%0 Journal Article
%A Giraldo, A.
%A Laguna, V. F.
%A Rodríguez Sanjurjo, José Manuel
%T Uniform persistence and Hopf bifurcations in R-+(n)
%D 2014
%@ 0022-0396
%U https://hdl.handle.net/20.500.14352/33507
%X 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.
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