---
res:
  bibo_abstract:
  - Bifurcation characterizes the qualitative changes in parameterized dynamical systems
    and is one of the major topics in the field. In this work, we study combinatorial
    bifurcations within the framework of combinatorial dynamical systems—a young but
    already well-established theory. We introduce the Conley–Morse persistence barcode,
    a compact algebraic descriptor of combinatorial bifurcations. This barcode captures
    structural changes in a dynamical system at the level of Morse decompositions
    and provides a characterization of the nature of observed transitions in terms
    of the Conley index. The construction of the Conley–Morse persistence barcode
    builds upon ideas from topological persistence. Specifically, we consider a persistence
    module obtained from the Conley index of invariant sets indexed over a poset.
    Using gentle algebras, we prove that this module decomposes into simple intervals
    (bars) and compute them by adapting the zigzag persistence algorithm to our purpose.@eng
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Tamal K.
      foaf_name: Dey, Tamal K.
      foaf_surname: Dey
  - foaf_Person:
      foaf_givenName: Michał
      foaf_name: Lipiński, Michał
      foaf_surname: Lipiński
      foaf_workInfoHomepage: http://www.librecat.org/personId=dfffb474-4317-11ee-8f5c-fe3fc95a425e
    orcid: 0000-0001-9789-9750
  - foaf_Person:
      foaf_givenName: Manuel
      foaf_name: Soriano Trigueros, Manuel
      foaf_surname: Soriano Trigueros
      foaf_workInfoHomepage: http://www.librecat.org/personId=15ebd7cf-15bf-11ee-aebd-bb4bb5121ea8
    orcid: 0000-0003-2449-1433
  bibo_doi: 10.1007/s10208-026-09766-6
  dct_date: 2026^xs_gYear
  dct_isPartOf:
  - http://id.crossref.org/issn/1615-3375
  - http://id.crossref.org/issn/1615-3383
  dct_language: eng
  dct_publisher: Springer@
  dct_subject:
  - Multivector field
  - Conley index
  - Morse decomposition
  - Bifurcation
  - Continuation
  - Zigzag persistence
  - Persistence barcode
  - Gentle algebra
  dct_title: 'Conley-Morse persistence barcode: A homological signature of combinatorial
    bifurcations@'
...