An Integrated and Evolutionary Dynamical Systems View of Climate Complexity

Walter Ritter Ortíz, Lorena Cruz

Sección de Bioclimatología, Centro de Ciencias de la Atmósfera, UNAM, Circuito Interior s/n, Ciudad Universitaria, Coyoacan, México.

DOI: 10.4236/ijg.2013.41006                

Abstract

The Earth shows a constant display of an organized complexity system, and its intrinsic capacity for sporadic self-organization constitutes its fundamental and profound mysterious property. A graphical method derived from the logistic phase space of precipitation is proposed to identify periods of abundance-scarcity of rain as well as El Nino presence in order to cope with climate change. The most striking result is that the majority of El Nino events on this graph are chaotic, in which the sign of the dominant eigenvalues of precipitation gives trends of scarcity on negative signs and abundance on positive signs, with eleven years periods.

Keywords

Climate Change; Complexity System; Earth

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	S. Y. Auyang, “Foundations of Complex System Theories in Economics, Evolutionary Biology and Statistical Phy sics,” Cambridge University Press, Cambridge, 1998.
[2]	S. Ellner and P. Turchin, “Chaos in a Noisy World: New Methods and Evidence from Time-Series Analyses,” The American Naturalist, Vol. 145, No. 3, 1995, pp. 343-375. doi:10.1086/285744
[3]	J. Guckenheimer and P. Holmes, “Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields,” Springer-Verlag, Berlin, 1983.
[4]	P. Kareva, “Predicting and Producing Chaos,” Nature, Vol. 375, No. 6528, 1995, pp. 189-190. doi:10.1038/375189a0
[5]	T. Y. Lee and Yorke, “Period Three Implies Chaos,” American Mathematical Monthly, Vol. 82, No. 10, 1975, pp. 985-992. doi:10.2307/2318254
[6]	R. M. May, “Biological Populations with Nonoverlapping Generations: Points, Stable Cycles and Chaos,” Science, Vol. 186, No. 4164, 1974, pp. 645-647. doi:10.1126/science.186.4164.645
[7]	R. M. May, “Simple Mathematical Models with Very Complicated Dynamics,” Nature, Vol. 261, No. 5560, 1976, pp. 459-467. doi:10.1038/261459a0
[8]	R. M. May, “Stability and Complexity in Model Ecosystems, Princeton Landmarks in Biology,” Princeton University Press, Princeton, 2001.
[9]	R. M. May and G. F. Oster, “Bifurcations and Dynamic Complexity in Simple Ecological Models,” The American Naturalist, Vol. 110, No. 974, 1976, pp. 573-599. doi:10.1086/283092
[10]	G. Sugihara and R. M. May, “Nonlinear Forecasting as a Way of Distinguishing Chaos from Measurement Error in time Series,” Nature, Vol. 344, No. 6268, 1990, pp. 734 741. doi:10.1038/344734a0
[11]	R. Pool, “It Is Chaos, or Is It Just Noise?” Science, Vol. 243, 4887, 1989, pp. 25-28. doi:10.1126/science.2911717
[12]	O. W. Ritter, P. A. Mosi?o and C. E. Buendía, “Dynamic Rain Model for Lineal Stochastic Environments,” Quaterly Journal of Meteorology, Vol. 49, No. 1, 1998, pp. 127-134.
[13]	O. W. Ritter, O. E. Jauregui, R. S. Guzman, B. A. Estrada, N. H. Mu?oz, S. J. Suarez and V. M. C. Corona, “Eco logical and Agricultural Productivity Indices and Their Dynamics in a Sub-Humid/Semi-Arid Region from Cen tral México,” Journal of Arid Environments, Vol. 59, No. 4, 2004, pp. 753-769. doi:10.1016/j.jaridenv.2004.02.009
[14]	O. W. Ritter and S. J. Suárez, “Predictability and Phase Space Relationships of Climatic Changes and Tuna Bio mass on the Eastern Pacific Ocean,” 6 eme Europeen de Science des Systemes Res-Systemica, Vol. No. 5, 2005.
[15]	O. W. Ritter and S. J. Suarez, “Impact of ENSO and the Optimum Use of Yellowfin Tuna in the Easthern Pacific Ocean Region,” Ingenieria de Recursos Naturales y del Ambiente, Cali Colombia, 2011, pp. 109-116.
[16]	S. J. Suarez, W. O. Ritter, C. G. Gay, J. Torres Jacome, “ENSO Tuna-Relations in the Eastern Pacific Ocean and Its Prediction as a Non-Linear Dynamic System,” Atmós fera, Vol. 17, No. 4, 2004, pp. 245-258.
[17]	G. A. F. Seber, “Multivariate Observations,” Jhon Wiley & Sons, New York, 1984. doi:10.1002/9780470316641
[18]	J. H. Vandermeer, “Elementary Mathematical Ecology,” John Wiley, New York, 1972.