Abstract
In the study of the black holes with a Higgs field appears in a natural way the Lotka-Volterra differential system ẋ=x(y-1),ẏ=y(1+y-2x 2-z 2),ż=zy, in ℝ 3. Here we provide the qualitative analysis of the flow of this system describing the α-limit set and the ω-limit set of all orbits of this system in the whole Poincaré ball, i.e. we identify ℝ 3 with the interior of the unit ball of ℝ 3 centered at the origin and we extend analytically this flow to its boundary, i.e. to the infinity. © 2012 Elsevier Ltd. All rights reserved.
Original language | English |
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Pages (from-to) | 4114-4125 |
Journal | Nonlinear Analysis, Theory, Methods and Applications |
Volume | 75 |
DOIs | |
Publication status | Published - 1 Jun 2012 |
Keywords
- Black hole
- Higgs field
- Lotka-Volterra system
- Phase portrait
- α-limit
- ω-limit