Determining mixed linear-nonlinear coupled differential equations from multivariate discrete time series sequences

Physica D: Nonlinear Phenomena

Volumn 102, Issue 1-2, 1997, Pages 15-36

  Irving, A D ^a   Dewson, T ^b  

^a RUTHERFORD APPLETON LABORATORY   (United Kingdom)

^b UNIVERSITY OF BRISTOL   (United Kingdom)

Author keywords

Coupled ODE's; Nonlinear vector ARMA; Time series analysis

Indexed keywords

EID: 0002564289     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(96)00248-5     Document Type: Article

References (51)

1. V. Volterra, Theory of Functionals and of Integral and Integro-differential Equations (Dover, New York, 1959).
2. T. Dewson and A.D. Irving, Linear and non-linear response function estimation from multi-input systems, Physica D 94 (1996) 19-35.
3. A.D. Irving, T. Dewson, G. Hong and N.H. Cunliffe, General nonlinear response of a single input system to stochastic excitations, Appl. Math. Modelling 19 (1995) 45-56.
4. A.D. Irving, B.R. Clayton and T. Dewson, Nonlinear thermoviscoelastic behaviour in complex materials, IUTAM Symp. on Inhomogenity, Anisotropy and Nonlinearity in Solid Mechanics (Elsevier, Amsterdam, 1995) pp. 125-132.
5. A.D. Irving, Stochastic sensitivity analysis, Appl. Math. Modelling 16 (1992) 1-12.
6. A.D. Irving and T. Dewson, General mixed linear-nonlinear response of evolutionary causal physical processes, in preparation.
7. P.G. Drazin, Nonlinear systems, Cambridge Texts in Applied Mathematics (Cambridge University Press, Cambridge, 1992).
8. E.A. Jackson, Perspectives of Nonlinear dynamics (Cambridge University Press, Cambridge, 1989).
9. F. Takens, Detecting strange attractors in fluid turbulence, in: Dynamical Systems and Turbulence, eds. D. Rand and L.S. Young (Springer, Berlin, 1981).
10. N.H. Packard, J.D. Crutchfield, R.S. Farmer and R.S. Shaw, Geometry from time series, Phys. Rev. Lett. 45 (1980) 712-716.
11. D.S. Broomhead, R. Jones and G.P. King, J. Phys. A 20 (1987) L563.
12. D.S. Broomhead and G.P. King, Extracting quantitative dynamics from experimental data, Physica D 20 (1986) 217-236.
13. J.F. Gibson, J. Doyne Farmer, M. Casdagli and S. Eubank, An analytical approach to practical state space reconstruction, Physica D 57 (1992) 1-30.
14. J. Cremers and A. Hubler, Construction of differential equations from experimental data, Z. Naturforsch. A 42 (1986) 797-802.
15. G. Gouesbet, Reconstruction of the vector fields of continuous dynamical systems from numerical scalar time series data, Phys. Rev. A 43 (1991) 5321-5330.
16. G. Rowlands and J.C. Sprott, Extraction of dynamical equations from chaotic data, Physica D 58 (1992) 251-259.
17. G. Gouesbet and J. Maquet, Construction of phenomenological models from numerical scalar time series, Physica D 58 (1992) 202-215.
18. M. Casdagli, Nonlinear prediction of chaotic time series, Physica D 35 (1989) 335-356.
19. J.D. Farmer and J.J. Sidovowich, Predicting chaotic time series, Phys. Rev. Lett. 59 (1987) 845-848.
20. R.S. Rivlin and J.L. Ericksen, Stress-deformation relations for isotropic materials, J. Ration. Mech. Anal. 4 (1955) 323-325.
21. J.L. Breeden and A. Hubler, Reconstructing equations of motion from experimental data with unobserved variables, Phys. Rev. A (10) (1990) 5817-5826.
22. G. Gouesbet and C. Letellier, Global vector-field reconstruction by using a multivariate polynomial L2 approximation on nets, Phys. Rev. E 49 (6) (1994) 4955-4972.
23. C. Letellier, L. Le-Sceller, P. Dutertre, G. Gouesbet, Z. Fei and J.L. Hudson, Topological characterisation and global vector field reconstruction of an experimental electrochemical system, J. Phys. Chem. 99 (1995) 7016-7027.
