Unidirectional Migration of Populations with Allee Effect

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In this note we consider two populations living on identical patches, connected by unidirectional migration, and subject to strong Allee effect. We show that by increasing the migration rate, there are more bifurcation sequences than previous works showed. In particular, the number of steady states can change from 9 (small migration) to 3 (large migration) at a single bifurcation point, or via a sequence of bifurcations with the system having 9, 7, 5, 3 steady states or 9, 7, 9, 3 steady states, depending on the Allee threshold. This is in contrast with the case of bidirectional migration, where the number of steady states always goes through the same bifurcation sequence of 9, 5, 3 steady states as we increase the migration rate, regardless of the value of the Allee threshold. These results have practical implications as well in spatial ecology.
Original languageEnglish
Pages (from-to)43-52
Number of pages10
JournalLetters in Biomathematics
Issue number1
Publication statusPublished - 10 Jan 2023

Bibliographical note

Letters in Biomathematics is an open-access, peer-reviewed journal that publishes mathematics and statistics research related to biological, ecological and environmental settings in a very broad sense, as well as other related topic fields.


  • population dynamics
  • migration
  • bifurcation
  • steady states
  • Allee effect
  • Cylindrical algebraic decomposition
  • cylindrical algebraic decomposition

ASJC Scopus subject areas

  • Applied Mathematics
  • Biochemistry, Genetics and Molecular Biology (miscellaneous)
  • Statistics and Probability


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