TY - JOUR
T1 - Bounds for compact invariant sets of the system describing dynamics of the nuclear spin generator
AU - Starkov, Konstantin E.
N1 - Funding Information:
This work was supported by the CONACYT project “ANÁLISIS DE LOCALIZACIÓN DE CONJUNTOS COMPACTOS INVARIANTES DE SISTEMAS NO LINEALES CON DINÁMICA COMPLEJA Y SUS APLICACIÓNES”, N. 000000000078890, MEXICO.
PY - 2009/6
Y1 - 2009/6
N2 - This paper is concerned with the localization problem of compact invariant sets of the system describing dynamics of the nuclear spin generator. We establish that all compact invariant sets of this system are located in the intersection of a ball with two frusta and compute its parameters. In addition, localization by using the two-parameter set of parabolic cylinders is described. Our results are obtained with help of the iteration theorem concerning a localization of compact invariant sets. One numerical example illustrating a localization of a chaotic attractor is presented as well.
AB - This paper is concerned with the localization problem of compact invariant sets of the system describing dynamics of the nuclear spin generator. We establish that all compact invariant sets of this system are located in the intersection of a ball with two frusta and compute its parameters. In addition, localization by using the two-parameter set of parabolic cylinders is described. Our results are obtained with help of the iteration theorem concerning a localization of compact invariant sets. One numerical example illustrating a localization of a chaotic attractor is presented as well.
KW - Compact invariant set
KW - Localization
KW - Nuclear spin generator equations
UR - http://www.scopus.com/inward/record.url?scp=58349105559&partnerID=8YFLogxK
U2 - 10.1016/j.cnsns.2008.08.005
DO - 10.1016/j.cnsns.2008.08.005
M3 - Artículo
SN - 1007-5704
VL - 14
SP - 2565
EP - 2570
JO - Communications in Nonlinear Science and Numerical Simulation
JF - Communications in Nonlinear Science and Numerical Simulation
IS - 6
ER -