Localization of periodic orbits of polynomial systems by ellipsoidal estimates

Chaos, Solitons and Fractals

Volumn 23, Issue 3, 2005, Pages 981-988

  Starkov, Konstantin E ^a,c   Krishchenko, Alexander P ^b  

^a INSTITUTO POLITÉCNICO NACIONAL   (Mexico)

^b BAUMAN MOSCOW STATE TECHNICAL UNIVERSITY   (Russian Federation)

^c CITEDI IPN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRA; CHAOS THEORY; EIGENVALUES AND EIGENFUNCTIONS; LASER BEAMS; MATRIX ALGEBRA; PROBLEM SOLVING; TIME VARYING SYSTEMS;

CONTINUOUS-TIME SYSTEMS; LAMB'S EQUATION; OPERATING CAVITY; RIKITAKE SYSTEM;

POLYNOMIALS;

EID: 4644232671     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0960-0779(04)00352-2     Document Type: Article

References (16)

1. Babloyantz A, Krishchenko A, Nosov A. Analysis and stabilization of nonlinear systems. Comput Math Appl 1997;34:356-69.
2. Crawford CR, Moon YS. Finding a positive definite linear combination of two Hermitian matrices. Linear Algebra Appl 1983;51:37-48.
3. Franceschini V, Giberti C, Zheng Z. Characterization of the Lorenz attractor by unstable periodic orbits. Nonlinearity 1993:251-8.
4. Hardy Y, Steeb WH. The Rikitake two-disk dynamo system and domains with periodic orbits. Internat. J Theor Phys 1999;38:2413-7.
5. Horn RA, Johnson CR. Matrix analysis. Cambridge: Cambridge University Press; 1986.
6. Kocarev L, Parlitz U, Hu B. Lie derivatives and dynamical systems. Chaos, Solitons & Fractals 1998;9:1359-66.
7. Krishchenko AP. Localization of limit cycles. Differen Equal 1995;31:1826-33.
8. Krishchenko AP. Estimation of domains with cycles. Comput Math Appl 1997;34:325-32.
9. Lamb Jr WE. Theory of an optical maser. Phys Rev 1964;134:A1429-50.
10. Pogromsky A, Nijmeijer H, Rooda K. A negative criterion for a class of hybrid systems, In Proc. 16th Int. Symp. Mathematical Theory of Networks and Systems MTNS'2004, Leuven, Belgium, 2004.
11. Rikitake T. Oscillations of a system of disk dynamos. Proc Cambridge Philos Soc 1958;54:89-105.
12. Starkov K. Some results on periodic orbits of polynomial systems. Stab Control: Theory Appl 2002;4:30-42.
13. Starkov K. Localization/nonuniqueness condition of periodic orbits of polynomial systems and its applications. In: CD-ROM with Proc. Int. Conf. Physics and Control, St. Petersburg, Russia. 2003.
14. Starkov K. Localization of periodic orbits of autonomous systems based on high order extremum conditions. Math Probl Eng, in press.
15. Starkov K, Krishchenko AP. Ellipsoidal estimates for domains containing all periodic orbits of general quadratic systems, In: Proc. 16th Int. Symp. Mathematical Theory of Networks and Systems MTNS'2004, Leuven, Belgium, 2004.
16. Stewart GW. Perturbation bounds for definite generalized eigenvalue problem. Linear Algebra Appl 1979;23:69-85.