On the low-dimensional modelling of Stratonovich stochastic differential equations

Physica A: Statistical Mechanics and its Applications

Volumn 225, Issue 1, 1996, Pages 62-80

  Xu, Chao ^a   Roberts, A J ^a  

^a UNIVERSITY OF SOUTHERN QUEENSLAND   (Australia)

Author keywords

Centre manifold; Fokker Planck equation; Low dimensional modelling; Noisy dynamical system; Stochastic differential equation

Indexed keywords

EID: 0042540192     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/0378-4371(95)00387-8     Document Type: Article

References (23)

1. A. Arneodo, P.H. Coullet and E.A. Spiegel, The dynamics of triple convection, Geophys. Astro. Fluid Dyn. 31 (1985) 1-48.
2. V. Balakotaiah and H.C. Chang, Dispersion of chemical solutes in chromatographs and reactors, Phil. Trans. R. Soc. Lond. A 351 (1995) 39-75.
3. E. Boe and H.C. Chang, Dynamics of delayed systems under feedback control, Chem. Eng. Sci. 44 (1989) 1281-1294.
4. P. Boxler, A stochastic version of the centre manifold theorem, Probab. Th. Rel. Fields 83 (1989) 509-545.
5. Chiarella, The elements of a nonlinear theory of economic dynamics, Lect. Notes in Eco and Math Systems 343 (1990).
6. P.H. Coullet, C. Elphick and E. Tirapegui, Normal form of a Hopf bifurcation with noise, Phys. Lett. 111A(6) (1985) 277-282.
7. S.M. Cox and A.J. Roberts, Centre manifolds of forced dynamical systems, J. Austral. Math. Soc. B 32 (1991) 401-436.
8. S.M. Cox and A.J. Roberts, Initialisation of models of dynamical systems, Physica D 85 (1995) 126-141.
9. P.E. Kloeden and E. Platen, Numerical solution of stochastic differential equations, Applications of Mathematics, Vol. 23 (Springer, Berlin, 1992).
10. E. Knobloch and K.A. Wiesenfeld, Bifurcations in fluctuating systems: The centre manifold approach, J. Stat. Phys. 33 (1983) 611-637.
11. G.N. Mercer and A.J. Roberts, A centre manifold description of contaminant dispersion in channels with varying flow properties, SIAM J. Appl. Math. 50 (1990) 1547-1565.
12. N. Sri Namachchivaya and G. Leng, Equivalence of stochastic averaging and stochastic normal forms, J. Appl. Mech. 57 (1990) 1011-1017.
13. N. Sri Namachchivaya and Y.K. Lin, Method of stochastic normal forms, Int. J. Nonlin. Mech. 26 (1991) 931-943.
14. A.J. Roberts, The application of centre manifold theory to the evolution of systems which vary slowly in space, J. Austral. Math. Soc. B 29 (1988) 480-500.
15. A.J. Roberts, Appropriate initial conditions for asymptotic descriptions of the long term evolution of dynamical systems, J. Austral. Math. Soc. B 31 (1989) 48-75.
16. A.J. Roberts, The utility of an invariant manifold description of the evolution of a dynamical system, SIAM J. Math. Anal. 20 (1989) 1447-1458.
17. A.J. Roberts, Boundary conditions for approximate differential equations, J. Austral. Math. Soc. B 34 (1992) 54-80.
18. A.J. Roberts, The invariant manifold of beam deformations, Part 1: the simple circular rod, J. Elas. 30 (1993) 1-54.
19. A.J. Roberts, Low-dimensional models of thin film fluid dynamics, Submitted to Phys. Lett. A, September 1994.
20. G. Schöner and H. Haken, The slaving principle for Stratonovich stochastic differential equations, Z. Phys. B 63 (1986) 493-504.
21. G. Schöner and H. Haken, A systematic elimination procedure for Ito stochastic differential equations and the adiabatic approximation, Z. Phys. B 68 (1987) 89-103.
22. S.W. Shaw and C. Pierre, Normal modes for non-linear vibratory systems, J. Sound Vibration 164(1) (1993) 85-124.
23. A. Wunderlin and H. Haken, Generalised Ginzburg-Landau equations, slaving principle and center manifold theorem, Z. Phys. B 44 (1981) 135-141.