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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

International Journal of Applied Mathematics and Computer Science
Volume 23 (2013): Issue 1 (March 2013)
By:
Open Access
|Mar 2013

References

  1. Albert, A. (1972). Regression and the Moore-Penrose Pseudoinverse, Academic Press, New York, NY.
    Search in Google Scholar
  2. Alexandrov, D. and Malygin, A. (2011). Nonlinear dynamics of phase transitions during seawater freezing with false bottom formation, Oceanology 51(6): 940-948.10.1134/S0001437011060014
    Search in Google Scholar
  3. Åström, K. (1970). Introduction to the Stochastic Control Theory, Academic Press, New York, NY.
    Search in Google Scholar
  4. Bashkirtseva, I. and Ryashko, L. (2000). Sensitivity analysis of the stochastically and periodically forced Brusselator, Physica A 278(1-2): 126-139.10.1016/S0378-4371(99)00453-7
    Search in Google Scholar
  5. Bashkirtseva, I. and Ryashko, L. (2005). Sensitivity and chaos control for the forced nonlinear oscillations, Chaos Solitonsand Fractals 26(5): 1437-1451.10.1016/j.chaos.2005.03.029
    Search in Google Scholar
  6. Bashkirtseva, I. and Ryashko, L. (2009). Constructive analysis of noise-induced transitions for coexisting periodic attractors of Lorenz model, Physical Review E79(4): 041106-041114.10.1103/PhysRevE.79.04110619518172
    Search in Google Scholar
  7. Bashkirtseva, I., Ryashko, L. and Stikhin, P. (2010). Noise-induced backward bifurcations of stochastic 3D-cycles, Fluctuation and Noise Letters 9(1): 89-106.10.1142/S0219477510000095
    Search in Google Scholar
  8. Bashkirtseva, I., Ryashko, L. and Tsvetkov, I. (2009). Sensitivity analysis of stochastic equilibria and cycles for the discrete dynamic systems, Dynamics of Continuous, Discreteand Impulsive Systems, Series A: Mathematical Analysis17(4): 501-515.
    Search in Google Scholar
  9. Chen, G. and Yu, X.E. (2003). Chaos Control: Theory and Applications, Springer-Verlag, New York, NY.
    Search in Google Scholar
  10. Digailova, I. and Kurzhanskii, A. (2004). Attainability problems under stochastic perturbations, Differential Equations40(11): 1573-1578.10.1007/s10625-004-0007-z
    Search in Google Scholar
  11. Elaydi, S. (1999). An Introduction to Difference Equations, Springer-Verlag, New York, NY.10.1007/978-1-4757-3110-1
    Search in Google Scholar
  12. Fedotov, S., Bashkirtseva, I. and Ryashko, L. (2004). Stochastic analysis of subcritical amplification of magnetic energy in a turbulent dynamo, Physica A 342(3-4): 491-506.10.1016/j.physa.2004.05.084
    Search in Google Scholar
  13. Fradkov, A. and Pogromsky, A. (1998). Introduction to Controlof Oscillations and Chaos, World Scientific Series of Nonlinear Science, Singapore.10.1142/3412
    Search in Google Scholar
  14. Gao, J., Hwang, S. and Liu, J. (1999). When can noise induce chaos?, Physical Review Letters 82(6): 1132-1135.10.1103/PhysRevLett.82.1132
    Search in Google Scholar
  15. Gassmann, F. (1997). Noise-induced chaos-order transitions, Physical Review E 55(3): 2215-2221.10.1103/PhysRevE.55.2215
    Search in Google Scholar
  16. Goswami, B. and Basu, S. (2002). Transforming complex multistability to controlled monostability, Physical ReviewE 66(2): 026214-026223.10.1103/PhysRevE.66.026214
    Search in Google Scholar
  17. Henon, M. (1976). A two-dimensional mapping with a strange attractor, Communications in MathematicalPhysics 50(1): 69-77.10.1007/BF01608556
    Search in Google Scholar
  18. Karthikeyan, S. and Balachandran, K. (2011). Constrained controllability of nonlinear stochastic impulsive systems, International Journal of Applied Mathematicsand Computer Science 21(2): 307-316, DOI: 10.2478/v10006-011-0023-0.10.2478/v10006-011-0023-0
