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.
|Journal||Nonlinear Analysis, Theory, Methods and Applications|
|Publication status||Published - 1 Jun 2012|
- Black hole
- Higgs field
- Lotka-Volterra system
- Phase portrait