Skip to main content
Have a personal or library account? Click to login
Attainability analysis in the problem of stochastic equilibria synthesis for nonlinear discrete systems Cover

Attainability analysis in the problem of stochastic equilibria synthesis for nonlinear discrete systems

Open Access
|Mar 2013

References

  1. Albert, A. (1972)., Academic Press, New York, NY.
  2. Alexandrov, D. and Malygin, A. (2011). Nonlinear dynamics of phase transitions during seawater freezing with false bottom formation,(6): 940-948.
  3. Åström, K. (1970)., Academic Press, New York, NY.
  4. Bashkirtseva, I. and Ryashko, L. (2000). Sensitivity analysis of the stochastically and periodically forced Brusselator,(1-2): 126-139.
  5. Bashkirtseva, I. and Ryashko, L. (2005). Sensitivity and chaos control for the forced nonlinear oscillations,(5): 1437-1451.
  6. Bashkirtseva, I. and Ryashko, L. (2009). Constructive analysis of noise-induced transitions for coexisting periodic attractors of Lorenz model,(4): 041106-041114.
  7. Bashkirtseva, I., Ryashko, L. and Stikhin, P. (2010). Noise-induced backward bifurcations of stochastic 3D-cycles,(1): 89-106.
  8. Bashkirtseva, I., Ryashko, L. and Tsvetkov, I. (2009). Sensitivity analysis of stochastic equilibria and cycles for the discrete dynamic systems,(4): 501-515.
  9. Chen, G. and Yu, X.E. (2003)., Springer-Verlag, New York, NY.
  10. Digailova, I. and Kurzhanskii, A. (2004). Attainability problems under stochastic perturbations,(11): 1573-1578.
  11. Elaydi, S. (1999)., Springer-Verlag, New York, NY.
  12. Fedotov, S., Bashkirtseva, I. and Ryashko, L. (2004). Stochastic analysis of subcritical amplification of magnetic energy in a turbulent dynamo,(3-4): 491-506.
  13. Fradkov, A. and Pogromsky, A. (1998)., World Scientific Series of Nonlinear Science, Singapore.
  14. Gao, J., Hwang, S. and Liu, J. (1999). When can noise induce chaos?,(6): 1132-1135.
  15. Gassmann, F. (1997). Noise-induced chaos-order transitions,(3): 2215-2221.
  16. Goswami, B. and Basu, S. (2002). Transforming complex multistability to controlled monostability,(2): 026214-026223.
  17. Henon, M. (1976). A two-dimensional mapping with a strange attractor,(1): 69-77.
  18. Karthikeyan, S. and Balachandran, K. (2011). Constrained controllability of nonlinear stochastic impulsive systems,(2): 307-316, DOI: 10.2478/v10006-011-0023-0.
  19. Kučera, V. (1973). Algebraic theory of discrete optimal control for single-variable systems, III: Closed-loop control,(4): 291-312.
  20. Martínez-Zéregaa, B. and Pisarchik, A. (2002). Stochastic control of attractor preference in a multistable system,(11): 4023-4028.
  21. Matsumoto, K. and Tsuda, I. (1983). Noise-induced order,(1): 87-106.
  22. McDonnell, M., Stocks, N., Pearce, C. and Abbott, D. (2008)., Cambridge University Press, Cambridge.
  23. Mil’shtein, G. and Ryashko, L. (1995). A first approximation of the quasipotential in problems of the stability of systems with random non-degenerate perturbations,(1): 47-56.
  24. Nayfeh, A. and Balachandran, B. (2006)., Wiley, New York, NY.
  25. Ott, E., Grebogi, C. and Yorke, J. (1990). Controlling chaos,(11): 1196-1199.
  26. Ryagin, M. and Ryashko, L. (2004). The analysis of the stochastically forced periodic attractors for Chua’s circuit,(11): 3981-3987.
  27. Ryashko, L. (1996). The stability of stochastically perturbed orbital motions,(4): 579-590.
  28. Ryashko, L. and Bashkirtseva, I. (2011a). Analysis of excitability for the FitzHugh-Nagumo model via a stochastic sensitivity function technique,(6): 061109-061116.
  29. Ryashko, L. and Bashkirtseva, I. (2011b). Control of equilibria for nonlinear stochastic discrete-time systems,(9): 2162-2166.
  30. Sanjuan, M. and Grebogi, C. (2010)., World Scientific, Singapore.
  31. Wonham, W. (1979)., Springer-Verlag, Berlin.
  32. Zhirabok, A. and Shumsky, A. (2012). An approach to the analysis of observability and controllability in nonlinear systems via linear methods,(3): 507-522, DOI: 10.2478/v10006-012-0038-1.
DOI: https://doi.org/10.2478/amcs-2013-0001 | Journal eISSN: 2083-8492 | Journal ISSN: 1641-876X
Language: English
Page range: 5 - 16
Published on: Mar 26, 2013
Published by: University of Zielona Góra
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year

© 2013 Irina Bashkirtseva, Lev Ryashko, published by University of Zielona Góra
This work is licensed under the Creative Commons License.