TY - JOUR
T1 - Estimation of the domain containing all compact invariant sets of a system modelling the amplitude of a plasma instability
AU - Krishchenko, Alexander
AU - Starkov, Konstantin
N1 - Funding Information:
The work of A. Krishchenko was supported by Grants 05-01-00840, 07-07-00375 from the Russian Foundation for Basic Research.
PY - 2007/7/16
Y1 - 2007/7/16
N2 - In this Letter we describe localization results of all compact invariant sets of a system modelling the amplitude of a plasma instability proposed by Pikovski, Rabinovich and Trakhtengerts. We derive ellipsoidal and polytopic localization sets for a number of domains in the 4-dimensional parametrical space of this system. Other localization sets have been obtained by using paraboloids of a revolution, a circular cylinder and an elliptic paraboloid. Our approach is based on the solution of the first order extremum problem. A comparison of our method with the method of semipermeable surfaces is presented as well.
AB - In this Letter we describe localization results of all compact invariant sets of a system modelling the amplitude of a plasma instability proposed by Pikovski, Rabinovich and Trakhtengerts. We derive ellipsoidal and polytopic localization sets for a number of domains in the 4-dimensional parametrical space of this system. Other localization sets have been obtained by using paraboloids of a revolution, a circular cylinder and an elliptic paraboloid. Our approach is based on the solution of the first order extremum problem. A comparison of our method with the method of semipermeable surfaces is presented as well.
UR - http://www.scopus.com/inward/record.url?scp=34347377164&partnerID=8YFLogxK
U2 - 10.1016/j.physleta.2007.02.088
DO - 10.1016/j.physleta.2007.02.088
M3 - Artículo
SN - 0375-9601
VL - 367
SP - 65
EP - 72
JO - Physics Letters, Section A: General, Atomic and Solid State Physics
JF - Physics Letters, Section A: General, Atomic and Solid State Physics
IS - 1-2
ER -