Abstract
Mathematical analysis of a predominantly bimodal chaotic attractor, Lu system, was carried out to investigate a possible application of the model as a prototype of monsoon intra-seasonal oscillation (ISO). Bifurcation structures of the system are explored as the system parameter c and the forcing parameter F are varied. Stability criteria of equilibrium points of the forced Lu system are also explored in detail. A sensitivity study is carried out, by changing forcing parameter F, to explore relationships between some of the derived variables of the model and, based on such relationships, an empirical rule is used for extended range prediction. Analogous variables are also derived from the ISO data and prediction results are compared. Application of the prediction rule of regime transition to the observed ISO and chaotic model data is purely based on the bimodal characteristics of ISO and neglects some of the intricate mechanisms therein. We have found that a forced Lu system can be a good prototype in the prediction of peak anomaly of the monsoon ISO when growth rates around a threshold value are taken as predictors.
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Acknowledgments
The authors thank the Indian National Center for Ocean Information Services (INCOIS) and National Center for Ocean and Antarctic Research (NCOAR), MoES, Government of India, for financial support. S. Mukherjee thanks Dr. Suneet Dwivedi, Department of Atmospheric and Ocean Science, University of Allahabad, for useful discussions.
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Mukherjee, S., Shukla, R.P., Mittal, A.K. et al. Mathematical analysis of a chaotic model in relevance to monsoon ISO. Meteorol Atmos Phys 114, 83 (2011). https://doi.org/10.1007/s00703-011-0159-3
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DOI: https://doi.org/10.1007/s00703-011-0159-3