Hopf bifurcation for non-densely defined Cauchy problems

Zhihua Liu, Pierre Magal, Shigui Ruan

Research output: Contribution to journalArticlepeer-review

54 Scopus citations


In this paper, we establish a Hopf bifurcation theorem for abstract Cauchy problems in which the linear operator is not densely defined and is not a Hille-Yosida operator. The theorem is proved using the center manifold theory for non-densely defined Cauchy problems associated with the integrated semigroup theory. As applications, the main theorem is used to obtain a known Hopf bifurcation result for functional differential equations and a general Hopf bifurcation theorem for age-structured models.

Original languageEnglish (US)
Pages (from-to)191-222
Number of pages32
JournalZeitschrift fur Angewandte Mathematik und Physik
Issue number2
StatePublished - Apr 2011


  • Age structured model
  • Cauchy problem
  • Functional differential equation
  • Hopf bifurcation
  • Non-dense domain
  • Periodic solution

ASJC Scopus subject areas

  • Mathematics(all)
  • Physics and Astronomy(all)
  • Applied Mathematics


Dive into the research topics of 'Hopf bifurcation for non-densely defined Cauchy problems'. Together they form a unique fingerprint.

Cite this