Hopf bifurcation for non-densely defined Cauchy problems

Zhihua Liu; Pierre Magal; Shigui Ruan

doi:10.1007/s00033-010-0088-x

Hopf bifurcation for non-densely defined Cauchy problems

Zhihua Liu, Pierre Magal, Shigui Ruan

Mathematics

Research output: Contribution to journal › Article › peer-review

54 Scopus citations

Abstract

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 language	English (US)
Pages (from-to)	191-222
Number of pages	32
Journal	Zeitschrift fur Angewandte Mathematik und Physik
Volume	62
Issue number	2
DOIs	https://doi.org/10.1007/s00033-010-0088-x
State	Published - Apr 2011

Keywords

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

Access to Document

10.1007/s00033-010-0088-x

Cite this

@article{7e96d9f74ed64271aff16441b2da72df,

title = "Hopf bifurcation for non-densely defined Cauchy problems",

abstract = "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.",

keywords = "Age structured model, Cauchy problem, Functional differential equation, Hopf bifurcation, Non-dense domain, Periodic solution",

author = "Zhihua Liu and Pierre Magal and Shigui Ruan",

year = "2011",

month = apr,

doi = "10.1007/s00033-010-0088-x",

language = "English (US)",

volume = "62",

pages = "191--222",

journal = "Zeitschrift fur Angewandte Mathematik und Physik",

issn = "0044-2275",

publisher = "Birkhauser Verlag Basel",

number = "2",

}

TY - JOUR

T1 - Hopf bifurcation for non-densely defined Cauchy problems

AU - Liu, Zhihua

AU - Magal, Pierre

AU - Ruan, Shigui

PY - 2011/4

Y1 - 2011/4

N2 - 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.

AB - 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.

KW - Age structured model

KW - Cauchy problem

KW - Functional differential equation

KW - Hopf bifurcation

KW - Non-dense domain

KW - Periodic solution

UR - http://www.scopus.com/inward/record.url?scp=79953677808&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79953677808&partnerID=8YFLogxK

U2 - 10.1007/s00033-010-0088-x

DO - 10.1007/s00033-010-0088-x

M3 - Article

AN - SCOPUS:79953677808

VL - 62

SP - 191

EP - 222

JO - Zeitschrift fur Angewandte Mathematik und Physik

JF - Zeitschrift fur Angewandte Mathematik und Physik

SN - 0044-2275

IS - 2

ER -

Hopf bifurcation for non-densely defined Cauchy problems

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this