Nonlinear Sciences – Chaotic Dynamics
Scientific paper
Dec 1980
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1980e%26psl..51..451i&link_type=abstract
Earth and Planetary Science Letters, Volume 51, Issue 2, p. 451-456.
Nonlinear Sciences
Chaotic Dynamics
36
Scientific paper
The chaotic dynamics of the Rikitake two-disc dynamo system is studied for a wide range of parameters and results are compared with the sequence of geomagnetic polarity reversals. The chaos of the Rikitake system belongs to the Lorenz type, which is characterized by irregular travelling of an orbit between two unstable fixed points. Travelling corresponds to the polarity reversal. The frequency of the polarity reversals depends strongly on the parameter μ representing the resistive dissipation in the core. In the center of the chaotic regime, there is a parameter region in which reversals seldom occur and the dynamics is less disordered. The Markov entropy of the Lorenz map for the system has a sharp minimum in this parameter region named as the minimum entropy regime (M.E.R.). The average frequency of reversals in the M.E.R. is less than 0.1 per cycle of oscillation, but is not uniform even seen through a 10-m.y.-long window. The non-uniformity as well as the low rate of reversals in the M.E.R. markedly resemble the behavior of geomagnetic reversals over the past 153 m.y. It is suggested that the Earth selected the minimum entropy regime on the principle of the minimum entropy production, as is known to be the case for other dissipative dynamical systems.
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