Reconstruction of stochastic nonlinear dynamical models from trajectory measurements

Proceedings of SPIE - The International Society for Optical Engineering

Volumn 5845, Issue , 2005, Pages 173-181

  Luchinsky, D G ^a,b   Smelyanskiy, V N ^a   Millonas, M ^a   McClintock, P V E ^a  

^a NASA AMES RESEARCH CENTER   (United States)

^b LANCASTER UNIVERSITY   (United Kingdom)

Author keywords

Bayesian inference; Nonlinear model reconstruction

Indexed keywords

MATHEMATICAL MODELS; RANDOM PROCESSES; SPURIOUS SIGNAL NOISE; TIME SERIES ANALYSIS; VECTORS;

BAYESIAN INFERENCE; NONLINEAR MODEL RECONSTRUCTION;

NONLINEAR SYSTEMS;

EID: 28444458496     PISSN: 0277786X     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1117/12.610457     Document Type: Conference Paper

References (23)

1. H. D. I. Abarbanel, "Challenges in modelling nonlinear systems: a worked example," in Nonlinear dynamics and statistics, A. I. Mees, ed., ch. I, pp. 1-30, Birkhäuser, Boston, 2001.
2. M. Willemsen, M. P. van Exter, and J. P. Woerdman, "Anatomy of a polarization switch of a vertical-cavity semiconductor laser," Phys. Rev. Lett. 84(19), pp. 4337-4340, 2000.
3. K. Visscher, M. J. Schnitzer, and S. M. Block, "Single kinezin molecules studied with a molecular force clamp," Nature 400, pp. 184-189, 1999.
4. C. Calder, M. Lavine, P. Müller, and J. S. Clark, "Incorporating multiple sources of stochasticity into dynamic population models," Ecology 84(6), pp. 1395-1402, 2003.
5. P. Congdon, Bayesian statistical modelling, Wiley series in probability and statistics, Wiley, Chichester, 2001.
6. G. D'Agostini, Bayesian reasoning in high-energy physics : principles and applications, CERN, Geneva, 1999.
7. http:/research.microsoft.com/~minka/papers/dynamic.html
8. S. Siegert, R. Friedrich, and J. Peinke, "Analysis of data sets of stochastic systems," Phys. Lett. A 253, pp. 275-280, 1998.
9. J. Gradisek, S. Siegert, R. Friedrich, and I. Grabec, "Analysis of time series from stochastic processes," Phys. Rev. E 62(3), pp. 3146-3155, 2000.
10. R. Friedrich, S. Siegert, J. Peinke, S. Luck, M. Siefert, M. Lindemann, J. Raethjen, G. Deuschl, and G. Pfister, "Extracting model equations from experimental data," Phys. Lett. A 271, pp. 217-222, 2000.
11. M. Siefert, A. Kittel, R. Friedrich, and J. Peinke, "On a quantitative method to analyze dynamical and measurement noise," Europhys. Lett. 61(4), pp. 466-472, 2003.
12. J. P. M. Heald and J. Stark, "Estimation of noise levels for models of chaotic dynamical systems," Phys. Rev. Lett. 84(11), pp. 2366-2369, 2000.
13. R. Meyer and N. Christensen, "Fast bayesian reconstruction of chaotic dynamical systems via extended kalman filtering," Phys. Rev. E 65, p. 016206, 2001.
14. C. L. Bremer and D. T. Kaplan, "Markov chain monte carlo estimation of nonlinear dynamics from time series," Physica D 160, pp. 116-126, 2001.
15. J.-M. Fullana and M. Rossi, "Identification methods for nonlinear stochastic systems," Physical Review E 65, p. 031107, 2002.
16. V. N. Smelyanskiy and D. G.'Luchinsky, "Model reconstruction of nonlinear dynamical systems driven by noise," in Noise in complex systems and stochastic dynamics II, Z. Gingl, J. M. Sancho, L. Schimansky-Geier, and J. Kertesz, eds., Proc. SPIE 5471, pp. 344-354, SPIE, (Bellingham), 2004.
17. V. N. Smelyanskiy, D. G. Luchinsky, A. Stefanovska, and P. V. E. McClintock, "Reconstruction of nonlinear cardiorespiratory interaction from univariate time-series," to appear in Phys. Rev. Lett.
18. R. Graham Z. Phys. B 26, p. 281, 1977.
19. E. Gozzi, "Functional-integral approach to parisi-wu stochastic quantization: Scalar theory," Physical Review D 28, pp. 1922-1930, 1983.
20. A. J. McKane, "Noise-induced escape rate over a potential barrier: Results for a general noise," Phys. Rev. A 40(7), pp. 4050-4053, 1989.
21. M. I. Dykman, "Large fluctuations and fluctuational transitions in systems driven by colored gaussian noise-a high frequency noise," Phys. Rev. A 42, pp. 2020-2029, 1990.
22. R. Graham, Tracts in Modern Physics, vol. 66, ch. Quantum Statistics in Optics and Solid-State Physics. Springer-Verlag, New York, 1973.
23. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in FORTRAN: The Art.of Scientific Computing, Cambridge University Press, Cambridge, England, 2 ed., 1992.