Model reduction for slow-fast stochastic systems with metastable behaviour

Journal of Chemical Physics

Volumn 140, Issue 17, 2014, Pages

  Bruna, Maria ^a,b   Chapman, S Jonathan ^a   Smith, Matthew J ^b  

^a UNIVERSITY OF OXFORD   (United Kingdom)

^b MICROSOFT RESEARCH   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

PREDATOR PREY SYSTEMS;

CHEMICAL SWITCHES; META-STABLE STATE; NUMBER OF DEGREES OF FREEDOM; PRACTICAL METHOD; PREDATOR - PREY SYSTEM; QUASI STEADY STATE APPROXIMATION; SLOW-FAST SYSTEMS; STOCHASTIC AVERAGING;

STOCHASTIC MODELS;

ALGORITHM; CHEMICAL MODEL; ECOLOGY; FOOD CHAIN; KINETICS; STATISTICS;

ALGORITHMS; ECOLOGY; FOOD CHAIN; KINETICS; MODELS, CHEMICAL; STOCHASTIC PROCESSES;

EID: 84900027242     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.4871694     Document Type: Article

References (47)

1. P. Thomas, A. V. Straube, and R. Grima, BMC Syst. Biol. 6, 39 (2012). 10.1186/1752-0509-6-39
2. H. H. McAdams and A. Arkin, Trends Genet. 15, 65 (1999). 10.1016/S0168-9525(98)01659-X
3. E. M. Ozbudak, M. Thattai, H. N. Lim, B. I. Shraiman, and A. van Oudenaarden, Nature (London) 427, 737 (2004). 10.1038/nature02298
4. J.-W. Veening, W. K. Smits, and O. P. Kuipers, Annu. Rev. Microbiol. 62, 193 (2008). 10.1146/annurev.micro.62.081307.163002
5. W. Horsthemke and R. Lefever, Noise-Induced Transitions: Theory and Applications in Physics, Chemistry, and Biology, 1st ed. (Springer-Verlag, Berlin, 1984), Vol. 15.
6. R. Wang, J. A. Dearing, P. G. Langdon, E. Zhang, X. Yang, V. Dakos, and M. Scheffer, Nature (London) 492, 419 (2012). 10.1038/nature11655
7. W. E, D. Liu, and E. Vanden-Eijnden, Commun. Pure Appl. Math. 58, 1544 (2005). 10.1002/cpa.20088
8. A. C. Staver, S. Archibald, and S. A. Levin, Science 334, 230 (2011). 10.1126/science.1210465
9. M. Scheffer, S. R. Carpenter, T. M. Lenton, J. Bascompte, W. Brock, V. Dakos, J. van de Koppel, I. A. van de Leemput, S. A. Levin, E. H. van Nes, M. Pascual, and J. Vandermeer, Science 338, 344 (2012). 10.1126/science.1225244
10. N. Fenichel, J. Differ. Equ. 31, 53 (1979). 10.1016/0022-0396(79)90152-9
11. M. Desroches, J. Guckenheimer, B. Krauskopf, C. Kuehn, H. M. Osinga, and M. Wechselberger, SIAM Rev. 54, 211 (2012). 10.1137/100791233
12. P. Boxler, Probab. Theory Rel. 83, 509 (1989). 10.1007/BF01845701
13. G. W. A. Constable, A. J. McKane, and T. Rogers, J. Phys. A: Math. Theor. 46, 295002 (2013). 10.1088/1751-8113/46/29/295002
14. G. Wainrib, Electron. Commun. Probab. 18, 51 (2013). 10.1214/ECP.v18-1975
15. C. W. Gardiner, Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences, 3rd ed. (Springer-Verlag, New York, 2004).
16. Y. Cao, D. T. Gillespie, and L. R. Petzold, J. Chem. Phys. 122, 014116 (2005). 10.1063/1.1824902
17. C. V. Rao and A. P. Arkin, J. Chem. Phys. 118, 4999 (2003). 10.1063/1.1545446
18. J. M. Newby and S. J. Chapman, " Metastable behavior in Markov processes with internal states," J. Math. Biol. (published online). 10.1007/s00285-013-0723-1
