Uniform persistence and Hopf bifurcations in R+n

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:256

Article

Giraldo, Antonio¹  Laguna, Victor F.²  Sanjurjo, Jose M. R.³ 

[1] Univ Politecn Madrid, Fac Informat, Dept Matemat Aplicada, E-28040 Madrid, Spain

[2] Univ Nacl Educ Distancia, Fac Ciencias, Dept Matemat Fundamentales, E-28040 Madrid, Spain

[3] Univ Complutense Madrid, Fac CC Matemat, Dept Geometria & Topol, E-28040 Madrid, Spain

关键词: Persistence;    Uniform continuation;    Dissipativeness;    Poincare-Andronov-Hopf bifurcation;    Morse decompositions;   

DOI  :  10.1016/j.jde.2014.01.025

来源: Elsevier

【 摘 要 】

We consider parameterized families of flows in locally compact metrizable spaces and give a characterization of those parameterized families of flows for which uniform persistence continues. On the other hand, we study the generalized Poincare-Andronov-Hopf bifurcations of parameterized families of flows at boundary points of R-+(n) or, more generally, of an n-dimensional manifold, and show that this kind of bifurcations produce a whole family of attractors evolving from the bifurcation point and having interesting topological properties. In particular, in some cases the bifurcation transforms a system with extreme non-permanence properties into a uniformly persistent one. We study in the paper when this phenomenon. happens and provide an example constructed by combining a Holling-type interaction with a pitchfork bifurcation. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free