{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:Q6XQXP4CUYRPIWVNL66MJ6ZH2X","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"93999d1568069f241b8a7582e6b101103d4d07f7a1fe7c5ea04df89e620ecc39","cross_cats_sorted":["math.AP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-01-29T06:39:20Z","title_canon_sha256":"e70da1428127f1231a1ef2d36c0de7780f074bc7eb358de4aa60fe34789e542c"},"schema_version":"1.0","source":{"id":"1201.6017","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.6017","created_at":"2026-05-18T04:03:33Z"},{"alias_kind":"arxiv_version","alias_value":"1201.6017v1","created_at":"2026-05-18T04:03:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.6017","created_at":"2026-05-18T04:03:33Z"},{"alias_kind":"pith_short_12","alias_value":"Q6XQXP4CUYRP","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"Q6XQXP4CUYRPIWVN","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"Q6XQXP4C","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:ffc1656d5dcc76ec138e789ea3a32af1c662fe251e5ecbfdacd391b4def495e5","target":"graph","created_at":"2026-05-18T04:03:33Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Nonlinear dynamical systems are sometimes under the influence of random fluctuations. It is desirable to examine possible bifurcations for stochastic dynamical systems when a parameter varies.\n  A computational analysis is conducted to investigate bifurcations of a simple dynamical system under non-Gaussian {\\alpha}-stable Levy motions, by examining the changes in stationary probability density functions for the solution orbits of this stochastic system. The stationary probability density functions are obtained by numerically solving a non local Fokker-Planck equation. This allows numerically ","authors_text":"Chengjian Zhang, Huiqin Chen, Jinqiao Duan","cross_cats":["math.AP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-01-29T06:39:20Z","title":"Elementary bifurcations for a simple dynamical system under non-Gaussian Levy noises"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.6017","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:0f9c3a23d784c561ce310975340e4a093f41ab17309b1a939e6287ce76214994","target":"record","created_at":"2026-05-18T04:03:33Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"93999d1568069f241b8a7582e6b101103d4d07f7a1fe7c5ea04df89e620ecc39","cross_cats_sorted":["math.AP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-01-29T06:39:20Z","title_canon_sha256":"e70da1428127f1231a1ef2d36c0de7780f074bc7eb358de4aa60fe34789e542c"},"schema_version":"1.0","source":{"id":"1201.6017","kind":"arxiv","version":1}},"canonical_sha256":"87af0bbf82a622f45aad5fbcc4fb27d5ed7f5c48cca561d22baa07d2a4bdf45f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"87af0bbf82a622f45aad5fbcc4fb27d5ed7f5c48cca561d22baa07d2a4bdf45f","first_computed_at":"2026-05-18T04:03:33.985239Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:03:33.985239Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5xLRyIs4egjjwOTn09LG7Qxs1HfSQRkKM+3CsUh5ky3kY1JSiyxK38vWN+j13UdkQSt5zX44iACppqCvl+OiDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:03:33.985888Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.6017","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0f9c3a23d784c561ce310975340e4a093f41ab17309b1a939e6287ce76214994","sha256:ffc1656d5dcc76ec138e789ea3a32af1c662fe251e5ecbfdacd391b4def495e5"],"state_sha256":"4b12ef406053e1b82f2b2fb34fa524acb3100d732edf7f0ea1bb4a9a522d67e0"}