The potential and flux landscape, Lyapunov function and non-equilibrium thermodynamics for dynamic systems and networks with an application to signal-induced Ca2+ oscillation

Nonlinearity

Volumn 26, Issue 2, 2013, Pages

  Xu, Li ^a   Zhang, Feng ^a,b   Wang, Erkang ^a   Wang, Jin ^a,b,c  

^a CHANGCHUN INSTITUTE OF APPLIED CHEMISTRY   (China)

^b JILIN UNIVERSITY   (China)

^c STONY BROOK UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84872739909     PISSN: 09517715     EISSN: 13616544     Source Type: Journal    
DOI: 10.1088/0951-7715/26/2/R69     Document Type: Article

References (38)

1. Wang J, Huang B, Xia X and Sun Z R 2006 PLoS Comp. Biol. 2 e147 (Pubitemid 44819925)
2. Kim K Y and Wang J 2007 PLoS Comput. Biol. 3 e60 (Pubitemid 46535748)
3. Han B and Wang J 2007 Biophys. J. 92 3755 (Pubitemid 46910564)
4. Lapidus S, Han B and Wang J 2008 Proc. Natl Acad. Sci. USA 105 6039 (Pubitemid 351758395)
5. Wang J, Xu L and Wang E K 2008 Proc. Natl Acad. Sci. USA 105 12271
6. Wang J, Zhang K and Wang E K 2010 J. Chem. Phys. 133 pp 69-84
7. Wang J, Zhang K, Xu L and Wang E K 2011 Proc. Natl Acad. Sci. USA 108 8257-62
8. Feng H and Wang J 2011 J. Chem. Phys. 135 234511
9. Zhang F, Xu L, Zhang K, Wang E K and Wang J 2012 J. Chem. Phys. 137 065102
10. Jackson E A 1989 Perspectives of Nonlinear Dynamics vol 1 and vol 2 (Cambridge: Cambridge Unversity Press)
11. Frauenfelder H, Sligar S G and Wolynes P G 1991 Science 254 1598
12. Wolynes P G, Onuchic J N and Thirumalai D 1995 Navigating the folding routes Science 267 1619
13. Wang J and Verkhivker G 2003 Phys. Rev. Lett. 90 188101
14. Haken H 1987 Advanced Synergetics (Berlin: Springer)
15. Graham R 1989 Noise in Nonlinear Dynamical Systems vol 1 ed F Moss (Cambridege: Cambridege Unviersity Press) p 225
16. Sasai M and Wolynes P G 2003 Proc. Natl Acad. Sci. USA 100 2374 (Pubitemid 36297506)
17. Ao P 2004 J. Phys. A. Math. Gen. 37 L25
18. Ao P 2008 Commun. Theor. Phys. 49 1073
19. Qian H 2006 J. Phys. Chem. B 110 15063 (Pubitemid 44334760)
20. Qian H 2009 Methods Enzymology 467 111
21. Van Kampen N G 2007 Stochastic Processes in Physics and Chemistry (Amsterdam: Elsevier)
22. Gardiner C W 2004 Handbook of Stochastic Methods (Berlin: Springer)
23. Swain P S, Elowitz M B and Siggia E D 2002 Proc. Natl Acad. Sci. USA 99 12795
24. Schnakenberg J 1976 Rev. Mod. Phys. 48 571
25. Prigogine I and Nicolis G 1977 Self Organization in Non-Equilibrium Systems (New York: John Wiley)
26. Lebowitz J and Bergmann P G 1957 Ann. Phys. 1 1
27. Oono Y and Paniconi M 1998 Prog. Theor. Phys. Suppl. 130 29
28. Van den Broeck C and Esposito M 2010 Phys. Rev. E 82 011144
29. Esposito M and Van den Broeck C 2010 The Three faces of the second law: II. Fokker-Planck formulation arXiv:1005.1686
30. Goldbeter A, Dupont G and Berridge M J 1990 Proc. Natl Acad. Sci. USA 87 1461
31. Gillespie D T 1977 J. Phys. Chem. 81 2340
32. Hu G 1986 Zeit. Phys. B 65 103
33. Ge H and Qian H 2010 Phys. Rev. E 81 051133
34. Crandall M and Lions P L 1983 Trans. Am. Math. Soc. 277 1-42
35. Osher S and Fedkiw R 2002 Level Set Methods and Dynamic Implicit Surfaces (Berlin: Springer)
36. Sethian J A 1999 Level Set Methods and Fast Marching Methods (Cambridge: Cambridge University Press)
37. Mitchell I M 2008 J. Sci. Comput. 35 300-29
38. Nevozhay D, Adams R M, Van Itallie E, Bennett M R and Balazsi G 2012 PLoS Comput. Biol. 8 e1002480