Probability distribution for the number of cycles between successive regime transitions for the Lorenz model

Physica D: Nonlinear Phenomena

Volumn 233, Issue 1, 2007, Pages 14-20

  Mittal, A K ^a   Dwivedi, S ^a   Yadav, R S ^a,b  

^a UNIVERSITY OF ALLAHABAD   (India)

^b Sirsa   (India)

Author keywords

Invariant manifold; Probability distribution; Regime transition; Return map

Indexed keywords

ALGORITHMS; CONFORMAL MAPPING; MATHEMATICAL MODELS; RAIN;

INVARIANT MANIFOLD; REGIME TRANSITION; RETURN MAP;

PROBABILITY DISTRIBUTIONS;

EID: 34547557011     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2007.06.014     Document Type: Article

References (38)

1. Lorenz E.N. Deterministic non-periodic flow. J. Atmospheric Sci. 20 (1963) 130-141
2. Haken H. Analogy between higher instabilities in fluids and lasers. Phys. Lett. A 53 1 (1975) 77-78
3. Malkus W.V.R. Non-periodic convection at high and low Prandtl number. Mem. Soc. R. Sci. Liege 4 6 (1972) 125-128
4. Yorke E.D., and Yorke J.A. Metastable chaos: Transition to sustained chaotic behaviour in the Lorenz model. J. Stat. Phys. 21 3 (1979) 263-277
5. Knobloch E. Chaos in a segmented disc dynamo. Phys. Lett. A 82 9 (1981) 439-440
6. Lorenz E.N. Noisy periodicity and reverse bifurcations. In: Hellerman R.H.G. (Ed). Nonlinear Dynamics, vol. 357 (1980), Annal. N.Y. Acad. Sci. 282-291
7. Pedlosky J. Limit cycles and unstable baroclinic waves. J. Atmospheric Sci. 29 1 (1972) 53-63
8. Pedlosky J., and Frenzen C. Chaotic and periodic behaviour of finite amplitude baroclinic waves. J. Atmospheric Sci. 37 (1980) 1177-1196
9. Brindley J., and Moroz I.M. Lorenz attractor behaviour in a continuously stratified baroclinic fluid. Phys. Lett. A 77 6 (1980) 441-444
10. Gibbon J.D., and McGuinness M.J. A derivation of the Lorenz equations for some unstable dispersive physical systems. Phys. Lett. A 77 5 (1980) 295-299
11. Gibbon J.D. Dispersive instabilities in nonlinear systems: The real and complex Lorenz equations. In: Haken H. (Ed). Chaos and Order in Nature, Synergetics (1982), Springer Verlag 92-101
12. Tong C., and Gluhovsky A. Phys. Rev. E 65 (2002) 046306-1
13. Kuhlmann H. Phys. Rev. A 32 (1985) 1703
14. Evans E., Bhatti N., Kinney J., Pann L., Pena M., Yang S.-C., Kalnay E., and Hansen J. RISE undergraduates find that regime changes in Lorenz's model are predictable. Bull. Am. Meteorol. Soc. 85 (2004) 520-524
15. Mittal A.K., Dwivedi S., and Pandey A.C. Bifurcation analysis of a paradigmatic model of monsoon prediction. Nonlinear Process. Geophys. 12 (2005) 707-715
16. Palmer T.N. Extended-range atmospheric prediction and the Lorenz model. Bull. Am. Meteorol. Soc. 74 (1993) 49-66
17. Palmer T.N. Chaos and predictability in forecasting the monsoons. Proc. Indian Nat. Sci. Acad. 60A (1994) 57-66
18. Palmer T.N. A nonlinear dynamical perspective on climate prediction. J. Clim. 12 (1998) 575-591
19. Yadav R.S., Dwivedi S., and Mittal A.K. Prediction rules for regime changes and length in a new regime for the Lorenz model. J. Atmospheric Sci. 62 (2005) 2316-2321
20. Moffatt H.K. Magnetic Field Generation in Electrically Conducting Fluids (1978), Cambridge University Press
21. Moffatt H.K. A self-consistent treatment of simple dynamo systems. Geophys. Astrophys. Fluid Dyn. 14 (1979) 147-166
22. Hilborn R.C. Chaos and Nonlinear Dynamics (2000), Oxford University Press
23. Sikka D.R., and Gadgil S. On the maximum cloud zone and the ITCZ over India longitude during the southwest monsoon. Mon. Weather Rev. 108 (1980) 1840-1853
24. Ajay Mohan R.S., and Goswami B.N. A common spatial mode for intra-seasonal and inter-annual variation and predictability of the Indian summer monsoon. Current Sci. 79 (2000) 1106-1111
25. Monahan A.H., Fyfe J.C., and Flato G. A regime view of Northern Hemisphere atmospheric variability and change under global warming. Geophys. Res. Lett. 27 (2000) 1139-1142
26. A. Weisheimer, D. Handorf, K. Dethloff, On the structure and variability of atmospheric circulation regimes in coupled climate models, Atmos. Sci. Lett. (2001) (doi:10.1006/asle.2001.0034)
27. Palmer T.N., Brankovic C., Viterbo P., and Miller M.J. Modeling interannual variations of summer monsoons. J. Clim. 5 (1992) 399-417
28. Kalnay E. Atmospheric Modeling, Data Assimilation and Predictability (2003), Cambridge University Press
29. Sprott J.C. Chaos and Time Series Analysis (2003), Oxford University Press
30. Graham R., and Scholz H.J. Analytic approximation of the Lorenz attractor by invariant manifolds. Phys. Rev. A 22 (1980) 1198-1204
31. Dorfle M., and Graham R. Probability density of the Lorenz model. Phys. Rev. A 27 (1983) 1096-1105
32. Mehta M., Mittal A.K., and Dwivedi S. The Double-Cusp Map for the Forced Lorenz System. Internat. J. Bifur. Chaos 13 (2003) 3029-3035
33. Nicolis G., and Nicolis C. Master-equation approach to deterministic chaos. Phys. Rev. A 38 (1988) 427-433
34. Tucker W. A rigorous ODE solver and Smale's 14th problem. Found. Comput. Math. 2 (2002) 53-117
35. Tucker W. Computing accurate Poincare maps. Phys. D. 171 (2002) 127-137
36. Tucker W. Validated Numerics for Pedestrians (2005), European Congress of Mathematics, Eur. Math. Soc., Zurich 851-860
37. Teng Q., Monahan A.H., and Fyfe J.C. Effects of time averaging on climate regimes. Geophys. Res. Lett. 31 (2004) (doi:10.1029/2004GL020840)
38. Yoden S., Taguchi M., and Naito Y. Numerical experiments on internal interannual variations of the Troposphere-Stratosphere coupled system, Stratospheric Processes and their Role in Climate (SPARC). Newsl. 16 (2001)