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When the prey-isocline has a single interior local extremum, we prove that the system has a unique nontrivial periodic orbit, which forms a relaxation oscillation. For some systems with prey-isocline possessing two interior local extrema, we show that either the positive equilibrium is globally stable, or the"},"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":"1801.02590","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-01-08T18:03:37Z","cross_cats_sorted":[],"title_canon_sha256":"64362fcb3eeef9b4a75985badc58600be2b93ffa9cf516f97724fc0b81f08295","abstract_canon_sha256":"2b447c239530afe087238cd15702aeb933319a9e6561594afc62e148aa96cf8e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:59.044429Z","signature_b64":"0gzzrOtXm6gc4fwEsgZ+HMyjRgl5EoFSFFbNFH3haHY57rRxs+IKuObd54YzuD/6QgRG8MAXHZDMRc+8SXVyCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"675a2042e591649154e1470e2f8340dcaf76ff980a3beed3b23d1b9514d7051e","last_reissued_at":"2026-05-17T23:42:59.044004Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:59.044004Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Number and Stability of Relaxation Oscillations for Predator-Prey Systems with Small Death Rates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Ting-Hao Hsu","submitted_at":"2018-01-08T18:03:37Z","abstract_excerpt":"We consider planar systems of predator-prey models with small predator death rate $\\epsilon>0$. 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