{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ZRD6EPCSXOYD2QCHZVH2E6E2AR","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":"c4985632e578db7ea4d847c4c79876a6cf9e1a90b20459ce7bc810ebe686e73c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-04-06T13:02:26Z","title_canon_sha256":"9732aa94e6788297bffce777867ff0a2cad5e74aaa525e80d4f284db2dfef1d6"},"schema_version":"1.0","source":{"id":"1604.01600","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.01600","created_at":"2026-05-18T00:36:41Z"},{"alias_kind":"arxiv_version","alias_value":"1604.01600v4","created_at":"2026-05-18T00:36:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.01600","created_at":"2026-05-18T00:36:41Z"},{"alias_kind":"pith_short_12","alias_value":"ZRD6EPCSXOYD","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"ZRD6EPCSXOYD2QCH","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"ZRD6EPCS","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:58a402fb0231d6341b6e71918f3831a5752b1d8f1faafb5a5ef28d3ad6f6eec8","target":"graph","created_at":"2026-05-18T00:36:41Z","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":"We describe the algorithms used in the Matlab continuation and bifurcation package pde2path for Hopf bifurcation and continuation of branches of periodic orbits in systems of PDEs in 1, 2, and 3 spatial dimensions, including the computation of Floquet multipliers. We first test the methods on three reaction diffusion examples, namely a complex Ginzburg-Landau equation as a toy problem, a reaction diffusion system on a disk with rotational waves including stable (anti) spirals bifurcating out of the trivial solution, and a Brusselator system with interaction of Turing and Turing-Hopf bifurcatio","authors_text":"Hannes Uecker","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-04-06T13:02:26Z","title":"Hopf bifurcation and time periodic orbits in reaction-diffusion systems with pde2path - algorithms and applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.01600","kind":"arxiv","version":4},"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:b5ad71b318599dae1fd3924cdd7703fe6f7004ae799ce182f894e49c57f27d93","target":"record","created_at":"2026-05-18T00:36:41Z","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":"c4985632e578db7ea4d847c4c79876a6cf9e1a90b20459ce7bc810ebe686e73c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-04-06T13:02:26Z","title_canon_sha256":"9732aa94e6788297bffce777867ff0a2cad5e74aaa525e80d4f284db2dfef1d6"},"schema_version":"1.0","source":{"id":"1604.01600","kind":"arxiv","version":4}},"canonical_sha256":"cc47e23c52bbb03d4047cd4fa2789a0450304243f4c6d1a2b36daff5e7d65f54","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cc47e23c52bbb03d4047cd4fa2789a0450304243f4c6d1a2b36daff5e7d65f54","first_computed_at":"2026-05-18T00:36:41.425154Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:41.425154Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Fe0Y1cpREzJezjwabWROmEnCps821ZSgDDcpNBbRUjg5Oc142KxkM+ES6T34IjW4igF3SONka7NwwuRnpUB3Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:41.425861Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.01600","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b5ad71b318599dae1fd3924cdd7703fe6f7004ae799ce182f894e49c57f27d93","sha256:58a402fb0231d6341b6e71918f3831a5752b1d8f1faafb5a5ef28d3ad6f6eec8"],"state_sha256":"6746813b208ab8fd97254fa0516b225c314cc04ac97609714c35b657ec7d73f0"}