Journal of Applied Mathematics

Stability Problems for Chua System with One Linear Control

Camelia Pop Arieşanu

Full-text: Open access

Abstract

A Hamilton-Poisson realization and some stability problems for a dynamical system arisen from Chua system are presented. The stability and dynamics of a linearized smooth version of the Chua system are analyzed using the Hamilton-Poisson formalism. This geometrical approach allows to deduce the nonlinear stabilization near different equilibria.

Article information

Source
J. Appl. Math., Volume 2013 (2013), Article ID 764108, 5 pages.

Dates
First available in Project Euclid: 14 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.jam/1394807927

Digital Object Identifier
doi:10.1155/2013/764108

Mathematical Reviews number (MathSciNet)
MR3039740

Zentralblatt MATH identifier
1266.93062

Citation

Arieşanu, Camelia Pop. Stability Problems for Chua System with One Linear Control. J. Appl. Math. 2013 (2013), Article ID 764108, 5 pages. doi:10.1155/2013/764108. https://projecteuclid.org/euclid.jam/1394807927


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References

  • L. O. Chua, “Nonlinear circuits,” IEEE Transactions on Circuits and Systems, vol. 31, no. 1, pp. 69–87, 1984, Centennial special issue.
  • J.-M. Ginoux and B. Rossetto, “Differential geometry and mechanics: applications to chaotic dynamical systems,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 16, no. 4, pp. 887–910, 2006.
  • M. W. Hirsch, S. Smale, and R. L. Devaney, Differential Equations, Dynamical Systems, and an Introduction to Chaos, Elsevier, Academic Press, New York, NY, USA, 2003.
  • B. Hernández-Bermejo and V. Fairén, “Simple evaluation of Casimir invariants in finite-dimensional Poisson systems,” Physics Letters A, vol. 241, no. 3, pp. 148–154, 1998.
  • P. Birtea, M. Puta, and R. M. Tudoran, “Periodic orbits in the case of a zero eigenvalue,” Comptes Rendus Mathématique. Académie des Sciences. Paris, vol. 344, no. 12, pp. 779–784, 2007.
  • P. A. Damianou, “Multiple Hamiltonian structures for Toda systems of type $A$-$B$-$C$,” Regular & Chaotic Dynamics, vol. 5, no. 1, pp. 17–32, 2000.
  • C. Pop, C. Petrişor, and D. Bălă, “Hamilton-Poisson realizations for the Lü system,” Mathematical Problems in Engineering, vol. 2011, Article ID 842325, 13 pages, 2011.
  • A. Aron, P. Birtea, M. Puta, P. Şuşoi, and R. Tudoran, “Stability, periodic solutions and numerical integration in the Kowalevski top dynamics,” International Journal of Geometric Methods in Modern Physics, vol. 3, no. 7, pp. 1323–1330, 2006.
  • A. Aron, G. Girban, and S. Kilyeni, “A geometric approach of a battery mathematical model for on-line energy monitoring,” in Proceedings of the International Conference on Computer as a Tool (EUROCON '11), pp. 1–4, Lisbon, Portugal, April 2011.