Identifying almost invariant sets in stochastic dynamical systems

Chaos

Volumn 18, Issue 2, 2008, Pages

  Billings, Lora ^a   Schwartz, Ira B ^b  

^a MONTCLAIR STATE UNIVERSITY   (United States)

^b NAVAL RESEARCH LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 46449119532     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2929748     Document Type: Article

References (22)

1. Billings, L., Bollt, E. M., and Schwartz, I. B., " Phase-space transport of stochastic chaos in population dynamics of virus spread.," Phys. Rev. Lett. 88, 234101 (2002).
2. Billings, L., and Schwartz, I. B., " Exciting chaos with noise: unexpected dynamics in epidemic outbreaks.," J. Math. Biol. 44, 31-48 (2002).
3. Bollt, E. M., Billings, L., and Schwartz, I. B., " A manifold independent approach to understanding transport in stochastic dynamical systems.," Physica D 173, 153-177 (2002).
4. Dellnitz, M., and Junge, O., " On the approximation of complicated dynamical behavior.," SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 36, 491-515 (1999).
5. Deuflhard, P., Husinga, W., Fischer, A., and Schutte, Ch., " Identification of almost invariant aggregates in reversible nearly uncoupled Markov cell.," Linear Algebr. Appl. 315, 39-59 (2000).
6. Deuflhard, P., and Weber, M., " Robust Perron cluster analysis in conformation dynamics.," Linear Algebr. Appl. 398, 161-184 (2005).
7. Dykman, M. I., Luchinsky, D. G., McClintock, P. V. E., and Smelyanskiy, V. N., " Corrals and critical behavior of the distribution of fluctuational paths.," Phys. Rev. Lett. 77, 5229-5232 (1996).
8. Freidlin, M. I., and Wentzel, A. D., Random Perturbations in Dynamical Systems (Springer-Verlag, Berlin, 1984).
9. Fritzsche, D., Mehrmann, V., Szyld, D. B., and Virnik, E., " An SVD approach to identifying meta-stable states for Markov chains.," Electron. Trans. Numer. Anal. 29, 46-69 (2008).
10. Froyland, G., " Statistically optimal almost-invariant sets.," Physica D 200, 205-219 (2005).
11. Froyland, G., and Dellnitz, M., " Detecting and locating near-optimal almost-invariant sets and cycles.," SIAM J. Sci. Comput. (USA) 24, 1839-1863 (2003).
12. Graham, R., and Tel, T., " Existence of a potential for dissipative dynamical systems.," Phys. Rev. Lett. 52, 9-12 (1984).
13. Hamm, A., T́l, T., and Graham, R., " Noise-induced attractor explosions near tangent bifurcations.," Phys. Lett. A 185, 313-320 (1994).
14. Kraut, S., Feudel, U., and Grebogi, C., " Preference of attractors in noisy multistable systems.," Phys. Rev. E 59, 5253-5260 (1999).
15. Lasota, A., and Mackey, M. C., Chaos, Fractals, and Noise, 2nd ed. (Springer-Verlag, New York, 1994).
16. Maier, R., and Stein, D., " Escape problem for irreversible systems.," Phys. Rev. E 48, 931-938 (1993).
17. Schwartz, I. B., Billings, L., and Bollt, E. M., " Dynamical epidemic suppression using stochastic prediction and control.," Phys. Rev. E 70, 046220 (2004).
18. Shi, J. B., and Malik, J., " Normalized cuts and image segmentation.," IEEE Trans. Pattern Anal. Mach. Intell. 22, 888-905 (2000).
19. van Kampen, N. G., Stochastic Processes in Physics and Chemistry, Lecture Notes in Mathematics Vol. 888 (North-Holland, Amsterdam, 1981).
20. Weber, M., Kube, S., Walter, L., and Deuflhard, P., " Stable computation of probability densities for metastable dynamical systems.," Multiscale Model. Simul. 6, 396-416 (2007).
21. Weber, M., Rungsarityotin, W., and Schliep, A., " Perron cluster analysis and its connection to graph partitioning for noisy data.," Technical Report No. ZR-04-39, Zuse Institute Berlin, 2004.
22. Wiggins, S., Chaotic Transport in Dynamical Systems (Springer-Verlag, New York, 1992).