TY - JOUR
T1 - Global dynamics of the Rikitake system
AU - Llibre, Jaume
AU - Messias, Marcelo
PY - 2009/1/1
Y1 - 2009/1/1
N2 - The Rikitake system is a three dimensional vector field obtained experimentally from a two-disk dynamo apparatus, which models the geomagnetic field and is used to explain the known irregular switch in its polarity. The system has a 3-dimensional Lorenz type chaotic attractor around its two singular points. However this attractor is not bounded by any ellipsoidal surface as in the Lorenz attractor. In this paper, by using the Poincaré compactification for polynomial vector fields in R3 we study the dynamics of the Rikitake system at infinity, showing that there are orbits which escape to, or come from, infinity, instead of going towards the attractor. Moreover we study, for particular values of the parameters, the flow over two invariant planes, and describe the global flow of the system when it has two independent first integrals and thus is completely integrable. The global analysis performed, allows us to give a numerical description of the creation of Rikitake attractor. © 2008 Elsevier B.V. All rights reserved.
AB - The Rikitake system is a three dimensional vector field obtained experimentally from a two-disk dynamo apparatus, which models the geomagnetic field and is used to explain the known irregular switch in its polarity. The system has a 3-dimensional Lorenz type chaotic attractor around its two singular points. However this attractor is not bounded by any ellipsoidal surface as in the Lorenz attractor. In this paper, by using the Poincaré compactification for polynomial vector fields in R3 we study the dynamics of the Rikitake system at infinity, showing that there are orbits which escape to, or come from, infinity, instead of going towards the attractor. Moreover we study, for particular values of the parameters, the flow over two invariant planes, and describe the global flow of the system when it has two independent first integrals and thus is completely integrable. The global analysis performed, allows us to give a numerical description of the creation of Rikitake attractor. © 2008 Elsevier B.V. All rights reserved.
KW - Geodynamo
KW - Lorenz attractor
KW - Poincaré compactification
KW - Rikitake attractor
KW - Strange attractor creation
KW - Unbounded orbits
UR - https://www.scopus.com/pages/publications/58149492531
U2 - 10.1016/j.physd.2008.10.011
DO - 10.1016/j.physd.2008.10.011
M3 - Article
SN - 0167-2789
VL - 238
SP - 241
EP - 252
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
ER -