TY - JOUR
T1 - Localization analysis of compact invariant sets of multi-dimensional nonlinear systems and symmetrical prolongations
AU - Krishchenko, Alexander P.
AU - Starkov, Konstantin E.
N1 - Funding Information:
This paper is supported by the CONACYT project “ANÁLISIS DE LOCALIZACIÓN DE CONJUNTOS COMPACTOS INVARIANTES DE SISTEMAS NO LINEALES CON DIN ÁMICA COMPLEJA Y SUS APLICACIONES”, No. 000000000078890, MEXICO. In addition, the first author is supported partially by the grants 08-01-00203 and 07-07-00375 from the Russian Foundation for Basic Research.
PY - 2010/5
Y1 - 2010/5
N2 - In our paper we study the localization problem of compact invariant sets of nonlinear systems. Methods of a solution of this problem are discussed and a new method is proposed which is based on using symmetrical prolongations and the first-order extremum condition. Our approach is applied to the system modeling the Rayleigh-Bénard convection for which the symmetrical prolongation with the Lorenz system has been constructed.
AB - In our paper we study the localization problem of compact invariant sets of nonlinear systems. Methods of a solution of this problem are discussed and a new method is proposed which is based on using symmetrical prolongations and the first-order extremum condition. Our approach is applied to the system modeling the Rayleigh-Bénard convection for which the symmetrical prolongation with the Lorenz system has been constructed.
KW - Compact invariant set
KW - Localization
KW - Lorenz system
KW - Rayleigh-Bénard convection
KW - Symmetrical prolongation
UR - http://www.scopus.com/inward/record.url?scp=70449525323&partnerID=8YFLogxK
U2 - 10.1016/j.cnsns.2009.05.068
DO - 10.1016/j.cnsns.2009.05.068
M3 - Artículo
SN - 1007-5704
VL - 15
SP - 1159
EP - 1165
JO - Communications in Nonlinear Science and Numerical Simulation
JF - Communications in Nonlinear Science and Numerical Simulation
IS - 5
ER -