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Uniform persistence and Hopf bifurcations in R-+(n)

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Giraldo, A. and Laguna, V. F. and Rodríguez Sanjurjo, José Manuel (2014) Uniform persistence and Hopf bifurcations in R-+(n). Journal of Differential Equations, 256 (8). pp. 2949-2964. ISSN 0022-0396

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Official URL: http://www.sciencedirect.com/science/article/pii/S0022039614000436


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Abstract

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.


Item Type:Article
Uncontrolled Keywords:Persistence; Uniform continuation; Dissipativeness; Poincare-Andronov-Hopf bifurcation; Morse decompositions
Subjects:Sciences > Mathematics > Geometry
Sciences > Mathematics > Topology
ID Code:24994
Deposited On:07 Apr 2014 10:15
Last Modified:12 Dec 2018 15:12

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