TITLE

CENTER-UNSTABLE MANIFOLDS FOR NONDENSELY DEFINED CAUCHY PROBLEMS AND APPLICATIONS TO STABILITY OF HOPF BIFURCATION

AUTHOR(S)
ZHIHUA LIU; MAGAL, PIERRE; SHIGUI RUAN
PUB. DATE
June 2012
SOURCE
Canadian Applied Mathematics Quarterly;Summer2012, Vol. 20 Issue 2, p135
SOURCE TYPE
Periodical
DOC. TYPE
Article
ABSTRACT
Center-unstable manifolds are very useful in investigating nonlinear dynamics of nonlinear evolution equations. In this paper, we first present a center-unstable manifold theory for abstract semilinear Cauchy problems with nondense domain. We especially focus on the stability property of the center-unstable manifold. Then we study the stability of Hopf bifurcation, that is, stability of the bifurcating periodic orbits for the nondensely defined Cauchy problem. Our goal is to prove that the stability of a periodic orbit to the reduced system (i.e., restricted to the center-unstable manifold) implies the stability of the periodic orbit for the original system. As an application, we demonstrate that these results apply to differential equations with infinite delay.
ACCESSION #
88151409

 

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