"attestation_state":"computed","paper":{"title":"Hopf bifurcation with additive noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.DS","authors_text":"Jeroen S.W. Lamb, Martin Rasmussen, Maximilian Engel, Thai Son Doan","submitted_at":"2017-10-26T11:41:22Z","abstract_excerpt":"We consider the dynamics of a two-dimensional ordinary differential equation exhibiting a Hopf bifurcation subject to additive white noise and identify three dynamical phases: (I) a random attractor with uniform synchronisation of trajectories, (II) a random attractor with non-uniform synchronisation of trajectories and (III) a random attractor without synchronisation of trajectories. The random attractors in phases (I) and (II) are random equilibrium points with negative Lyapunov exponents while in phase (III) there is a so-called random strange attractor with positive Lyapunov exponent.\n  We"},"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":"1710.09649","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-10-26T11:41:22Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"f08c8255495625839c7d1d6d45f8846440a78425420c5434a9ba9dcfa3e66452","abstract_canon_sha256":"77c1402fb50f49d299c7a3379b9b51be834686f818d8b3865d4516e47a48f114"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:41.253598Z","signature_b64":"Xnp7y4uDjcJ5AiUFbYLMwioCMK0gFdNIQzk2Uxh1anYS4shbDFwMk10fIzTHhuLNnNJSKwW5bcwDDjQD9hUsCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"69dc388ffb31144742ee5e57a9c388d23b44b955ada001e5544f601e30c626f1","last_reissued_at":"2026-05-18T00:06:41.252960Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:41.252960Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hopf bifurcation with additive noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.DS","authors_text":"Jeroen S.W. Lamb, Martin Rasmussen, Maximilian Engel, Thai Son Doan","submitted_at":"2017-10-26T11:41:22Z","abstract_excerpt":"We consider the dynamics of a two-dimensional ordinary differential equation exhibiting a Hopf bifurcation subject to additive white noise and identify three dynamical phases: (I) a random attractor with uniform synchronisation of trajectories, (II) a random attractor with non-uniform synchronisation of trajectories and (III) a random attractor without synchronisation of trajectories. The random attractors in phases (I) and (II) are random equilibrium points with negative Lyapunov exponents while in phase (III) there is a so-called random strange attractor with positive Lyapunov exponent.\n  We"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.09649","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":"1710.09649","created_at":"2026-05-18T00:06:41.253050+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.09649v1","created_at":"2026-05-18T00:06:41.253050+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.09649","created_at":"2026-05-18T00:06:41.253050+00:00"},{"alias_kind":"pith_short_12","alias_value":"NHODRD73GEKE","created_at":"2026-05-18T12:31:31.346846+00:00"},{"alias_kind":"pith_short_16","alias_value":"NHODRD73GEKEOQXO","created_at":"2026-05-18T12:31:31.346846+00:00"},{"alias_kind":"pith_short_8","alias_value":"NHODRD73","created_at":"2026-05-18T12:31:31.346846+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/NHODRD73GEKEOQXOLZL2TQ4I2I","json":"https://pith.science/pith/NHODRD73GEKEOQXOLZL2TQ4I2I.json","graph_json":"https://pith.science/api/pith-number/NHODRD73GEKEOQXOLZL2TQ4I2I/graph.json","events_json":"https://pith.science/api/pith-number/NHODRD73GEKEOQXOLZL2TQ4I2I/events.json","paper":"https://pith.science/paper/NHODRD73"},"agent_actions":{"view_html":"https://pith.science/pith/NHODRD73GEKEOQXOLZL2TQ4I2I","download_json":"https://pith.science/pith/NHODRD73GEKEOQXOLZL2TQ4I2I.json","view_paper":"https://pith.science/paper/NHODRD73","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.09649&json=true","fetch_graph":"https://pith.science/api/pith-number/NHODRD73GEKEOQXOLZL2TQ4I2I/graph.json","fetch_events":"https://pith.science/api/pith-number/NHODRD73GEKEOQXOLZL2TQ4I2I/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NHODRD73GEKEOQXOLZL2TQ4I2I/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NHODRD73GEKEOQXOLZL2TQ4I2I/action/storage_attestation","attest_author":"https://pith.science/pith/NHODRD73GEKEOQXOLZL2TQ4I2I/action/author_attestation","sign_citation":"https://pith.science/pith/NHODRD73GEKEOQXOLZL2TQ4I2I/action/citation_signature","submit_replication":"https://pith.science/pith/NHODRD73GEKEOQXOLZL2TQ4I2I/action/replication_record"}},"created_at":"2026-05-18T00:06:41.253050+00:00","updated_at":"2026-05-18T00:06:41.253050+00:00"}