24. N. Wiener, Response of a nonlinear system in the presence of noise, MIT Radiation Laboratory Report No. 165 (1942).
25. J. Barrett, Hermite functional expansions and the calculation of output autocorrelation and spectrum for any time-invariant nonlinear system, J. Electronics and control 16 (1964) 107-113.
26. R. Cameron and W. Martin, The orthogonal development of nonlinear functionals in series of Hermite-Legendre Functionals, Ann. Math. 48 (1947) 385-392.
27. J.H. Peng, E.J. Ding, M. Ding and W. Yang, Synchronizing hyperchaos with a scalar transmitted signal, Phys. Rev. Lett. 76 (6) (1996) 904-907.
28. J. Schweizer, A stochastic approach to spread spectrum communication using chaos, SPIE Vol. 2612, pp. 115-125.
29. P. Celka, Experimental verification of chaotic self-synchronization in an integrated optical based system, SPIE Vol. 2612, pp. 15-24.
30. N.B. Tufillaro, P. Wyckoff, R. Brown, T. Schreiber and T. Molteno, Topological time-series analysis of a string experiment and its synchronised model, Phys. Rev. E 51 (1) (1995) 164-174.
31. R. Brown, N.F. Rulkov and N.B. Tufillaro, Synchronization of chaotic systems: The effects of additive noise and drift in the dynamics of the driving, Phys. Rev. E 50 (6) (1994) 4488-4508.
32. L.A. Aguirre and S.A. Billings, Dynamical effects of overparameterisation in nonlinear models, Physica D 80 (1995) 26-40.
33. A.D. Irving and T. Dewson, The analysis of complex times series data, Appl. Math. Modelling 20 (1996) 35-47.
34. M.B. Priestly, Spectral Analysis and Time Series (Academic Press, London, 1981).
35. J.A. Bittencourt and Chryssafidis, Comparison of IRI predictions with low ionospheric observations, Adv. Space Sci. 11 (10) (1991) 97-100.
36. K. Rawer, Ionospheric mapping in the polar and equatorial zones, Adv. Space Sci. 16 (1) (1995) 9-12.
37. A.S. Besprogvannaya, Empirical modelling of the F2 peak at 50-70 invariant latitude using magnetic conjugacy, Adv. Space Sci. 11 (10) (1991) 23-28.
38. E.M. Lorenz, Deterministic nonperiodic flow, J. Atmospheric Sci. 20 (1963) 130-141.
39. R.C. Merton, Optimum consumption and portfolio rules in a continuous-time model, J. Econom. Theory 3 (1971) 373-413.
40. K. Ito, On stochastic differential equations, Mem. Amer. Math. Soc. (4) (1951) 1-51.
41. K. Ito and H.P. McKean, Diffusion Processes and Their Sample Paths (Academic Press, New York, 1964).
42. J.C. Hull, Options, Futures and Other Derivative Securities (Prentice-Hall, London, 1993).
43. D. Assaf, M. Taksar and M.J. Klass, A diffusion model of optimal portfolio selection in the presence of brokerage fees, Math. Oper. Res. 13 (1988) 277-294.
44. C. Atkinson and P. Wilmott, Portfolio management with transaction costs: An asymptotic analysis of the Morton and Pilska model, Math. Finance 5 (4) (1995) 357-367.
45. M. Davis and A. Normann, Portfolio selection with transaction costs, Math. Oper. Res. 15 (1990) 676-713.
46. D. Duffie and T. Sun, Transaction costs and portfolio choice in a discrete-continuous time setting, J. Econom. Dynamics Control 14 (1990) 577-597.
47. B. Dumas and E. Luciano, An exact solution to a dynamical portfolio choice problem under transaction costs, J. Finance 46 (1991) 577-595.
48. J.F. Eastham and K.J. Hastings, Optimal impulse control of portfolios, Math. Oper. Res. 13 (1988) 588-605.
49. I. Karatzas, Optimisation problems in the theory of continuous trading, SIAM J. Control Optm. 27 (1989) 1221-1259.
50. A.J. Morton and R.S. Pilska, Optimal portfolio management with fixed transaction costs, Math. Finance 5 (4) (1995) 337-356.
51. A.N. Refenes, ed., Neural Networks in the Capital Markets, Proc. 1st Int. Workshop, London Business School, 1993.