19. M. J. Ward, in Analyzing Multiscale Phenomena Using Singular Perturbation Methods, edited by J. Cronin and R. O'Malley (AMS Publications, Providence, RI, 1998), pp. 151-184.
20. R. Hinch and S. J. Chapman, Eur. J. Appl. Math. 16, 427 (2005). 10.1017/S0956792505006194
21. J. M. Newby, Phys. Biol. 9, 026002 (2012). 10.1088/1478-3975/9/2/026002
22. C. Hartmann, R. Banisch, M. Sarich, T. Badowski, and C. Schütte, Entropy 16, 350 (2013). 10.3390/e16010350
23. F. Schlögl, Z. Phys. 253, 147 (1972). 10.1007/BF01379769
24. R. Erban, S. J. Chapman, I. G. Kevrekidis, and T. Vejchodský, SIAM J. Appl. Math. 70, 984 (2009). 10.1137/080731360
25. D. T. Gillespie, J. Phys. Chem. 81, 2340 (1977). 10.1021/j100540a008
26. M. A. Gibson and J. Bruck, J. Phys. Chem. A 104, 1876 (2000). 10.1021/jp993732q
27. Y. Cao, D. T. Gillespie, and L. R. Petzold, J. Chem. Phys. 124, 044109 (2006). 10.1063/1.2159468
28. D. T. Gillespie, J. Chem. Phys. 113, 297 (2000). 10.1063/1.481811
29. H. Risken, " The Fokker-Planck equation," in Methods of Solution and Applications (Springer, 1996).
30. C. Le Bris, T. Lelièvre, M. Luskin, and D. Perez, Monte Carlo Methods Appl. 18, 119 (2012). 10.1515/mcma-2012-0003
31. O. Ovaskainen and B. Meerson, Trends Ecol. Evol. 25, 643 (2010). 10.1016/j.tree.2010.07.009
32. C. E. Brassil, Ecol. Model. 143, 9 (2001). 10.1016/S0304-3800(01)00351-9
33. B. Dennis, Oikos 96, 389 (2002). 10.1034/j.1600-0706.2002.960301.x
34. S. J. Schreiber, Theor. Popul. Biol. 64, 201 (2003). 10.1016/S0040- 5809(03)00072-8
35. G. M. Palamara, G. W. Delius, M. J. Smith, and O. L. Petchey, J. Theor. Biol. 334, 61 (2013). 10.1016/j.jtbi.2013.06.007
36. I. Nåsell, J. Theor. Biol. 211, 11 (2001). 10.1006/jtbi.2001.2328
37. P. Turchin, Complex Population Dynamics: A Theoretical/Empirical Synthesis (Princeton University Press, 2003).
38. J. Grasman and R. HilleRisLambers, Ecol. Model. 103, 71 (1997). 10.1016/S0304-3800(97)00079-3
39. D. A. Kessler and N. M. Shnerb, J. Stat. Phys. 127, 861 (2007). 10.1007/s10955-007-9312-2
40. M. Assaf and B. Meerson, Phys. Rev. E 81, 021116 (2010). 10.1103/PhysRevE.81.021116
41. J.-H. Prinz, H. Wu, M. Sarich, B. Keller, M. Senne, M. Held, J. D. Chodera, C. Schütte, and F. Noé, J. Chem. Phys. 134, 174105 (2011). 10.1063/1.3565032
42. E. Abad, J. Reingruber, and M. S. P. Sansom, J. Chem. Phys. 130, 085101 (2009). 10.1063/1.3077205
43. W. Chen, R. Erban, and S. J. Chapman, SIAM J. Appl. Math. 74, 208 (2014). 10.1137/120882780
44. P. C. Bressloff and J. M. Newby, SIAM J. Appl. Dyn. Syst. 12, 1394 (2013). 10.1137/120898978
45. V. Dakos, S. R. Carpenter, W. A. Brock, A. M. Ellison, V. Guttal, A. R. Ives, S. Kéfi, V. Livina, D. A. Seekell, E. H. van Nes, and M. Scheffer, PLoS ONE 7, e41010 (2012). 10.1371/journal.pone.0041010
46. M. Geissbuehler and T. Lasser, Opt. Express 21, 9862 (2013). 10.1364/OE.21.009862
47. P. C. Bressloff, and J. M. Newby, in First-Passage Phenomena and Their Applications, edited by R. Metzler, G. Oshanin, and S. Redner (World Scientific, 2013), pp. 1-29.