    Search in Google Scholar
  19. Kučera, V. (1973). Algebraic theory of discrete optimal control for single-variable systems, III: Closed-loop control, Kybernetika9(4): 291-312.
    Search in Google Scholar
  20. Martínez-Zéregaa, B. and Pisarchik, A. (2002). Stochastic control of attractor preference in a multistable system, Communications in Nonlinear Science and Numerical Simulation17(11): 4023-4028.10.1016/j.cnsns.2012.03.010
    Search in Google Scholar
  21. Matsumoto, K. and Tsuda, I. (1983). Noise-induced order, Journalof Statistical Physics 31(1): 87-106.10.1007/BF01010923
    Search in Google Scholar
  22. McDonnell, M., Stocks, N., Pearce, C. and Abbott, D. (2008). Stochastic Resonance: From Suprathreshold StochasticResonance to Stochastic Signal Quantization, Cambridge University Press, Cambridge.10.1017/CBO9780511535239
    Search in Google Scholar
  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, Journal of AppliedMathematics and Mechanics 59(1): 47-56.10.1016/0021-8928(95)00006-B
    Search in Google Scholar
  24. Nayfeh, A. and Balachandran, B. (2006). Applied NonlinearDynamics: Analytical, Computational, and ExperimentalMethods, Wiley, New York, NY.
    Search in Google Scholar
  25. Ott, E., Grebogi, C. and Yorke, J. (1990). Controlling chaos, Physical Review Letters 64(11): 1196-1199.10.1103/PhysRevLett.64.119610041332
    Search in Google Scholar
  26. Ryagin, M. and Ryashko, L. (2004). The analysis of the stochastically forced periodic attractors for Chua’s circuit, International Journal of Bifurcation and Chaos in AppliedSciences and Engineering 14(11): 3981-3987.10.1142/S0218127404011600
    Search in Google Scholar
  27. Ryashko, L. (1996). The stability of stochastically perturbed orbital motions, Journal of Applied Mathematics and Mechanics60(4): 579-590.10.1016/S0021-8928(96)00073-1
    Search in Google Scholar
  28. Ryashko, L. and Bashkirtseva, I. (2011a). Analysis of excitability for the FitzHugh-Nagumo model via a stochastic sensitivity function technique, Physical ReviewE 83(6): 061109-061116.10.1103/PhysRevE.83.06110921797304
    Search in Google Scholar
  29. Ryashko, L. and Bashkirtseva, I. (2011b). Control of equilibria for nonlinear stochastic discrete-time systems, IEEETransactions on Automatic Control 56(9): 2162-2166.10.1109/TAC.2011.2142630
    Search in Google Scholar
  30. Sanjuan, M. and Grebogi, C. (2010). Recent Progress in ControllingChaos, World Scientific, Singapore.10.1142/7563
    Search in Google Scholar
  31. Wonham, W. (1979). Linear Multivariable Control: A GeometricApproach, Springer-Verlag, Berlin.10.1007/978-1-4684-0068-7
    Search in Google Scholar
  32. Zhirabok, A. and Shumsky, A. (2012). An approach to the analysis of observability and controllability in nonlinear systems via linear methods, International Journal of AppliedMathematics and Computer Science 22(3): 507-522, DOI: 10.2478/v10006-012-0038-1.10.2478/v10006-012-0038-1
    Search in Google Scholar
DOI: https://doi.org/10.2478/amcs-2013-0001 | Journal eISSN: 2083-8492 | Journal ISSN: 1641-876X
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Language: English
Page range: 5 - 16
Published on: Mar 26, 2013
Published by: Sciendo
In partnership with: Paradigm Publishing Services
Publication frequency: 4 times per year
Keywords:
stochastic sensitivity function,
attainability,
chaos suppression
Related subjects:
Mathematics,
Applied mathematics

© 2013 Irina Bashkirtseva, Lev Ryashko, published by Sciendo
This work is licensed under the Creative Commons License.

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