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Probability distribution for the number of cycles between successive regime transitions for the Lorenz model |
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| Authors: | AK Mittal S Dwivedi RS Yadav |
| Institution: | a Department of Physics, University of Allahabad, Allahabad, Pin-211002, India b M.N. Saha Centre of Space Studies, Institute of Interdisciplinary Studies, University of Allahabad, Allahabad, Pin-211002, India c K. Banerjee Centre of Atmospheric and Ocean Studies, Institute of Interdisciplinary Studies, University of Allahabad, Allahabad, Pin-211002, India d Sri Ram Pratap Inter College, Sirsa, Allahabad, India |
| Abstract: | The Lorenz model has been widely used for exploring many real world problems. In this paper we obtain, with the help of an invariant manifold technique, the return map for the maximum value of the variable x of the model and use this return map to derive the simple, empirically obtained, regime transition rules for forecasting regime changes and length in the new regime for the model. The probability distribution for number of cycles between successive regime transitions of the Lorenz model may be of interest in many disciplines. We apply the Perron-Frobenius algorithm over the return map to estimate the probability distribution for the number of cycles between successive regime transitions. These probabilities are also estimated for the forced Lorenz model, which is a conceptual model to explore the effects of sea surface temperature on seasonal rainfall. |
| Keywords: | Return map Probability distribution Regime transition Invariant manifold |
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