Identifying stochastic basin hopping by partitioning with graph modularity

Physica D: Nonlinear Phenomena

Volumn 231, Issue 2, 2007, Pages 95-107

  Santitissadeekorn, N ^a   Bollt, E M ^a  

^a CLARKSON UNIVERSITY   (United States)

Author keywords

Basin hopping; Frobenius Perron operator; Graph modularity; Multistability; Noise; Phase space partition; Stochastic; Ulam's method

Indexed keywords

CATCHMENTS; GRAPH THEORY; MATHEMATICAL MODELS; PHASE SPACE METHODS;

BASIN HOPPING; FROBENIUS-PERRON OPERATOR; GRAPH MODULARITY; MULTISTABILITY; PHASE SPACE PARTITION; PSEUDOBARRIERS; ULAM'S METHOD;

STOCHASTIC CONTROL SYSTEMS;

EID: 34250721681     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2007.04.008     Document Type: Article

References (32)

1. Bollt E., Billings L., and Schwartz I. A manifold independent approach to understanding transport in stochastic dynamical systems. Physica D 173 (2002) 153-177
2. Billings L., Bollt E., and Schwartz I.B. Phase-space transport of stochastic chaos in population dynamics of virus spread. Phys. Rev. Lett. 88 (2002) 234101
3. Kraut S., and Feudel U. Multistability, noise and attractor-hopping: The crucial role of chaotic saddles. Physica D 181 (2003) 222-234
4. Kraut S., and Feudel U. Enhancement of noise-induced escape through the existence of a chaotic saddle. Phys. Rev. E 67 (2003) 1-4
5. de Souza S.L.T., and Caldas I.L. Basin of attraction and transient chaos in a gear-rattling model. J. Vib. Control. 7 (2004) 849-862
6. de Souza S.L.T., Caldas I.L., Viana R.L., Batista A.M., and Kapitaniak T. Noise-induced basin hopping in a gearbox model. Chaos Solitons Fractals 26 (2005) 1523-1531
7. Dellnitz M., and Junge O. On the approximation of complicated dynamical behavior. SIAM J. Numer. Anal. 36 2 (1999) 491-515
8. Preis R., and Dellnitz M. Congestion and almost invariant sets in dynamical systems. Proceedings of Symbolic and Numerical Scientific Computation. SNSC'01 (2003), Springer
9. R. Preis, M. Dellnitz, M. Hessel, Ch. Schtte, E. Meerbach, Dominant paths between almost invariant sets of dynamical systems. Preprint 154 of the DFG Schwerpunktprogramm 1095, 2004
10. K. Padberg, R. Preis, M. Dellnitz, Integrating multilevel graph partitioning with hierarchical set oriented methods for the analysis of dynamical systems. Preprint 152 of the DFG Schwerpunktprogramm 1095, 2004
11. Newman M.E.J., and Girvan M. Finding and evaluating community structure in networks. Phys. Rev. E 69 (2004) 026113
12. L. Dannon, A. Diaz-Guilera, J. Duch, A. Arenas, Comparing community structure identification. Preprint cond-mat/0505245, 2005
13. Dellnitz M., Junge O., Koon W.S., Lekien F., Lo M.W., Marsden J.E., Padberg K., Preis R., Ross S.D.S.D., and Thiere B. Transport in dynamical astronomy and multibody problems. Internat. J. Bifur. Chaos Appl. Sci. Engrg. 15 (2005) 699-727
14. R. Preis, M. Dellnitz, M. Hessel, Ch. Schtte, E. Meerbach, Dominant paths between almost invariant sets of dynamical systems. Preprint cond-mat/0505245, 2004
15. Newman M.E.J., and Girvan M. Statistical Mechanics of Complex Networks (2004), Springer, Berlin
16. Newman M.E.J. Fast algorithm for detecting community structure in networks. Phys. Rev. E 69 (2004) 066133
17. Lasota A., and Mackey M.C. Chaos, fractals, and noise, Stochastic Aspects of Dynamics. 2nd edition (1994), Springer, New York
18. Li T.Y. Finite approximation for the Frobenius-Perron operator. a solution to Ulam's conjecture. J. Approx. Theory 17 2 (1976) 177-186
19. G. Froyland, Estimating physical invariant measures and space averages of dynamical systems indicators. Ph.D. Thesis, University of Western Australia, 1996
20. Froyland G. Finite approximation of Sinai-Bowen-Ruelle measure for Anosov systems in two dimension. Random Comput. Dynam. 3 4 (1995) 251-263
21. Chui C., Du Q., and Li T. Error estimates of the Markov finite approximation of the Frobenius Perron operator. Nonlinear Anal. 19 4 (1992) 291-308
22. Ding J., and Zhou A. The projection method for computing multidimensional absolutely continuous invariant measures. J. Stat. Phys. 77 3-4 (1994) 899-908
23. Hunt F. Approximating the invariant measures of randomly perturbed dissipative maps. J. Math. Anal. Appl. 198 2 (1996) 534-551
24. Boyarsky A., and Lou Y.S. Approximating measure invariant under higher-dimensional chaotic transformation. J. Approx. Theory 65 2 (1991) 231-244
25. Ulam S.M. Problems in Modern Mathematics. Science editions (1970), Wiley, New York
26. Bollobás B. Modern Graph Theory (1998), Springer, NewYork
27. Van Kampen N.G. Stochastic Processes in Physics and Chemistry. 4th edition (2003), North-Holland
28. Bagrow J.P., and Bollt E.M. A local method for detecting communities. Phys. Rev. E 72 (2005) 046108
29. Clauset A., Newman M.E.J., and Moore C. Finding community structure in very large networks. Phys. Rev. E 70 (2004) 066111
30. Pfeiffer F., and Kunert A. Rattling models from deterministic to stochastic precesses. Nonlinear Dynam. 1 (1991) 63-74
31. Arnold L. Random Dynamical Systems. 2nd edition (2003), Springer, New York
32. Ott E. Chaos in Dynamical Systems. 1st edition (1993), Cambridge University Press