TY - JOUR
T1 - On the ultimate dynamics of the four-dimensional Rössler system
AU - Starkov, Konstantin E.
N1 - Publisher Copyright:
© 2014 World Scientific Publishing Company.
PY - 2014/11/25
Y1 - 2014/11/25
N2 - In this paper, we construct the polytope which contains all compact ω-limit sets of the four-dimensional Rössler system which is a generalization of the hyperchaotic Rössler system for the case of positive parameters. Further, we find a few three-dimensional planes containing all compact ω-limit sets for bounded positive half-trajectories located in some subdomains in the half-space z > 0. Besides, we analyze one case in which all compact ω-limit sets in the half-space z > 0 are contained in one three-dimensional plane. Our approach is based on a combination of the LaSalle theorem and the extreme-based localization method of compact invariant sets.
AB - In this paper, we construct the polytope which contains all compact ω-limit sets of the four-dimensional Rössler system which is a generalization of the hyperchaotic Rössler system for the case of positive parameters. Further, we find a few three-dimensional planes containing all compact ω-limit sets for bounded positive half-trajectories located in some subdomains in the half-space z > 0. Besides, we analyze one case in which all compact ω-limit sets in the half-space z > 0 are contained in one three-dimensional plane. Our approach is based on a combination of the LaSalle theorem and the extreme-based localization method of compact invariant sets.
KW - Four-dimensional Rössler system
KW - localization
KW - omega-limit set
UR - http://www.scopus.com/inward/record.url?scp=84928343470&partnerID=8YFLogxK
U2 - 10.1142/S0218127414501491
DO - 10.1142/S0218127414501491
M3 - Artículo
SN - 0218-1274
VL - 24
JO - International Journal of Bifurcation and Chaos
JF - International Journal of Bifurcation and Chaos
IS - 11
M1 - 1450149
ER -