Localization of hidden attractors in smooth Chua's systems

International Conference on Applied and Computational Mathematics

Volumn , Issue , 2011, Pages 26-33

  Kuznetsov, N V ^a,b   Vagaitsev, V I ^a,b   Leonov, G A ^a   Seledzhi, S M ^a  

^a ST PETERSBURG STATE UNIVERSITY   (Russian Federation)

^b UNIVERSITY OF JYVÄSKYLÄ   (Finland)

Author keywords

Attractor localization; Describing function method; Harmonic balance; Hidden attractor; Smooth Chua's circuit

Indexed keywords

ATTRACTOR LOCALIZATION; CHUA'S CIRCUIT; DESCRIBING FUNCTION METHOD; HARMONIC BALANCE; HIDDEN ATTRACTOR;

ALGORITHMS; NUMERICAL METHODS;

DYNAMICAL SYSTEMS;

EID: 82755198491     PISSN: 22232877     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (18)

1. E.N. Lorenz, Deterministic nonperiodic flow, J. Atmos. Sci., V.20, 1963, pp.130-141.
2. O.E. Rossler, An Equation for Continuous Chaos, Physics Letters, V.57A, No.5, 1976, pp.397-398.
3. L.O. Chua, G.N. Lin, Canonical Realization of Chua's Circuit Family, IEEE Transactions on Circuits and Systems, V.37, No.4, 1990, pp.885-902.
4. G. Chen, & T. Ueta, Yet another chaotic attractor, /it Int. J. Bifurcation and Chaos No.9, 1999, pp.1465-1466. (Pubitemid 129292251)
5. G.A. Leonov, N.V. Kuznetsov, V.I. Vagaitsev, Localization of hidden Chua's attractors, Physics Letters, Section A, Vol. 375, is. 35, 2011, pp. 2230-2233 (doi:10.1016/j.physleta.2011.04.037).
6. G.A. Leonov, On harmonic linearization method, Doklady Akademii Nauk. Physcis, 424(4), 2009, pp. 462-464.
7. G.A. Leonov, On harmonic linearization method, Automation and remote controle, 5, 2009, pp. 65-75.
8. G.A. Leonov, On Aizerman problem, Automation and remote control, No.7, 2009, pp. 37-49.
9. G.A. Leonov, Effective methods for periodic oscillations search in dynamical systems, App. math. & mech., 74(1), 2010, pp. 37-73.
10. G.A. Leonov, V.I. Vagaitsev, N.V. Kuznetsov, Algorithm for localizing Chua attractors based on the harmonic linearization method, Doklady Mathematics, 82(1), 2010, pp.663-666.
11. G.A. Leonov, V.O. Bragin, N.V. Kuznetsov, Algorithm for Constructing Counterexamples to the Kalman Problem, Doklady Mathematics, 82(1), 2010, pp. 540-542.
12. L.O. Chua, A Zoo of Strange Attractors from the Canonical Chua's Circuits, Proceedings of the IEEE 35th Midwest Symposium on Circuits and Systems (Cat. No.92CH3099-9), V.2, 1992, pp.916-926.
13. L.O. Chua, A Glimpse of Nonlinear Phenomena from Chua's Oscillator, Philosophical Transactions: Physical Sciences and Engineering, V.353, No.1701, 1995, pp.3-12.
14. E. Bilotta, P. Pantano, A gallery of Chua attractors, World scientific series on nonlinear science, Series A, V.61, 2008.
15. Z. Shi, S. Hong and K. Chen, Experimental study on tracking the state of analog Chua's circuit with particle filter for chaos synchronization, Physics Letters A, Vol. 372, Iss. 34, 2008, pp. 5575-5580.
16. V.S. Anishchenko, T. Kapitaniak, M.A. Safonova and O.V. Sosnovzeva, Birth of double-double scroll attractor in coupled Chua circuits, Physics Letters A, Vol.192, Iss.2-4, 1994, pp. 207-214.
17. G.A. Leonov, Strange attractors and classical stability theory, St. Petersburg university Press, 2008.
18. G.A. Leonov, N.V. Kuznetsov, Time-Varying Linearization and the Perron effects, International Journal of Bifurcation and Chaos, Vol. 17, No.4, 2007, pp. 1079-1107. (Pubitemid 46905045)